376.28/115.64
376.28/115.64
(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
active(terms(N)) → mark(cons(recip(sqr(N)), terms(s(N))))
376.28/115.64
active(sqr(0)) → mark(0)
376.28/115.64
active(sqr(s(X))) → mark(s(add(sqr(X), dbl(X))))
376.28/115.64
active(dbl(0)) → mark(0)
376.28/115.64
active(dbl(s(X))) → mark(s(s(dbl(X))))
376.28/115.64
active(add(0, X)) → mark(X)
376.28/115.64
active(add(s(X), Y)) → mark(s(add(X, Y)))
376.28/115.64
active(first(0, X)) → mark(nil)
376.28/115.64
active(first(s(X), cons(Y, Z))) → mark(cons(Y, first(X, Z)))
376.28/115.64
active(half(0)) → mark(0)
376.28/115.64
active(half(s(0))) → mark(0)
376.28/115.64
active(half(s(s(X)))) → mark(s(half(X)))
376.28/115.64
active(half(dbl(X))) → mark(X)
376.28/115.64
active(terms(X)) → terms(active(X))
376.28/115.64
active(cons(X1, X2)) → cons(active(X1), X2)
376.28/115.64
active(recip(X)) → recip(active(X))
376.28/115.64
active(sqr(X)) → sqr(active(X))
376.28/115.64
active(s(X)) → s(active(X))
376.28/115.64
active(add(X1, X2)) → add(active(X1), X2)
376.28/115.64
active(add(X1, X2)) → add(X1, active(X2))
376.28/115.64
active(dbl(X)) → dbl(active(X))
376.28/115.64
active(first(X1, X2)) → first(active(X1), X2)
376.28/115.64
active(first(X1, X2)) → first(X1, active(X2))
380.50/117.98
active(half(X)) → half(active(X))
380.50/117.98
terms(mark(X)) → mark(terms(X))
380.50/117.98
cons(mark(X1), X2) → mark(cons(X1, X2))
380.50/117.98
recip(mark(X)) → mark(recip(X))
380.50/117.98
sqr(mark(X)) → mark(sqr(X))
380.50/117.98
s(mark(X)) → mark(s(X))
380.50/117.98
add(mark(X1), X2) → mark(add(X1, X2))
380.50/117.98
add(X1, mark(X2)) → mark(add(X1, X2))
380.50/117.98
dbl(mark(X)) → mark(dbl(X))
380.50/117.98
first(mark(X1), X2) → mark(first(X1, X2))
380.50/117.98
first(X1, mark(X2)) → mark(first(X1, X2))
380.50/117.98
half(mark(X)) → mark(half(X))
380.50/117.98
proper(terms(X)) → terms(proper(X))
380.50/117.98
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
380.50/117.98
proper(recip(X)) → recip(proper(X))
380.50/117.98
proper(sqr(X)) → sqr(proper(X))
380.50/117.98
proper(s(X)) → s(proper(X))
380.50/117.98
proper(0) → ok(0)
380.50/117.98
proper(add(X1, X2)) → add(proper(X1), proper(X2))
380.50/117.98
proper(dbl(X)) → dbl(proper(X))
380.50/117.98
proper(first(X1, X2)) → first(proper(X1), proper(X2))
380.50/117.98
proper(nil) → ok(nil)
380.50/117.98
proper(half(X)) → half(proper(X))
380.50/117.98
terms(ok(X)) → ok(terms(X))
380.50/117.98
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
380.50/117.98
recip(ok(X)) → ok(recip(X))
380.50/117.98
sqr(ok(X)) → ok(sqr(X))
380.50/117.98
s(ok(X)) → ok(s(X))
380.50/117.98
add(ok(X1), ok(X2)) → ok(add(X1, X2))
380.50/117.98
dbl(ok(X)) → ok(dbl(X))
380.50/117.98
first(ok(X1), ok(X2)) → ok(first(X1, X2))
380.50/117.98
half(ok(X)) → ok(half(X))
380.50/117.98
top(mark(X)) → top(proper(X))
380.50/117.98
top(ok(X)) → top(active(X))
Rewrite Strategy: INNERMOST
380.50/117.98
380.50/117.98
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
380.50/117.98
380.50/117.98
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
380.50/117.98
active(sqr(0)) → mark(0)
380.50/117.98
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
380.50/117.98
active(dbl(0)) → mark(0)
380.50/117.98
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
380.50/117.98
active(add(0, z0)) → mark(z0)
380.50/117.98
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
380.50/117.98
active(first(0, z0)) → mark(nil)
380.50/117.98
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
380.50/117.98
active(half(0)) → mark(0)
380.50/117.98
active(half(s(0))) → mark(0)
380.50/117.98
active(half(s(s(z0)))) → mark(s(half(z0)))
380.50/117.98
active(half(dbl(z0))) → mark(z0)
380.50/117.98
active(terms(z0)) → terms(active(z0))
380.50/117.98
active(cons(z0, z1)) → cons(active(z0), z1)
380.50/117.98
active(recip(z0)) → recip(active(z0))
380.50/117.98
active(sqr(z0)) → sqr(active(z0))
380.50/117.98
active(s(z0)) → s(active(z0))
380.50/117.98
active(add(z0, z1)) → add(active(z0), z1)
380.50/117.98
active(add(z0, z1)) → add(z0, active(z1))
380.50/117.98
active(dbl(z0)) → dbl(active(z0))
380.50/117.98
active(first(z0, z1)) → first(active(z0), z1)
380.50/117.98
active(first(z0, z1)) → first(z0, active(z1))
380.50/117.98
active(half(z0)) → half(active(z0))
380.50/117.98
terms(mark(z0)) → mark(terms(z0))
380.50/117.98
terms(ok(z0)) → ok(terms(z0))
380.50/117.98
cons(mark(z0), z1) → mark(cons(z0, z1))
380.50/117.98
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
380.50/117.98
recip(mark(z0)) → mark(recip(z0))
380.50/117.98
recip(ok(z0)) → ok(recip(z0))
380.50/117.98
sqr(mark(z0)) → mark(sqr(z0))
380.50/117.98
sqr(ok(z0)) → ok(sqr(z0))
380.50/117.98
s(mark(z0)) → mark(s(z0))
380.50/117.98
s(ok(z0)) → ok(s(z0))
380.50/117.98
add(mark(z0), z1) → mark(add(z0, z1))
380.50/117.98
add(z0, mark(z1)) → mark(add(z0, z1))
380.50/117.98
add(ok(z0), ok(z1)) → ok(add(z0, z1))
380.50/117.98
dbl(mark(z0)) → mark(dbl(z0))
380.50/117.98
dbl(ok(z0)) → ok(dbl(z0))
380.50/117.98
first(mark(z0), z1) → mark(first(z0, z1))
380.50/117.98
first(z0, mark(z1)) → mark(first(z0, z1))
380.50/117.98
first(ok(z0), ok(z1)) → ok(first(z0, z1))
380.50/117.98
half(mark(z0)) → mark(half(z0))
380.50/117.98
half(ok(z0)) → ok(half(z0))
380.50/117.98
proper(terms(z0)) → terms(proper(z0))
380.50/117.98
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
380.50/117.98
proper(recip(z0)) → recip(proper(z0))
380.50/117.98
proper(sqr(z0)) → sqr(proper(z0))
380.50/117.98
proper(s(z0)) → s(proper(z0))
380.50/117.98
proper(0) → ok(0)
380.50/117.98
proper(add(z0, z1)) → add(proper(z0), proper(z1))
380.50/117.98
proper(dbl(z0)) → dbl(proper(z0))
380.50/117.98
proper(first(z0, z1)) → first(proper(z0), proper(z1))
380.50/117.98
proper(nil) → ok(nil)
380.50/117.98
proper(half(z0)) → half(proper(z0))
380.50/117.98
top(mark(z0)) → top(proper(z0))
380.50/117.98
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(terms(z0)) → c(CONS(recip(sqr(z0)), terms(s(z0))), RECIP(sqr(z0)), SQR(z0), TERMS(s(z0)), S(z0))
380.50/117.98
ACTIVE(sqr(s(z0))) → c2(S(add(sqr(z0), dbl(z0))), ADD(sqr(z0), dbl(z0)), SQR(z0), DBL(z0))
380.50/117.98
ACTIVE(dbl(s(z0))) → c4(S(s(dbl(z0))), S(dbl(z0)), DBL(z0))
380.50/117.98
ACTIVE(add(s(z0), z1)) → c6(S(add(z0, z1)), ADD(z0, z1))
380.50/117.98
ACTIVE(first(s(z0), cons(z1, z2))) → c8(CONS(z1, first(z0, z2)), FIRST(z0, z2))
380.50/117.98
ACTIVE(half(s(s(z0)))) → c11(S(half(z0)), HALF(z0))
380.50/117.98
ACTIVE(terms(z0)) → c13(TERMS(active(z0)), ACTIVE(z0))
380.50/117.98
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
380.50/117.98
ACTIVE(recip(z0)) → c15(RECIP(active(z0)), ACTIVE(z0))
380.50/117.98
ACTIVE(sqr(z0)) → c16(SQR(active(z0)), ACTIVE(z0))
380.50/117.98
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
380.50/117.98
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
380.50/117.98
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
380.50/117.98
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
380.50/117.98
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
380.50/117.98
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
380.50/117.98
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
380.50/117.98
TERMS(mark(z0)) → c24(TERMS(z0))
380.50/117.98
TERMS(ok(z0)) → c25(TERMS(z0))
380.50/117.98
CONS(mark(z0), z1) → c26(CONS(z0, z1))
380.50/117.98
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
380.50/117.98
RECIP(mark(z0)) → c28(RECIP(z0))
380.50/117.98
RECIP(ok(z0)) → c29(RECIP(z0))
380.50/117.98
SQR(mark(z0)) → c30(SQR(z0))
380.50/117.98
SQR(ok(z0)) → c31(SQR(z0))
380.50/117.98
S(mark(z0)) → c32(S(z0))
380.50/117.98
S(ok(z0)) → c33(S(z0))
380.50/117.98
ADD(mark(z0), z1) → c34(ADD(z0, z1))
380.50/117.98
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
380.50/117.98
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
380.50/117.98
DBL(mark(z0)) → c37(DBL(z0))
380.50/117.98
DBL(ok(z0)) → c38(DBL(z0))
380.50/117.98
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
380.50/117.98
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
380.50/117.98
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
380.50/117.98
HALF(mark(z0)) → c42(HALF(z0))
380.50/117.98
HALF(ok(z0)) → c43(HALF(z0))
380.50/117.98
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
380.50/117.98
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.98
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
380.50/117.98
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
380.50/117.98
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
380.50/117.98
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
380.50/117.99
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
380.50/117.99
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
S tuples:
ACTIVE(terms(z0)) → c(CONS(recip(sqr(z0)), terms(s(z0))), RECIP(sqr(z0)), SQR(z0), TERMS(s(z0)), S(z0))
380.50/117.99
ACTIVE(sqr(s(z0))) → c2(S(add(sqr(z0), dbl(z0))), ADD(sqr(z0), dbl(z0)), SQR(z0), DBL(z0))
380.50/117.99
ACTIVE(dbl(s(z0))) → c4(S(s(dbl(z0))), S(dbl(z0)), DBL(z0))
380.50/117.99
ACTIVE(add(s(z0), z1)) → c6(S(add(z0, z1)), ADD(z0, z1))
380.50/117.99
ACTIVE(first(s(z0), cons(z1, z2))) → c8(CONS(z1, first(z0, z2)), FIRST(z0, z2))
380.50/117.99
ACTIVE(half(s(s(z0)))) → c11(S(half(z0)), HALF(z0))
380.50/117.99
ACTIVE(terms(z0)) → c13(TERMS(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
380.50/117.99
ACTIVE(recip(z0)) → c15(RECIP(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(sqr(z0)) → c16(SQR(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
380.50/117.99
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
380.50/117.99
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
380.50/117.99
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
380.50/117.99
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
380.50/117.99
TERMS(mark(z0)) → c24(TERMS(z0))
380.50/117.99
TERMS(ok(z0)) → c25(TERMS(z0))
380.50/117.99
CONS(mark(z0), z1) → c26(CONS(z0, z1))
380.50/117.99
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
380.50/117.99
RECIP(mark(z0)) → c28(RECIP(z0))
380.50/117.99
RECIP(ok(z0)) → c29(RECIP(z0))
380.50/117.99
SQR(mark(z0)) → c30(SQR(z0))
380.50/117.99
SQR(ok(z0)) → c31(SQR(z0))
380.50/117.99
S(mark(z0)) → c32(S(z0))
380.50/117.99
S(ok(z0)) → c33(S(z0))
380.50/117.99
ADD(mark(z0), z1) → c34(ADD(z0, z1))
380.50/117.99
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
380.50/117.99
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
380.50/117.99
DBL(mark(z0)) → c37(DBL(z0))
380.50/117.99
DBL(ok(z0)) → c38(DBL(z0))
380.50/117.99
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
380.50/117.99
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
380.50/117.99
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
380.50/117.99
HALF(mark(z0)) → c42(HALF(z0))
380.50/117.99
HALF(ok(z0)) → c43(HALF(z0))
380.50/117.99
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
380.50/117.99
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
380.50/117.99
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c, c2, c4, c6, c8, c11, 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, c50, c51, c52, c54, c55, c56
380.50/117.99
380.50/117.99
(3) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 9 trailing tuple parts
380.50/117.99
380.50/117.99
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
380.50/117.99
active(sqr(0)) → mark(0)
380.50/117.99
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
380.50/117.99
active(dbl(0)) → mark(0)
380.50/117.99
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
380.50/117.99
active(add(0, z0)) → mark(z0)
380.50/117.99
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
380.50/117.99
active(first(0, z0)) → mark(nil)
380.50/117.99
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
380.50/117.99
active(half(0)) → mark(0)
380.50/117.99
active(half(s(0))) → mark(0)
380.50/117.99
active(half(s(s(z0)))) → mark(s(half(z0)))
380.50/117.99
active(half(dbl(z0))) → mark(z0)
380.50/117.99
active(terms(z0)) → terms(active(z0))
380.50/117.99
active(cons(z0, z1)) → cons(active(z0), z1)
380.50/117.99
active(recip(z0)) → recip(active(z0))
380.50/117.99
active(sqr(z0)) → sqr(active(z0))
380.50/117.99
active(s(z0)) → s(active(z0))
380.50/117.99
active(add(z0, z1)) → add(active(z0), z1)
380.50/117.99
active(add(z0, z1)) → add(z0, active(z1))
380.50/117.99
active(dbl(z0)) → dbl(active(z0))
380.50/117.99
active(first(z0, z1)) → first(active(z0), z1)
380.50/117.99
active(first(z0, z1)) → first(z0, active(z1))
380.50/117.99
active(half(z0)) → half(active(z0))
380.50/117.99
terms(mark(z0)) → mark(terms(z0))
380.50/117.99
terms(ok(z0)) → ok(terms(z0))
380.50/117.99
cons(mark(z0), z1) → mark(cons(z0, z1))
380.50/117.99
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
380.50/117.99
recip(mark(z0)) → mark(recip(z0))
380.50/117.99
recip(ok(z0)) → ok(recip(z0))
380.50/117.99
sqr(mark(z0)) → mark(sqr(z0))
380.50/117.99
sqr(ok(z0)) → ok(sqr(z0))
380.50/117.99
s(mark(z0)) → mark(s(z0))
380.50/117.99
s(ok(z0)) → ok(s(z0))
380.50/117.99
add(mark(z0), z1) → mark(add(z0, z1))
380.50/117.99
add(z0, mark(z1)) → mark(add(z0, z1))
380.50/117.99
add(ok(z0), ok(z1)) → ok(add(z0, z1))
380.50/117.99
dbl(mark(z0)) → mark(dbl(z0))
380.50/117.99
dbl(ok(z0)) → ok(dbl(z0))
380.50/117.99
first(mark(z0), z1) → mark(first(z0, z1))
380.50/117.99
first(z0, mark(z1)) → mark(first(z0, z1))
380.50/117.99
first(ok(z0), ok(z1)) → ok(first(z0, z1))
380.50/117.99
half(mark(z0)) → mark(half(z0))
380.50/117.99
half(ok(z0)) → ok(half(z0))
380.50/117.99
proper(terms(z0)) → terms(proper(z0))
380.50/117.99
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
380.50/117.99
proper(recip(z0)) → recip(proper(z0))
380.50/117.99
proper(sqr(z0)) → sqr(proper(z0))
380.50/117.99
proper(s(z0)) → s(proper(z0))
380.50/117.99
proper(0) → ok(0)
380.50/117.99
proper(add(z0, z1)) → add(proper(z0), proper(z1))
380.50/117.99
proper(dbl(z0)) → dbl(proper(z0))
380.50/117.99
proper(first(z0, z1)) → first(proper(z0), proper(z1))
380.50/117.99
proper(nil) → ok(nil)
380.50/117.99
proper(half(z0)) → half(proper(z0))
380.50/117.99
top(mark(z0)) → top(proper(z0))
380.50/117.99
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(first(s(z0), cons(z1, z2))) → c8(CONS(z1, first(z0, z2)), FIRST(z0, z2))
380.50/117.99
ACTIVE(terms(z0)) → c13(TERMS(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
380.50/117.99
ACTIVE(recip(z0)) → c15(RECIP(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(sqr(z0)) → c16(SQR(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
380.50/117.99
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
380.50/117.99
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
380.50/117.99
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
380.50/117.99
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
380.50/117.99
TERMS(mark(z0)) → c24(TERMS(z0))
380.50/117.99
TERMS(ok(z0)) → c25(TERMS(z0))
380.50/117.99
CONS(mark(z0), z1) → c26(CONS(z0, z1))
380.50/117.99
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
380.50/117.99
RECIP(mark(z0)) → c28(RECIP(z0))
380.50/117.99
RECIP(ok(z0)) → c29(RECIP(z0))
380.50/117.99
SQR(mark(z0)) → c30(SQR(z0))
380.50/117.99
SQR(ok(z0)) → c31(SQR(z0))
380.50/117.99
S(mark(z0)) → c32(S(z0))
380.50/117.99
S(ok(z0)) → c33(S(z0))
380.50/117.99
ADD(mark(z0), z1) → c34(ADD(z0, z1))
380.50/117.99
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
380.50/117.99
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
380.50/117.99
DBL(mark(z0)) → c37(DBL(z0))
380.50/117.99
DBL(ok(z0)) → c38(DBL(z0))
380.50/117.99
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
380.50/117.99
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
380.50/117.99
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
380.50/117.99
HALF(mark(z0)) → c42(HALF(z0))
380.50/117.99
HALF(ok(z0)) → c43(HALF(z0))
380.50/117.99
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
380.50/117.99
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
380.50/117.99
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(terms(z0)) → c(SQR(z0), S(z0))
380.50/117.99
ACTIVE(sqr(s(z0))) → c2(SQR(z0), DBL(z0))
380.50/117.99
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
380.50/117.99
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
380.50/117.99
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
S tuples:
ACTIVE(first(s(z0), cons(z1, z2))) → c8(CONS(z1, first(z0, z2)), FIRST(z0, z2))
380.50/117.99
ACTIVE(terms(z0)) → c13(TERMS(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
380.50/117.99
ACTIVE(recip(z0)) → c15(RECIP(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(sqr(z0)) → c16(SQR(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
380.50/117.99
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
380.50/117.99
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
380.50/117.99
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
380.50/117.99
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
380.50/117.99
TERMS(mark(z0)) → c24(TERMS(z0))
380.50/117.99
TERMS(ok(z0)) → c25(TERMS(z0))
380.50/117.99
CONS(mark(z0), z1) → c26(CONS(z0, z1))
380.50/117.99
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
380.50/117.99
RECIP(mark(z0)) → c28(RECIP(z0))
380.50/117.99
RECIP(ok(z0)) → c29(RECIP(z0))
380.50/117.99
SQR(mark(z0)) → c30(SQR(z0))
380.50/117.99
SQR(ok(z0)) → c31(SQR(z0))
380.50/117.99
S(mark(z0)) → c32(S(z0))
380.50/117.99
S(ok(z0)) → c33(S(z0))
380.50/117.99
ADD(mark(z0), z1) → c34(ADD(z0, z1))
380.50/117.99
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
380.50/117.99
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
380.50/117.99
DBL(mark(z0)) → c37(DBL(z0))
380.50/117.99
DBL(ok(z0)) → c38(DBL(z0))
380.50/117.99
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
380.50/117.99
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
380.50/117.99
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
380.50/117.99
HALF(mark(z0)) → c42(HALF(z0))
380.50/117.99
HALF(ok(z0)) → c43(HALF(z0))
380.50/117.99
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
380.50/117.99
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
380.50/117.99
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(terms(z0)) → c(SQR(z0), S(z0))
380.50/117.99
ACTIVE(sqr(s(z0))) → c2(SQR(z0), DBL(z0))
380.50/117.99
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
380.50/117.99
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
380.50/117.99
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c8, 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, c50, c51, c52, c54, c55, c56, c, c2, c4, c6, c11
380.50/117.99
380.50/117.99
(5) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
380.50/117.99
380.50/117.99
(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
380.50/117.99
active(sqr(0)) → mark(0)
380.50/117.99
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
380.50/117.99
active(dbl(0)) → mark(0)
380.50/117.99
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
380.50/117.99
active(add(0, z0)) → mark(z0)
380.50/117.99
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
380.50/117.99
active(first(0, z0)) → mark(nil)
380.50/117.99
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
380.50/117.99
active(half(0)) → mark(0)
380.50/117.99
active(half(s(0))) → mark(0)
380.50/117.99
active(half(s(s(z0)))) → mark(s(half(z0)))
380.50/117.99
active(half(dbl(z0))) → mark(z0)
380.50/117.99
active(terms(z0)) → terms(active(z0))
380.50/117.99
active(cons(z0, z1)) → cons(active(z0), z1)
380.50/117.99
active(recip(z0)) → recip(active(z0))
380.50/117.99
active(sqr(z0)) → sqr(active(z0))
380.50/117.99
active(s(z0)) → s(active(z0))
380.50/117.99
active(add(z0, z1)) → add(active(z0), z1)
380.50/117.99
active(add(z0, z1)) → add(z0, active(z1))
380.50/117.99
active(dbl(z0)) → dbl(active(z0))
380.50/117.99
active(first(z0, z1)) → first(active(z0), z1)
380.50/117.99
active(first(z0, z1)) → first(z0, active(z1))
380.50/117.99
active(half(z0)) → half(active(z0))
380.50/117.99
terms(mark(z0)) → mark(terms(z0))
380.50/117.99
terms(ok(z0)) → ok(terms(z0))
380.50/117.99
cons(mark(z0), z1) → mark(cons(z0, z1))
380.50/117.99
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
380.50/117.99
recip(mark(z0)) → mark(recip(z0))
380.50/117.99
recip(ok(z0)) → ok(recip(z0))
380.50/117.99
sqr(mark(z0)) → mark(sqr(z0))
380.50/117.99
sqr(ok(z0)) → ok(sqr(z0))
380.50/117.99
s(mark(z0)) → mark(s(z0))
380.50/117.99
s(ok(z0)) → ok(s(z0))
380.50/117.99
add(mark(z0), z1) → mark(add(z0, z1))
380.50/117.99
add(z0, mark(z1)) → mark(add(z0, z1))
380.50/117.99
add(ok(z0), ok(z1)) → ok(add(z0, z1))
380.50/117.99
dbl(mark(z0)) → mark(dbl(z0))
380.50/117.99
dbl(ok(z0)) → ok(dbl(z0))
380.50/117.99
first(mark(z0), z1) → mark(first(z0, z1))
380.50/117.99
first(z0, mark(z1)) → mark(first(z0, z1))
380.50/117.99
first(ok(z0), ok(z1)) → ok(first(z0, z1))
380.50/117.99
half(mark(z0)) → mark(half(z0))
380.50/117.99
half(ok(z0)) → ok(half(z0))
380.50/117.99
proper(terms(z0)) → terms(proper(z0))
380.50/117.99
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
380.50/117.99
proper(recip(z0)) → recip(proper(z0))
380.50/117.99
proper(sqr(z0)) → sqr(proper(z0))
380.50/117.99
proper(s(z0)) → s(proper(z0))
380.50/117.99
proper(0) → ok(0)
380.50/117.99
proper(add(z0, z1)) → add(proper(z0), proper(z1))
380.50/117.99
proper(dbl(z0)) → dbl(proper(z0))
380.50/117.99
proper(first(z0, z1)) → first(proper(z0), proper(z1))
380.50/117.99
proper(nil) → ok(nil)
380.50/117.99
proper(half(z0)) → half(proper(z0))
380.50/117.99
top(mark(z0)) → top(proper(z0))
380.50/117.99
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(terms(z0)) → c13(TERMS(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
380.50/117.99
ACTIVE(recip(z0)) → c15(RECIP(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(sqr(z0)) → c16(SQR(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
380.50/117.99
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
380.50/117.99
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
380.50/117.99
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
380.50/117.99
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
380.50/117.99
TERMS(mark(z0)) → c24(TERMS(z0))
380.50/117.99
TERMS(ok(z0)) → c25(TERMS(z0))
380.50/117.99
CONS(mark(z0), z1) → c26(CONS(z0, z1))
380.50/117.99
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
380.50/117.99
RECIP(mark(z0)) → c28(RECIP(z0))
380.50/117.99
RECIP(ok(z0)) → c29(RECIP(z0))
380.50/117.99
SQR(mark(z0)) → c30(SQR(z0))
380.50/117.99
SQR(ok(z0)) → c31(SQR(z0))
380.50/117.99
S(mark(z0)) → c32(S(z0))
380.50/117.99
S(ok(z0)) → c33(S(z0))
380.50/117.99
ADD(mark(z0), z1) → c34(ADD(z0, z1))
380.50/117.99
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
380.50/117.99
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
380.50/117.99
DBL(mark(z0)) → c37(DBL(z0))
380.50/117.99
DBL(ok(z0)) → c38(DBL(z0))
380.50/117.99
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
380.50/117.99
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
380.50/117.99
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
380.50/117.99
HALF(mark(z0)) → c42(HALF(z0))
380.50/117.99
HALF(ok(z0)) → c43(HALF(z0))
380.50/117.99
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
380.50/117.99
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
380.50/117.99
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
380.50/117.99
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
380.50/117.99
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
380.50/117.99
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
380.50/117.99
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
380.50/117.99
ACTIVE(terms(z0)) → c1(SQR(z0))
380.50/117.99
ACTIVE(terms(z0)) → c1(S(z0))
380.50/117.99
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
380.50/117.99
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
S tuples:
ACTIVE(terms(z0)) → c13(TERMS(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
380.50/117.99
ACTIVE(recip(z0)) → c15(RECIP(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(sqr(z0)) → c16(SQR(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
380.50/117.99
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
380.50/117.99
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
380.50/117.99
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
380.50/117.99
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
380.50/117.99
TERMS(mark(z0)) → c24(TERMS(z0))
380.50/117.99
TERMS(ok(z0)) → c25(TERMS(z0))
380.50/117.99
CONS(mark(z0), z1) → c26(CONS(z0, z1))
380.50/117.99
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
380.50/117.99
RECIP(mark(z0)) → c28(RECIP(z0))
380.50/117.99
RECIP(ok(z0)) → c29(RECIP(z0))
380.50/117.99
SQR(mark(z0)) → c30(SQR(z0))
380.50/117.99
SQR(ok(z0)) → c31(SQR(z0))
380.50/117.99
S(mark(z0)) → c32(S(z0))
380.50/117.99
S(ok(z0)) → c33(S(z0))
380.50/117.99
ADD(mark(z0), z1) → c34(ADD(z0, z1))
380.50/117.99
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
380.50/117.99
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
380.50/117.99
DBL(mark(z0)) → c37(DBL(z0))
380.50/117.99
DBL(ok(z0)) → c38(DBL(z0))
380.50/117.99
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
380.50/117.99
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
380.50/117.99
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
380.50/117.99
HALF(mark(z0)) → c42(HALF(z0))
380.50/117.99
HALF(ok(z0)) → c43(HALF(z0))
380.50/117.99
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
380.50/117.99
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/117.99
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
380.50/117.99
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
380.50/117.99
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
380.50/117.99
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
380.50/117.99
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
380.50/117.99
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
380.50/117.99
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
380.50/117.99
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
380.50/117.99
ACTIVE(terms(z0)) → c1(SQR(z0))
380.50/117.99
ACTIVE(terms(z0)) → c1(S(z0))
380.50/117.99
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
380.50/117.99
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
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, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1
380.50/117.99
380.50/117.99
(7) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
terms(
z0)) →
c13(
TERMS(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
380.50/117.99
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)), ACTIVE(sqr(0)))
380.50/117.99
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
380.50/117.99
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
380.50/117.99
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
380.50/118.02
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
380.50/118.02
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
380.50/118.02
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
380.50/118.02
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
380.50/118.02
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
380.50/118.02
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
380.50/118.02
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
380.50/118.02
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
380.50/118.02
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
380.50/118.02
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
380.50/118.02
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
380.50/118.02
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
380.50/118.02
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
380.50/118.02
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
380.50/118.02
380.50/118.02
(8) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
380.50/118.02
active(sqr(0)) → mark(0)
380.50/118.02
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
380.50/118.02
active(dbl(0)) → mark(0)
380.50/118.02
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
380.50/118.02
active(add(0, z0)) → mark(z0)
380.50/118.02
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
380.50/118.02
active(first(0, z0)) → mark(nil)
380.50/118.02
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
380.50/118.02
active(half(0)) → mark(0)
380.50/118.02
active(half(s(0))) → mark(0)
380.50/118.02
active(half(s(s(z0)))) → mark(s(half(z0)))
380.50/118.02
active(half(dbl(z0))) → mark(z0)
380.50/118.02
active(terms(z0)) → terms(active(z0))
380.50/118.02
active(cons(z0, z1)) → cons(active(z0), z1)
380.50/118.02
active(recip(z0)) → recip(active(z0))
380.50/118.02
active(sqr(z0)) → sqr(active(z0))
380.50/118.02
active(s(z0)) → s(active(z0))
380.50/118.02
active(add(z0, z1)) → add(active(z0), z1)
380.50/118.02
active(add(z0, z1)) → add(z0, active(z1))
380.50/118.02
active(dbl(z0)) → dbl(active(z0))
380.50/118.02
active(first(z0, z1)) → first(active(z0), z1)
380.50/118.02
active(first(z0, z1)) → first(z0, active(z1))
380.50/118.02
active(half(z0)) → half(active(z0))
380.50/118.02
terms(mark(z0)) → mark(terms(z0))
380.50/118.02
terms(ok(z0)) → ok(terms(z0))
380.50/118.02
cons(mark(z0), z1) → mark(cons(z0, z1))
380.50/118.02
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
380.50/118.02
recip(mark(z0)) → mark(recip(z0))
380.50/118.02
recip(ok(z0)) → ok(recip(z0))
380.50/118.02
sqr(mark(z0)) → mark(sqr(z0))
380.50/118.02
sqr(ok(z0)) → ok(sqr(z0))
380.50/118.02
s(mark(z0)) → mark(s(z0))
380.50/118.02
s(ok(z0)) → ok(s(z0))
380.50/118.02
add(mark(z0), z1) → mark(add(z0, z1))
380.50/118.02
add(z0, mark(z1)) → mark(add(z0, z1))
380.50/118.02
add(ok(z0), ok(z1)) → ok(add(z0, z1))
380.50/118.02
dbl(mark(z0)) → mark(dbl(z0))
380.50/118.02
dbl(ok(z0)) → ok(dbl(z0))
380.50/118.02
first(mark(z0), z1) → mark(first(z0, z1))
380.50/118.02
first(z0, mark(z1)) → mark(first(z0, z1))
380.50/118.02
first(ok(z0), ok(z1)) → ok(first(z0, z1))
380.50/118.02
half(mark(z0)) → mark(half(z0))
380.50/118.02
half(ok(z0)) → ok(half(z0))
380.50/118.02
proper(terms(z0)) → terms(proper(z0))
380.50/118.02
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
380.50/118.02
proper(recip(z0)) → recip(proper(z0))
380.50/118.02
proper(sqr(z0)) → sqr(proper(z0))
380.50/118.02
proper(s(z0)) → s(proper(z0))
380.50/118.02
proper(0) → ok(0)
380.50/118.02
proper(add(z0, z1)) → add(proper(z0), proper(z1))
380.50/118.02
proper(dbl(z0)) → dbl(proper(z0))
380.50/118.02
proper(first(z0, z1)) → first(proper(z0), proper(z1))
380.50/118.02
proper(nil) → ok(nil)
380.50/118.02
proper(half(z0)) → half(proper(z0))
380.50/118.02
top(mark(z0)) → top(proper(z0))
380.50/118.02
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
380.50/118.02
ACTIVE(recip(z0)) → c15(RECIP(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(sqr(z0)) → c16(SQR(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
380.50/118.02
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
380.50/118.02
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
380.50/118.02
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
380.50/118.02
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
380.50/118.02
TERMS(mark(z0)) → c24(TERMS(z0))
380.50/118.02
TERMS(ok(z0)) → c25(TERMS(z0))
380.50/118.02
CONS(mark(z0), z1) → c26(CONS(z0, z1))
380.50/118.02
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
380.50/118.02
RECIP(mark(z0)) → c28(RECIP(z0))
380.50/118.02
RECIP(ok(z0)) → c29(RECIP(z0))
380.50/118.02
SQR(mark(z0)) → c30(SQR(z0))
380.50/118.02
SQR(ok(z0)) → c31(SQR(z0))
380.50/118.02
S(mark(z0)) → c32(S(z0))
380.50/118.02
S(ok(z0)) → c33(S(z0))
380.50/118.02
ADD(mark(z0), z1) → c34(ADD(z0, z1))
380.50/118.02
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
380.50/118.02
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
380.50/118.02
DBL(mark(z0)) → c37(DBL(z0))
380.50/118.02
DBL(ok(z0)) → c38(DBL(z0))
380.50/118.02
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
380.50/118.02
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
380.50/118.02
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
380.50/118.02
HALF(mark(z0)) → c42(HALF(z0))
380.50/118.02
HALF(ok(z0)) → c43(HALF(z0))
380.50/118.02
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/118.02
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/118.02
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/118.02
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
380.50/118.02
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
380.50/118.02
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
380.50/118.02
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
380.50/118.02
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
380.50/118.02
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
380.50/118.02
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
380.50/118.02
ACTIVE(terms(z0)) → c1(SQR(z0))
380.50/118.02
ACTIVE(terms(z0)) → c1(S(z0))
380.50/118.02
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
380.50/118.02
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
380.50/118.02
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)), ACTIVE(sqr(0)))
380.50/118.02
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
380.50/118.02
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
380.50/118.02
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
380.50/118.02
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
380.50/118.02
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
380.50/118.02
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
380.50/118.02
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
380.50/118.02
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
380.50/118.02
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
380.50/118.02
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
380.50/118.02
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
380.50/118.02
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
380.50/118.02
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
380.50/118.02
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
380.50/118.02
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
380.50/118.02
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
380.50/118.02
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
S tuples:
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
380.50/118.02
ACTIVE(recip(z0)) → c15(RECIP(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(sqr(z0)) → c16(SQR(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
380.50/118.02
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
380.50/118.02
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
380.50/118.02
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
380.50/118.02
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
380.50/118.02
TERMS(mark(z0)) → c24(TERMS(z0))
380.50/118.02
TERMS(ok(z0)) → c25(TERMS(z0))
380.50/118.02
CONS(mark(z0), z1) → c26(CONS(z0, z1))
380.50/118.02
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
380.50/118.02
RECIP(mark(z0)) → c28(RECIP(z0))
380.50/118.02
RECIP(ok(z0)) → c29(RECIP(z0))
380.50/118.02
SQR(mark(z0)) → c30(SQR(z0))
380.50/118.02
SQR(ok(z0)) → c31(SQR(z0))
380.50/118.02
S(mark(z0)) → c32(S(z0))
380.50/118.02
S(ok(z0)) → c33(S(z0))
380.50/118.02
ADD(mark(z0), z1) → c34(ADD(z0, z1))
380.50/118.02
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
380.50/118.02
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
380.50/118.02
DBL(mark(z0)) → c37(DBL(z0))
380.50/118.02
DBL(ok(z0)) → c38(DBL(z0))
380.50/118.02
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
380.50/118.02
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
380.50/118.02
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
380.50/118.02
HALF(mark(z0)) → c42(HALF(z0))
380.50/118.02
HALF(ok(z0)) → c43(HALF(z0))
380.50/118.02
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/118.02
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/118.02
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/118.02
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
380.50/118.02
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
380.50/118.02
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
380.50/118.02
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
380.50/118.02
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
380.50/118.02
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
380.50/118.02
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
380.50/118.02
ACTIVE(terms(z0)) → c1(SQR(z0))
380.50/118.02
ACTIVE(terms(z0)) → c1(S(z0))
380.50/118.02
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
380.50/118.02
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
380.50/118.02
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)), ACTIVE(sqr(0)))
380.50/118.02
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
380.50/118.02
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
380.50/118.02
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
380.50/118.02
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
380.50/118.02
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
380.50/118.02
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
380.50/118.02
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
380.50/118.02
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
380.50/118.02
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
380.50/118.02
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
380.50/118.02
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
380.50/118.02
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
380.50/118.02
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
380.50/118.02
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
380.50/118.02
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
380.50/118.02
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
380.50/118.02
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
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, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13
380.50/118.02
380.50/118.02
(9) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
cons(
z0,
z1)) →
c14(
CONS(
active(
z0),
z1),
ACTIVE(
z0)) by
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(sqr(0)))
380.50/118.02
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
380.50/118.02
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(dbl(0)))
380.50/118.02
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
380.50/118.02
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
380.50/118.02
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
380.50/118.02
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
380.50/118.02
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
380.50/118.02
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
380.50/118.02
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
380.50/118.02
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
380.50/118.02
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
380.50/118.02
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
380.50/118.02
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
380.50/118.02
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
380.50/118.02
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
380.50/118.02
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
380.50/118.02
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
380.50/118.02
380.50/118.02
(10) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
380.50/118.02
active(sqr(0)) → mark(0)
380.50/118.02
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
380.50/118.02
active(dbl(0)) → mark(0)
380.50/118.02
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
380.50/118.02
active(add(0, z0)) → mark(z0)
380.50/118.02
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
380.50/118.02
active(first(0, z0)) → mark(nil)
380.50/118.02
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
380.50/118.02
active(half(0)) → mark(0)
380.50/118.02
active(half(s(0))) → mark(0)
380.50/118.02
active(half(s(s(z0)))) → mark(s(half(z0)))
380.50/118.02
active(half(dbl(z0))) → mark(z0)
380.50/118.02
active(terms(z0)) → terms(active(z0))
380.50/118.02
active(cons(z0, z1)) → cons(active(z0), z1)
380.50/118.02
active(recip(z0)) → recip(active(z0))
380.50/118.02
active(sqr(z0)) → sqr(active(z0))
380.50/118.02
active(s(z0)) → s(active(z0))
380.50/118.02
active(add(z0, z1)) → add(active(z0), z1)
380.50/118.02
active(add(z0, z1)) → add(z0, active(z1))
380.50/118.02
active(dbl(z0)) → dbl(active(z0))
380.50/118.02
active(first(z0, z1)) → first(active(z0), z1)
380.50/118.02
active(first(z0, z1)) → first(z0, active(z1))
380.50/118.02
active(half(z0)) → half(active(z0))
380.50/118.02
terms(mark(z0)) → mark(terms(z0))
380.50/118.02
terms(ok(z0)) → ok(terms(z0))
380.50/118.02
cons(mark(z0), z1) → mark(cons(z0, z1))
380.50/118.02
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
380.50/118.02
recip(mark(z0)) → mark(recip(z0))
380.50/118.02
recip(ok(z0)) → ok(recip(z0))
380.50/118.02
sqr(mark(z0)) → mark(sqr(z0))
380.50/118.02
sqr(ok(z0)) → ok(sqr(z0))
380.50/118.02
s(mark(z0)) → mark(s(z0))
380.50/118.02
s(ok(z0)) → ok(s(z0))
380.50/118.02
add(mark(z0), z1) → mark(add(z0, z1))
380.50/118.02
add(z0, mark(z1)) → mark(add(z0, z1))
380.50/118.02
add(ok(z0), ok(z1)) → ok(add(z0, z1))
380.50/118.02
dbl(mark(z0)) → mark(dbl(z0))
380.50/118.02
dbl(ok(z0)) → ok(dbl(z0))
380.50/118.02
first(mark(z0), z1) → mark(first(z0, z1))
380.50/118.02
first(z0, mark(z1)) → mark(first(z0, z1))
380.50/118.02
first(ok(z0), ok(z1)) → ok(first(z0, z1))
380.50/118.02
half(mark(z0)) → mark(half(z0))
380.50/118.02
half(ok(z0)) → ok(half(z0))
380.50/118.02
proper(terms(z0)) → terms(proper(z0))
380.50/118.02
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
380.50/118.02
proper(recip(z0)) → recip(proper(z0))
380.50/118.02
proper(sqr(z0)) → sqr(proper(z0))
380.50/118.02
proper(s(z0)) → s(proper(z0))
380.50/118.02
proper(0) → ok(0)
380.50/118.02
proper(add(z0, z1)) → add(proper(z0), proper(z1))
380.50/118.02
proper(dbl(z0)) → dbl(proper(z0))
380.50/118.02
proper(first(z0, z1)) → first(proper(z0), proper(z1))
380.50/118.02
proper(nil) → ok(nil)
380.50/118.02
proper(half(z0)) → half(proper(z0))
380.50/118.02
top(mark(z0)) → top(proper(z0))
380.50/118.02
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(recip(z0)) → c15(RECIP(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(sqr(z0)) → c16(SQR(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
380.50/118.02
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
380.50/118.02
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
380.50/118.02
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
380.50/118.02
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
380.50/118.02
TERMS(mark(z0)) → c24(TERMS(z0))
380.50/118.02
TERMS(ok(z0)) → c25(TERMS(z0))
380.50/118.02
CONS(mark(z0), z1) → c26(CONS(z0, z1))
380.50/118.02
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
380.50/118.02
RECIP(mark(z0)) → c28(RECIP(z0))
380.50/118.02
RECIP(ok(z0)) → c29(RECIP(z0))
380.50/118.02
SQR(mark(z0)) → c30(SQR(z0))
380.50/118.02
SQR(ok(z0)) → c31(SQR(z0))
380.50/118.02
S(mark(z0)) → c32(S(z0))
380.50/118.02
S(ok(z0)) → c33(S(z0))
380.50/118.02
ADD(mark(z0), z1) → c34(ADD(z0, z1))
380.50/118.02
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
380.50/118.02
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
380.50/118.02
DBL(mark(z0)) → c37(DBL(z0))
380.50/118.02
DBL(ok(z0)) → c38(DBL(z0))
380.50/118.02
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
380.50/118.02
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
380.50/118.02
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
380.50/118.02
HALF(mark(z0)) → c42(HALF(z0))
380.50/118.02
HALF(ok(z0)) → c43(HALF(z0))
380.50/118.02
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/118.02
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/118.02
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/118.02
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
380.50/118.02
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
380.50/118.02
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
380.50/118.02
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
380.50/118.02
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
380.50/118.02
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
380.50/118.02
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
380.50/118.02
ACTIVE(terms(z0)) → c1(SQR(z0))
380.50/118.02
ACTIVE(terms(z0)) → c1(S(z0))
380.50/118.02
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
380.50/118.02
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
380.50/118.02
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)), ACTIVE(sqr(0)))
380.50/118.02
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
380.50/118.02
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
380.50/118.02
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
380.50/118.02
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
380.50/118.02
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
380.50/118.02
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
380.50/118.02
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
380.50/118.02
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
380.50/118.02
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
380.50/118.02
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
380.50/118.02
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
380.50/118.02
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
380.50/118.02
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
380.50/118.02
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
380.50/118.02
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
380.50/118.02
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
380.50/118.02
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
380.50/118.02
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(sqr(0)))
380.50/118.02
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
380.50/118.02
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(dbl(0)))
380.50/118.02
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
380.50/118.02
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
380.50/118.02
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
380.50/118.02
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
380.50/118.02
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
380.50/118.02
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
380.50/118.02
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
380.50/118.02
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
380.50/118.02
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
380.50/118.02
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
380.50/118.02
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
380.50/118.02
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
380.50/118.02
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
380.50/118.02
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
380.50/118.02
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
S tuples:
ACTIVE(recip(z0)) → c15(RECIP(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(sqr(z0)) → c16(SQR(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
380.50/118.02
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
380.50/118.02
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
380.50/118.02
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
380.50/118.02
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
380.50/118.02
TERMS(mark(z0)) → c24(TERMS(z0))
380.50/118.02
TERMS(ok(z0)) → c25(TERMS(z0))
380.50/118.02
CONS(mark(z0), z1) → c26(CONS(z0, z1))
380.50/118.02
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
380.50/118.02
RECIP(mark(z0)) → c28(RECIP(z0))
380.50/118.02
RECIP(ok(z0)) → c29(RECIP(z0))
380.50/118.02
SQR(mark(z0)) → c30(SQR(z0))
380.50/118.02
SQR(ok(z0)) → c31(SQR(z0))
380.50/118.02
S(mark(z0)) → c32(S(z0))
380.50/118.02
S(ok(z0)) → c33(S(z0))
380.50/118.02
ADD(mark(z0), z1) → c34(ADD(z0, z1))
380.50/118.02
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
380.50/118.02
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
380.50/118.02
DBL(mark(z0)) → c37(DBL(z0))
380.50/118.02
DBL(ok(z0)) → c38(DBL(z0))
380.50/118.02
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
380.50/118.02
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
380.50/118.02
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
380.50/118.02
HALF(mark(z0)) → c42(HALF(z0))
380.50/118.02
HALF(ok(z0)) → c43(HALF(z0))
380.50/118.02
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/118.02
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/118.02
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
380.50/118.02
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.50/118.02
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
380.50/118.02
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
380.50/118.02
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
380.50/118.02
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
380.50/118.02
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
380.50/118.02
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
380.50/118.02
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
380.50/118.02
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
380.50/118.02
ACTIVE(terms(z0)) → c1(SQR(z0))
380.50/118.02
ACTIVE(terms(z0)) → c1(S(z0))
380.50/118.02
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
380.50/118.02
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
380.50/118.02
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)), ACTIVE(sqr(0)))
380.50/118.02
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
380.50/118.02
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
380.50/118.02
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
380.50/118.02
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
380.50/118.02
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
380.50/118.02
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
380.50/118.02
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
380.50/118.02
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
380.50/118.02
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
380.50/118.02
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
380.50/118.02
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
380.50/118.02
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
380.50/118.02
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
380.50/118.02
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
380.50/118.02
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
380.50/118.02
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
380.50/118.02
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
380.50/118.02
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(sqr(0)))
380.50/118.02
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
380.50/118.02
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(dbl(0)))
380.50/118.02
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
380.50/118.02
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
380.50/118.02
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
380.50/118.02
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
380.50/118.02
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
380.50/118.02
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
380.50/118.02
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
380.50/118.02
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
380.50/118.02
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
380.50/118.02
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
380.50/118.02
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
380.50/118.02
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
380.50/118.02
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
380.50/118.02
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
380.50/118.02
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
380.50/118.02
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
380.50/118.02
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
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, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14
380.50/118.02
380.50/118.02
(11) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
recip(
z0)) →
c15(
RECIP(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
380.50/118.02
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)), ACTIVE(sqr(0)))
380.50/118.02
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
380.50/118.02
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)), ACTIVE(dbl(0)))
380.50/118.02
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
380.50/118.02
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
380.50/118.02
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
380.73/118.06
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
380.73/118.06
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
380.73/118.06
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
380.73/118.06
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
380.73/118.06
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
380.73/118.06
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
380.73/118.06
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
380.73/118.06
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
380.73/118.06
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
380.73/118.06
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
380.73/118.06
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
380.73/118.06
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
380.73/118.06
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
380.73/118.06
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
380.73/118.06
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
380.73/118.06
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
380.73/118.06
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
380.73/118.06
380.73/118.06
(12) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
380.73/118.06
active(sqr(0)) → mark(0)
380.73/118.06
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
380.73/118.06
active(dbl(0)) → mark(0)
380.73/118.06
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
380.73/118.06
active(add(0, z0)) → mark(z0)
380.73/118.06
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
380.73/118.06
active(first(0, z0)) → mark(nil)
380.73/118.06
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
380.73/118.06
active(half(0)) → mark(0)
380.73/118.06
active(half(s(0))) → mark(0)
380.73/118.06
active(half(s(s(z0)))) → mark(s(half(z0)))
380.73/118.06
active(half(dbl(z0))) → mark(z0)
380.73/118.06
active(terms(z0)) → terms(active(z0))
380.73/118.06
active(cons(z0, z1)) → cons(active(z0), z1)
380.73/118.06
active(recip(z0)) → recip(active(z0))
380.73/118.06
active(sqr(z0)) → sqr(active(z0))
380.73/118.06
active(s(z0)) → s(active(z0))
380.73/118.06
active(add(z0, z1)) → add(active(z0), z1)
380.73/118.06
active(add(z0, z1)) → add(z0, active(z1))
380.73/118.06
active(dbl(z0)) → dbl(active(z0))
380.73/118.06
active(first(z0, z1)) → first(active(z0), z1)
380.73/118.06
active(first(z0, z1)) → first(z0, active(z1))
380.73/118.06
active(half(z0)) → half(active(z0))
380.73/118.06
terms(mark(z0)) → mark(terms(z0))
380.73/118.06
terms(ok(z0)) → ok(terms(z0))
380.73/118.06
cons(mark(z0), z1) → mark(cons(z0, z1))
380.73/118.06
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
380.73/118.06
recip(mark(z0)) → mark(recip(z0))
380.73/118.06
recip(ok(z0)) → ok(recip(z0))
380.73/118.06
sqr(mark(z0)) → mark(sqr(z0))
380.73/118.06
sqr(ok(z0)) → ok(sqr(z0))
380.73/118.06
s(mark(z0)) → mark(s(z0))
380.73/118.06
s(ok(z0)) → ok(s(z0))
380.73/118.06
add(mark(z0), z1) → mark(add(z0, z1))
380.73/118.06
add(z0, mark(z1)) → mark(add(z0, z1))
380.73/118.06
add(ok(z0), ok(z1)) → ok(add(z0, z1))
380.73/118.06
dbl(mark(z0)) → mark(dbl(z0))
380.73/118.06
dbl(ok(z0)) → ok(dbl(z0))
380.73/118.06
first(mark(z0), z1) → mark(first(z0, z1))
380.73/118.06
first(z0, mark(z1)) → mark(first(z0, z1))
380.73/118.06
first(ok(z0), ok(z1)) → ok(first(z0, z1))
380.73/118.06
half(mark(z0)) → mark(half(z0))
380.73/118.06
half(ok(z0)) → ok(half(z0))
380.73/118.06
proper(terms(z0)) → terms(proper(z0))
380.73/118.06
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
380.73/118.06
proper(recip(z0)) → recip(proper(z0))
380.73/118.06
proper(sqr(z0)) → sqr(proper(z0))
380.73/118.06
proper(s(z0)) → s(proper(z0))
380.73/118.06
proper(0) → ok(0)
380.73/118.06
proper(add(z0, z1)) → add(proper(z0), proper(z1))
380.73/118.06
proper(dbl(z0)) → dbl(proper(z0))
380.73/118.06
proper(first(z0, z1)) → first(proper(z0), proper(z1))
380.73/118.06
proper(nil) → ok(nil)
380.73/118.06
proper(half(z0)) → half(proper(z0))
380.73/118.06
top(mark(z0)) → top(proper(z0))
380.73/118.06
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sqr(z0)) → c16(SQR(active(z0)), ACTIVE(z0))
380.73/118.06
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
380.73/118.06
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
380.73/118.06
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
380.73/118.06
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
380.73/118.06
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
380.73/118.06
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
380.73/118.06
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
380.73/118.06
TERMS(mark(z0)) → c24(TERMS(z0))
380.73/118.06
TERMS(ok(z0)) → c25(TERMS(z0))
380.73/118.06
CONS(mark(z0), z1) → c26(CONS(z0, z1))
380.73/118.06
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
380.73/118.06
RECIP(mark(z0)) → c28(RECIP(z0))
380.73/118.06
RECIP(ok(z0)) → c29(RECIP(z0))
380.73/118.06
SQR(mark(z0)) → c30(SQR(z0))
380.73/118.06
SQR(ok(z0)) → c31(SQR(z0))
380.73/118.06
S(mark(z0)) → c32(S(z0))
380.73/118.06
S(ok(z0)) → c33(S(z0))
380.73/118.06
ADD(mark(z0), z1) → c34(ADD(z0, z1))
380.73/118.06
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
380.73/118.06
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
380.73/118.06
DBL(mark(z0)) → c37(DBL(z0))
380.73/118.06
DBL(ok(z0)) → c38(DBL(z0))
380.73/118.06
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
380.73/118.06
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
380.73/118.06
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
380.73/118.06
HALF(mark(z0)) → c42(HALF(z0))
380.73/118.06
HALF(ok(z0)) → c43(HALF(z0))
380.73/118.06
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
380.73/118.06
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.73/118.06
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
380.73/118.06
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
380.73/118.06
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
380.73/118.06
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.73/118.06
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
380.73/118.06
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.73/118.06
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
380.73/118.06
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
380.73/118.06
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
380.73/118.06
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
380.73/118.06
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
380.73/118.06
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
380.73/118.06
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
380.73/118.06
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
380.73/118.06
ACTIVE(terms(z0)) → c1(SQR(z0))
380.73/118.06
ACTIVE(terms(z0)) → c1(S(z0))
380.73/118.06
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
380.73/118.06
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
380.73/118.06
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
380.73/118.06
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)), ACTIVE(sqr(0)))
380.73/118.06
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
380.73/118.06
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
380.73/118.06
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
380.73/118.06
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
380.73/118.06
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
380.73/118.06
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
380.73/118.06
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
380.73/118.06
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
380.73/118.06
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
380.73/118.06
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
380.73/118.06
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
380.73/118.06
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
380.73/118.06
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
380.73/118.06
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
380.73/118.06
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
380.73/118.06
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
380.73/118.06
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
380.73/118.06
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
380.73/118.06
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
380.73/118.06
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
380.73/118.06
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
380.73/118.06
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
380.73/118.06
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
380.73/118.06
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(sqr(0)))
380.73/118.06
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
380.73/118.06
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(dbl(0)))
380.73/118.06
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
380.73/118.06
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
380.73/118.06
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
380.73/118.06
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
380.73/118.06
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
380.73/118.06
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
380.73/118.06
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
380.73/118.06
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
380.73/118.06
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
380.73/118.06
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
380.73/118.06
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
380.73/118.06
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
380.73/118.06
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
380.73/118.06
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
380.73/118.07
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
380.73/118.07
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
380.73/118.07
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
380.73/118.07
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
380.73/118.07
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
380.73/118.07
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
380.73/118.07
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
380.73/118.07
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)), ACTIVE(sqr(0)))
380.73/118.07
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
380.73/118.07
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)), ACTIVE(dbl(0)))
380.73/118.07
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
380.73/118.07
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
380.73/118.07
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
380.73/118.07
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
380.73/118.07
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
380.73/118.07
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
380.73/118.07
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
380.73/118.07
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
380.73/118.07
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
380.73/118.07
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
380.73/118.07
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
380.73/118.07
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
380.73/118.07
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
380.73/118.07
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
380.73/118.07
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
380.73/118.07
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
380.73/118.07
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
380.73/118.07
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
380.73/118.07
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
380.73/118.07
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
S tuples:
ACTIVE(sqr(z0)) → c16(SQR(active(z0)), ACTIVE(z0))
380.73/118.07
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
380.73/118.07
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
380.73/118.07
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
380.73/118.07
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
380.73/118.07
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
380.73/118.07
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
380.73/118.07
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
380.73/118.07
TERMS(mark(z0)) → c24(TERMS(z0))
380.73/118.07
TERMS(ok(z0)) → c25(TERMS(z0))
380.73/118.07
CONS(mark(z0), z1) → c26(CONS(z0, z1))
380.73/118.07
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
380.73/118.07
RECIP(mark(z0)) → c28(RECIP(z0))
380.73/118.07
RECIP(ok(z0)) → c29(RECIP(z0))
380.73/118.07
SQR(mark(z0)) → c30(SQR(z0))
380.73/118.07
SQR(ok(z0)) → c31(SQR(z0))
380.73/118.07
S(mark(z0)) → c32(S(z0))
380.73/118.07
S(ok(z0)) → c33(S(z0))
380.73/118.07
ADD(mark(z0), z1) → c34(ADD(z0, z1))
380.73/118.07
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
380.73/118.07
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
380.73/118.07
DBL(mark(z0)) → c37(DBL(z0))
380.73/118.07
DBL(ok(z0)) → c38(DBL(z0))
380.73/118.07
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
380.73/118.07
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
380.73/118.07
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
380.73/118.07
HALF(mark(z0)) → c42(HALF(z0))
380.73/118.07
HALF(ok(z0)) → c43(HALF(z0))
380.73/118.07
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
380.73/118.07
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.73/118.07
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
380.73/118.07
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
380.73/118.07
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
380.73/118.07
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.73/118.07
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
380.73/118.07
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.73/118.07
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
380.73/118.07
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
380.73/118.07
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
380.73/118.07
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
380.73/118.07
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
380.73/118.07
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
380.73/118.07
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
380.73/118.07
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
380.73/118.07
ACTIVE(terms(z0)) → c1(SQR(z0))
380.73/118.07
ACTIVE(terms(z0)) → c1(S(z0))
380.73/118.07
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
380.73/118.07
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
380.73/118.07
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
380.73/118.07
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)), ACTIVE(sqr(0)))
380.73/118.07
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
380.73/118.07
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
380.73/118.07
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
380.73/118.07
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
380.73/118.07
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
380.73/118.07
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
380.73/118.07
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
380.73/118.07
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
380.73/118.07
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
380.73/118.07
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
380.73/118.07
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
380.73/118.07
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
380.73/118.07
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
380.73/118.07
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
380.73/118.07
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
380.73/118.07
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
380.73/118.07
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
380.73/118.07
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
380.73/118.07
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
380.73/118.07
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
380.73/118.07
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
380.73/118.07
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
380.73/118.07
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
380.73/118.07
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(sqr(0)))
380.73/118.07
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
380.73/118.07
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(dbl(0)))
380.73/118.07
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
380.73/118.07
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
380.73/118.07
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
380.73/118.07
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
380.73/118.07
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
380.73/118.07
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
380.73/118.07
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
380.73/118.07
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
380.73/118.07
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
380.73/118.07
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
380.73/118.07
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
380.73/118.07
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
380.73/118.07
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
380.73/118.07
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
380.73/118.07
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
380.73/118.07
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
380.73/118.07
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
380.73/118.07
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
380.73/118.07
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
380.73/118.07
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
380.73/118.07
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
380.73/118.07
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)), ACTIVE(sqr(0)))
380.73/118.07
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
380.73/118.07
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)), ACTIVE(dbl(0)))
380.73/118.07
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
380.73/118.07
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
380.73/118.07
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
380.73/118.07
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
380.73/118.07
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
380.73/118.07
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
380.73/118.07
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
380.73/118.07
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
380.73/118.07
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
380.73/118.07
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
380.73/118.07
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
380.73/118.07
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
380.73/118.07
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
380.73/118.07
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
380.73/118.07
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
380.73/118.07
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
380.73/118.07
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
380.73/118.07
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
380.73/118.07
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
380.73/118.07
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
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, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15
380.73/118.07
380.73/118.07
(13) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
sqr(
z0)) →
c16(
SQR(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
380.73/118.07
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)), ACTIVE(sqr(0)))
380.73/118.11
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
380.73/118.11
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)), ACTIVE(dbl(0)))
380.73/118.11
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
380.73/118.11
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
380.73/118.11
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
380.73/118.11
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
380.73/118.11
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
380.73/118.11
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)), ACTIVE(half(0)))
380.73/118.11
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
380.73/118.11
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
380.73/118.11
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
380.73/118.11
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
380.73/118.11
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
380.73/118.11
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
380.73/118.11
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
380.73/118.11
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
380.73/118.11
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
380.73/118.11
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
380.73/118.11
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
380.73/118.11
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
380.73/118.11
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
380.73/118.11
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
380.73/118.11
380.73/118.11
(14) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
380.73/118.11
active(sqr(0)) → mark(0)
380.73/118.11
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
380.73/118.11
active(dbl(0)) → mark(0)
380.73/118.11
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
380.73/118.11
active(add(0, z0)) → mark(z0)
380.73/118.11
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
380.73/118.11
active(first(0, z0)) → mark(nil)
380.73/118.11
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
380.73/118.11
active(half(0)) → mark(0)
380.73/118.11
active(half(s(0))) → mark(0)
380.73/118.11
active(half(s(s(z0)))) → mark(s(half(z0)))
380.73/118.11
active(half(dbl(z0))) → mark(z0)
380.73/118.11
active(terms(z0)) → terms(active(z0))
380.73/118.11
active(cons(z0, z1)) → cons(active(z0), z1)
380.73/118.11
active(recip(z0)) → recip(active(z0))
380.73/118.11
active(sqr(z0)) → sqr(active(z0))
380.73/118.11
active(s(z0)) → s(active(z0))
380.73/118.11
active(add(z0, z1)) → add(active(z0), z1)
380.73/118.11
active(add(z0, z1)) → add(z0, active(z1))
380.73/118.11
active(dbl(z0)) → dbl(active(z0))
380.73/118.11
active(first(z0, z1)) → first(active(z0), z1)
380.73/118.11
active(first(z0, z1)) → first(z0, active(z1))
380.73/118.11
active(half(z0)) → half(active(z0))
380.73/118.11
terms(mark(z0)) → mark(terms(z0))
380.73/118.11
terms(ok(z0)) → ok(terms(z0))
380.73/118.11
cons(mark(z0), z1) → mark(cons(z0, z1))
380.73/118.11
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
380.73/118.11
recip(mark(z0)) → mark(recip(z0))
380.73/118.11
recip(ok(z0)) → ok(recip(z0))
380.73/118.11
sqr(mark(z0)) → mark(sqr(z0))
380.73/118.11
sqr(ok(z0)) → ok(sqr(z0))
380.73/118.11
s(mark(z0)) → mark(s(z0))
380.73/118.11
s(ok(z0)) → ok(s(z0))
380.73/118.11
add(mark(z0), z1) → mark(add(z0, z1))
380.73/118.11
add(z0, mark(z1)) → mark(add(z0, z1))
380.73/118.11
add(ok(z0), ok(z1)) → ok(add(z0, z1))
380.73/118.11
dbl(mark(z0)) → mark(dbl(z0))
380.73/118.11
dbl(ok(z0)) → ok(dbl(z0))
380.73/118.11
first(mark(z0), z1) → mark(first(z0, z1))
380.73/118.11
first(z0, mark(z1)) → mark(first(z0, z1))
380.73/118.11
first(ok(z0), ok(z1)) → ok(first(z0, z1))
380.73/118.11
half(mark(z0)) → mark(half(z0))
380.73/118.11
half(ok(z0)) → ok(half(z0))
380.73/118.11
proper(terms(z0)) → terms(proper(z0))
380.73/118.11
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
380.73/118.11
proper(recip(z0)) → recip(proper(z0))
380.73/118.11
proper(sqr(z0)) → sqr(proper(z0))
380.73/118.11
proper(s(z0)) → s(proper(z0))
380.73/118.11
proper(0) → ok(0)
380.73/118.11
proper(add(z0, z1)) → add(proper(z0), proper(z1))
380.73/118.11
proper(dbl(z0)) → dbl(proper(z0))
380.73/118.11
proper(first(z0, z1)) → first(proper(z0), proper(z1))
380.73/118.11
proper(nil) → ok(nil)
380.73/118.11
proper(half(z0)) → half(proper(z0))
380.73/118.11
top(mark(z0)) → top(proper(z0))
380.73/118.11
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
380.73/118.11
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
380.73/118.11
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
380.73/118.11
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
380.73/118.11
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
380.73/118.11
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
380.73/118.11
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
380.73/118.11
TERMS(mark(z0)) → c24(TERMS(z0))
380.73/118.11
TERMS(ok(z0)) → c25(TERMS(z0))
380.73/118.11
CONS(mark(z0), z1) → c26(CONS(z0, z1))
380.73/118.11
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
380.73/118.11
RECIP(mark(z0)) → c28(RECIP(z0))
380.73/118.11
RECIP(ok(z0)) → c29(RECIP(z0))
380.73/118.11
SQR(mark(z0)) → c30(SQR(z0))
380.73/118.11
SQR(ok(z0)) → c31(SQR(z0))
380.73/118.11
S(mark(z0)) → c32(S(z0))
380.73/118.11
S(ok(z0)) → c33(S(z0))
380.73/118.11
ADD(mark(z0), z1) → c34(ADD(z0, z1))
380.73/118.11
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
380.73/118.11
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
380.73/118.11
DBL(mark(z0)) → c37(DBL(z0))
380.73/118.11
DBL(ok(z0)) → c38(DBL(z0))
380.73/118.11
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
380.73/118.11
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
380.73/118.11
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
380.73/118.11
HALF(mark(z0)) → c42(HALF(z0))
380.73/118.11
HALF(ok(z0)) → c43(HALF(z0))
380.73/118.11
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
380.73/118.11
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.73/118.11
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
380.73/118.11
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
380.73/118.11
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
380.73/118.11
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.73/118.11
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
380.73/118.11
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
380.73/118.11
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
380.73/118.11
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
380.73/118.11
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
380.73/118.11
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
380.73/118.11
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
380.73/118.11
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
380.73/118.11
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
380.73/118.11
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
380.73/118.11
ACTIVE(terms(z0)) → c1(SQR(z0))
380.73/118.11
ACTIVE(terms(z0)) → c1(S(z0))
380.73/118.11
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
380.73/118.11
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
380.73/118.11
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
380.73/118.11
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)), ACTIVE(sqr(0)))
380.73/118.11
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
380.73/118.11
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
380.73/118.11
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
380.73/118.11
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
380.73/118.11
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
380.73/118.11
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
380.73/118.11
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
380.73/118.11
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
380.73/118.11
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
380.73/118.11
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
380.73/118.11
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
380.73/118.11
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
380.73/118.11
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
380.73/118.11
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
380.73/118.11
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
380.73/118.11
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
380.73/118.11
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
380.73/118.11
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
380.73/118.11
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
380.73/118.11
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
380.73/118.11
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
380.73/118.11
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
380.73/118.11
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
380.73/118.11
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(sqr(0)))
380.73/118.11
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
380.73/118.11
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(dbl(0)))
380.73/118.11
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
380.73/118.11
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
380.73/118.11
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
380.73/118.11
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
380.73/118.11
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
380.73/118.11
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
380.73/118.11
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
380.73/118.11
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
380.73/118.11
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
380.73/118.11
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
380.73/118.11
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
380.73/118.11
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
380.73/118.11
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
380.73/118.11
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
380.73/118.11
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
380.73/118.11
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
380.73/118.11
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
380.73/118.11
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
380.73/118.11
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
380.73/118.11
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
380.73/118.11
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
380.73/118.11
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)), ACTIVE(sqr(0)))
380.73/118.11
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
380.73/118.11
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)), ACTIVE(dbl(0)))
380.73/118.11
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
380.73/118.11
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
380.73/118.11
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
380.73/118.11
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
380.73/118.11
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
380.73/118.11
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
380.73/118.11
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
380.73/118.11
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
380.73/118.11
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
380.73/118.11
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
380.73/118.11
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
380.73/118.11
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
380.73/118.11
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
380.73/118.11
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
380.73/118.11
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
380.73/118.11
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
380.73/118.11
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
380.73/118.11
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
380.73/118.11
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
380.73/118.11
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
380.73/118.11
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
380.73/118.11
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)), ACTIVE(sqr(0)))
380.73/118.11
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
380.73/118.11
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)), ACTIVE(dbl(0)))
380.73/118.11
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
380.73/118.11
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
380.73/118.11
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
380.73/118.11
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
380.73/118.11
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
380.73/118.11
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)), ACTIVE(half(0)))
380.73/118.11
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
380.73/118.11
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
380.73/118.11
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
380.73/118.11
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
380.73/118.11
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
380.73/118.11
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
380.73/118.11
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
380.73/118.11
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
380.73/118.11
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
380.73/118.11
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
380.73/118.11
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
380.73/118.11
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
380.73/118.11
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
380.73/118.11
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
S tuples:
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
380.73/118.11
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
380.73/118.11
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
380.73/118.11
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
380.73/118.11
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
380.73/118.11
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
380.73/118.11
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
380.73/118.11
TERMS(mark(z0)) → c24(TERMS(z0))
380.73/118.11
TERMS(ok(z0)) → c25(TERMS(z0))
380.73/118.11
CONS(mark(z0), z1) → c26(CONS(z0, z1))
380.73/118.11
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
380.73/118.11
RECIP(mark(z0)) → c28(RECIP(z0))
380.73/118.11
RECIP(ok(z0)) → c29(RECIP(z0))
380.73/118.11
SQR(mark(z0)) → c30(SQR(z0))
380.73/118.11
SQR(ok(z0)) → c31(SQR(z0))
380.73/118.11
S(mark(z0)) → c32(S(z0))
380.73/118.11
S(ok(z0)) → c33(S(z0))
380.73/118.11
ADD(mark(z0), z1) → c34(ADD(z0, z1))
380.73/118.11
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.08/118.11
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.08/118.11
DBL(mark(z0)) → c37(DBL(z0))
381.08/118.11
DBL(ok(z0)) → c38(DBL(z0))
381.08/118.11
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.08/118.11
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.08/118.11
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.08/118.11
HALF(mark(z0)) → c42(HALF(z0))
381.08/118.11
HALF(ok(z0)) → c43(HALF(z0))
381.08/118.11
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
381.08/118.11
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.08/118.11
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.08/118.11
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.08/118.11
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.08/118.11
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.08/118.11
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.08/118.11
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.08/118.11
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.08/118.11
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.08/118.11
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.08/118.11
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.08/118.11
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.08/118.11
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.08/118.11
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.08/118.11
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.08/118.11
ACTIVE(terms(z0)) → c1(SQR(z0))
381.08/118.11
ACTIVE(terms(z0)) → c1(S(z0))
381.08/118.11
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.08/118.11
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.08/118.11
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.08/118.11
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)), ACTIVE(sqr(0)))
381.08/118.11
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.08/118.11
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
381.08/118.11
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.08/118.11
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.08/118.11
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.08/118.11
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.08/118.11
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.08/118.11
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
381.08/118.11
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.08/118.11
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.08/118.11
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.08/118.11
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.08/118.11
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.08/118.11
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.08/118.11
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.08/118.11
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.08/118.11
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.08/118.11
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.08/118.11
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.08/118.11
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.08/118.11
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.08/118.11
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.08/118.11
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.08/118.11
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(sqr(0)))
381.08/118.11
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.08/118.11
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(dbl(0)))
381.08/118.11
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.08/118.11
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.08/118.11
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.08/118.11
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.08/118.11
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.08/118.11
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
381.08/118.11
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.08/118.11
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.08/118.11
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.08/118.11
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.08/118.11
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.08/118.11
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.08/118.11
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.08/118.11
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.08/118.11
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.08/118.11
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.08/118.11
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.08/118.11
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.08/118.11
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.08/118.11
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.08/118.11
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.08/118.11
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)), ACTIVE(sqr(0)))
381.08/118.11
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.08/118.11
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)), ACTIVE(dbl(0)))
381.08/118.11
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.08/118.11
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.08/118.11
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.08/118.11
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.08/118.11
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.08/118.11
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
381.08/118.11
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.08/118.11
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.08/118.11
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.08/118.11
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.08/118.11
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.08/118.11
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.08/118.11
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.08/118.11
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.08/118.11
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.08/118.11
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.08/118.11
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.08/118.11
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.08/118.19
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)), ACTIVE(sqr(0)))
381.08/118.19
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.08/118.19
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)), ACTIVE(dbl(0)))
381.08/118.19
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.08/118.19
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.08/118.19
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.08/118.19
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.08/118.19
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.08/118.19
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)), ACTIVE(half(0)))
381.08/118.19
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.08/118.19
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.08/118.19
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.08/118.19
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.08/118.19
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.08/118.19
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.08/118.19
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.08/118.19
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.08/118.19
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
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, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16
381.08/118.19
381.08/118.19
(15) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
381.08/118.19
381.08/118.19
(16) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.08/118.19
active(sqr(0)) → mark(0)
381.08/118.19
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.08/118.19
active(dbl(0)) → mark(0)
381.08/118.19
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.08/118.19
active(add(0, z0)) → mark(z0)
381.08/118.19
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.08/118.19
active(first(0, z0)) → mark(nil)
381.08/118.19
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.08/118.19
active(half(0)) → mark(0)
381.08/118.19
active(half(s(0))) → mark(0)
381.08/118.19
active(half(s(s(z0)))) → mark(s(half(z0)))
381.08/118.19
active(half(dbl(z0))) → mark(z0)
381.08/118.19
active(terms(z0)) → terms(active(z0))
381.08/118.19
active(cons(z0, z1)) → cons(active(z0), z1)
381.08/118.19
active(recip(z0)) → recip(active(z0))
381.08/118.19
active(sqr(z0)) → sqr(active(z0))
381.08/118.19
active(s(z0)) → s(active(z0))
381.08/118.19
active(add(z0, z1)) → add(active(z0), z1)
381.08/118.19
active(add(z0, z1)) → add(z0, active(z1))
381.08/118.19
active(dbl(z0)) → dbl(active(z0))
381.08/118.19
active(first(z0, z1)) → first(active(z0), z1)
381.08/118.19
active(first(z0, z1)) → first(z0, active(z1))
381.08/118.19
active(half(z0)) → half(active(z0))
381.08/118.19
terms(mark(z0)) → mark(terms(z0))
381.08/118.19
terms(ok(z0)) → ok(terms(z0))
381.08/118.19
cons(mark(z0), z1) → mark(cons(z0, z1))
381.08/118.19
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.08/118.19
recip(mark(z0)) → mark(recip(z0))
381.08/118.19
recip(ok(z0)) → ok(recip(z0))
381.08/118.19
sqr(mark(z0)) → mark(sqr(z0))
381.08/118.19
sqr(ok(z0)) → ok(sqr(z0))
381.08/118.19
s(mark(z0)) → mark(s(z0))
381.08/118.19
s(ok(z0)) → ok(s(z0))
381.08/118.19
add(mark(z0), z1) → mark(add(z0, z1))
381.08/118.19
add(z0, mark(z1)) → mark(add(z0, z1))
381.08/118.19
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.08/118.19
dbl(mark(z0)) → mark(dbl(z0))
381.08/118.19
dbl(ok(z0)) → ok(dbl(z0))
381.08/118.19
first(mark(z0), z1) → mark(first(z0, z1))
381.08/118.19
first(z0, mark(z1)) → mark(first(z0, z1))
381.08/118.19
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.08/118.19
half(mark(z0)) → mark(half(z0))
381.08/118.19
half(ok(z0)) → ok(half(z0))
381.08/118.19
proper(terms(z0)) → terms(proper(z0))
381.08/118.19
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.08/118.19
proper(recip(z0)) → recip(proper(z0))
381.08/118.19
proper(sqr(z0)) → sqr(proper(z0))
381.08/118.19
proper(s(z0)) → s(proper(z0))
381.08/118.19
proper(0) → ok(0)
381.08/118.19
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.08/118.19
proper(dbl(z0)) → dbl(proper(z0))
381.08/118.19
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.08/118.19
proper(nil) → ok(nil)
381.08/118.19
proper(half(z0)) → half(proper(z0))
381.08/118.19
top(mark(z0)) → top(proper(z0))
381.08/118.19
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
381.08/118.19
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.08/118.19
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.08/118.19
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
381.08/118.19
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.08/118.19
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.08/118.19
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
381.08/118.19
TERMS(mark(z0)) → c24(TERMS(z0))
381.08/118.19
TERMS(ok(z0)) → c25(TERMS(z0))
381.08/118.19
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.08/118.19
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.08/118.19
RECIP(mark(z0)) → c28(RECIP(z0))
381.08/118.19
RECIP(ok(z0)) → c29(RECIP(z0))
381.08/118.19
SQR(mark(z0)) → c30(SQR(z0))
381.08/118.19
SQR(ok(z0)) → c31(SQR(z0))
381.08/118.19
S(mark(z0)) → c32(S(z0))
381.08/118.19
S(ok(z0)) → c33(S(z0))
381.08/118.19
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.08/118.19
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.08/118.19
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.08/118.19
DBL(mark(z0)) → c37(DBL(z0))
381.08/118.19
DBL(ok(z0)) → c38(DBL(z0))
381.08/118.19
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.08/118.19
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.08/118.19
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.08/118.19
HALF(mark(z0)) → c42(HALF(z0))
381.08/118.19
HALF(ok(z0)) → c43(HALF(z0))
381.08/118.19
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
381.08/118.19
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.08/118.19
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.08/118.19
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.08/118.19
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.08/118.19
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.08/118.19
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.08/118.19
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.08/118.19
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.08/118.19
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.08/118.19
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.08/118.19
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.08/118.19
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.08/118.19
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.08/118.19
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.08/118.19
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.08/118.19
ACTIVE(terms(z0)) → c1(SQR(z0))
381.08/118.19
ACTIVE(terms(z0)) → c1(S(z0))
381.08/118.19
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.08/118.19
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.08/118.19
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.08/118.19
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
381.08/118.19
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.08/118.19
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.08/118.19
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.08/118.19
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.08/118.19
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.08/118.19
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
381.08/118.19
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.08/118.19
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.08/118.19
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.08/118.19
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.08/118.19
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.08/118.19
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.08/118.19
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.08/118.19
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.08/118.19
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.08/118.19
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.08/118.19
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(dbl(0)))
381.08/118.19
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.08/118.19
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.08/118.19
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.08/118.19
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.08/118.19
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.08/118.19
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
381.08/118.19
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.08/118.19
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.08/118.19
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.08/118.19
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.08/118.19
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.08/118.19
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.08/118.19
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.08/118.19
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.08/118.19
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.08/118.19
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.08/118.19
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)), ACTIVE(dbl(0)))
381.08/118.19
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.08/118.19
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.08/118.19
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.08/118.19
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.08/118.19
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.08/118.19
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
381.08/118.19
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.08/118.19
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.08/118.19
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.08/118.19
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.08/118.19
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.08/118.19
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.08/118.19
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.08/118.19
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.08/118.19
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.08/118.19
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.08/118.19
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)), ACTIVE(dbl(0)))
381.08/118.19
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.08/118.19
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.08/118.19
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.08/118.19
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.08/118.19
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.08/118.19
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)), ACTIVE(half(0)))
381.08/118.19
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.08/118.19
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.08/118.19
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.08/118.19
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.08/118.19
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.08/118.19
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.08/118.19
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.08/118.19
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.08/118.19
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.08/118.19
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.08/118.19
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.08/118.19
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.08/118.19
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
S tuples:
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0))
381.08/118.19
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.08/118.19
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.08/118.19
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
381.08/118.19
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.08/118.19
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.08/118.19
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
381.08/118.19
TERMS(mark(z0)) → c24(TERMS(z0))
381.08/118.19
TERMS(ok(z0)) → c25(TERMS(z0))
381.08/118.19
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.08/118.19
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.08/118.19
RECIP(mark(z0)) → c28(RECIP(z0))
381.08/118.19
RECIP(ok(z0)) → c29(RECIP(z0))
381.08/118.19
SQR(mark(z0)) → c30(SQR(z0))
381.08/118.19
SQR(ok(z0)) → c31(SQR(z0))
381.08/118.19
S(mark(z0)) → c32(S(z0))
381.08/118.19
S(ok(z0)) → c33(S(z0))
381.08/118.19
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.08/118.19
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.08/118.19
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.08/118.19
DBL(mark(z0)) → c37(DBL(z0))
381.08/118.19
DBL(ok(z0)) → c38(DBL(z0))
381.08/118.19
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.08/118.19
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.08/118.19
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.08/118.19
HALF(mark(z0)) → c42(HALF(z0))
381.08/118.19
HALF(ok(z0)) → c43(HALF(z0))
381.08/118.19
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
381.08/118.19
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.08/118.19
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.08/118.19
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.08/118.19
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.08/118.19
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.08/118.19
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.08/118.19
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.08/118.19
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.08/118.19
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.08/118.19
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.08/118.19
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.08/118.19
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.08/118.19
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.08/118.19
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.08/118.19
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.08/118.19
ACTIVE(terms(z0)) → c1(SQR(z0))
381.08/118.19
ACTIVE(terms(z0)) → c1(S(z0))
381.08/118.19
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.08/118.19
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.08/118.19
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.08/118.19
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
381.08/118.19
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.08/118.19
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.08/118.19
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.08/118.19
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.08/118.19
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.08/118.19
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
381.08/118.19
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.08/118.19
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.08/118.19
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.08/118.19
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.08/118.19
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.08/118.19
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.08/118.19
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.08/118.19
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.08/118.19
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.08/118.19
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.08/118.19
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(dbl(0)))
381.08/118.19
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.08/118.19
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.08/118.19
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.08/118.19
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.08/118.19
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.08/118.19
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
381.08/118.19
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.08/118.19
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.08/118.19
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.08/118.19
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.08/118.19
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.08/118.19
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.08/118.19
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.08/118.19
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.08/118.19
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.08/118.19
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.08/118.19
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)), ACTIVE(dbl(0)))
381.08/118.19
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.08/118.19
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.08/118.19
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.08/118.19
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.08/118.19
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.08/118.19
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
381.08/118.19
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.08/118.19
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.08/118.19
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.08/118.19
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.08/118.19
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.08/118.19
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.08/118.19
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.08/118.19
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.08/118.19
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.08/118.19
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.08/118.19
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)), ACTIVE(dbl(0)))
381.08/118.19
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.08/118.19
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.08/118.19
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.08/118.19
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.08/118.19
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.08/118.19
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)), ACTIVE(half(0)))
381.08/118.19
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.08/118.19
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.08/118.19
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.08/118.19
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.08/118.19
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.08/118.19
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.08/118.19
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.08/118.19
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.08/118.19
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.08/118.19
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.08/118.19
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.08/118.19
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.42/118.22
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.42/118.22
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.22
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.42/118.22
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
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, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16
381.42/118.22
381.42/118.22
(17) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
s(
z0)) →
c17(
S(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(s(sqr(0))) → c17(S(mark(0)), ACTIVE(sqr(0)))
381.42/118.22
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.22
ACTIVE(s(dbl(0))) → c17(S(mark(0)), ACTIVE(dbl(0)))
381.42/118.22
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.22
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.22
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.22
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.22
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.22
ACTIVE(s(half(0))) → c17(S(mark(0)), ACTIVE(half(0)))
381.42/118.22
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.42/118.22
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.22
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.22
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.22
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.22
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.22
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.42/118.22
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.22
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.42/118.22
381.42/118.22
(18) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.42/118.22
active(sqr(0)) → mark(0)
381.42/118.22
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.42/118.22
active(dbl(0)) → mark(0)
381.42/118.22
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.42/118.22
active(add(0, z0)) → mark(z0)
381.42/118.22
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.42/118.22
active(first(0, z0)) → mark(nil)
381.42/118.22
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.42/118.22
active(half(0)) → mark(0)
381.42/118.22
active(half(s(0))) → mark(0)
381.42/118.22
active(half(s(s(z0)))) → mark(s(half(z0)))
381.42/118.22
active(half(dbl(z0))) → mark(z0)
381.42/118.22
active(terms(z0)) → terms(active(z0))
381.42/118.22
active(cons(z0, z1)) → cons(active(z0), z1)
381.42/118.22
active(recip(z0)) → recip(active(z0))
381.42/118.22
active(sqr(z0)) → sqr(active(z0))
381.42/118.22
active(s(z0)) → s(active(z0))
381.42/118.22
active(add(z0, z1)) → add(active(z0), z1)
381.42/118.22
active(add(z0, z1)) → add(z0, active(z1))
381.42/118.22
active(dbl(z0)) → dbl(active(z0))
381.42/118.22
active(first(z0, z1)) → first(active(z0), z1)
381.42/118.22
active(first(z0, z1)) → first(z0, active(z1))
381.42/118.22
active(half(z0)) → half(active(z0))
381.42/118.22
terms(mark(z0)) → mark(terms(z0))
381.42/118.22
terms(ok(z0)) → ok(terms(z0))
381.42/118.22
cons(mark(z0), z1) → mark(cons(z0, z1))
381.42/118.22
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.42/118.22
recip(mark(z0)) → mark(recip(z0))
381.42/118.22
recip(ok(z0)) → ok(recip(z0))
381.42/118.22
sqr(mark(z0)) → mark(sqr(z0))
381.42/118.22
sqr(ok(z0)) → ok(sqr(z0))
381.42/118.22
s(mark(z0)) → mark(s(z0))
381.42/118.22
s(ok(z0)) → ok(s(z0))
381.42/118.22
add(mark(z0), z1) → mark(add(z0, z1))
381.42/118.22
add(z0, mark(z1)) → mark(add(z0, z1))
381.42/118.22
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.42/118.22
dbl(mark(z0)) → mark(dbl(z0))
381.42/118.22
dbl(ok(z0)) → ok(dbl(z0))
381.42/118.22
first(mark(z0), z1) → mark(first(z0, z1))
381.42/118.22
first(z0, mark(z1)) → mark(first(z0, z1))
381.42/118.22
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.42/118.22
half(mark(z0)) → mark(half(z0))
381.42/118.22
half(ok(z0)) → ok(half(z0))
381.42/118.22
proper(terms(z0)) → terms(proper(z0))
381.42/118.22
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.42/118.22
proper(recip(z0)) → recip(proper(z0))
381.42/118.22
proper(sqr(z0)) → sqr(proper(z0))
381.42/118.22
proper(s(z0)) → s(proper(z0))
381.42/118.22
proper(0) → ok(0)
381.42/118.22
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.42/118.22
proper(dbl(z0)) → dbl(proper(z0))
381.42/118.22
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.42/118.22
proper(nil) → ok(nil)
381.42/118.22
proper(half(z0)) → half(proper(z0))
381.42/118.22
top(mark(z0)) → top(proper(z0))
381.42/118.22
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.42/118.22
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.42/118.22
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
381.42/118.22
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.42/118.22
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.42/118.22
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
381.42/118.22
TERMS(mark(z0)) → c24(TERMS(z0))
381.42/118.22
TERMS(ok(z0)) → c25(TERMS(z0))
381.42/118.22
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.42/118.22
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.42/118.22
RECIP(mark(z0)) → c28(RECIP(z0))
381.42/118.22
RECIP(ok(z0)) → c29(RECIP(z0))
381.42/118.22
SQR(mark(z0)) → c30(SQR(z0))
381.42/118.22
SQR(ok(z0)) → c31(SQR(z0))
381.42/118.22
S(mark(z0)) → c32(S(z0))
381.42/118.22
S(ok(z0)) → c33(S(z0))
381.42/118.22
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.42/118.22
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.42/118.22
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.42/118.22
DBL(mark(z0)) → c37(DBL(z0))
381.42/118.22
DBL(ok(z0)) → c38(DBL(z0))
381.42/118.22
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.42/118.22
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.42/118.22
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.42/118.22
HALF(mark(z0)) → c42(HALF(z0))
381.42/118.22
HALF(ok(z0)) → c43(HALF(z0))
381.42/118.22
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
381.42/118.22
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.22
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.42/118.22
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.42/118.22
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.42/118.22
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.22
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.42/118.22
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.22
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.42/118.22
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.42/118.22
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.42/118.22
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.42/118.22
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.42/118.22
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.42/118.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.42/118.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.42/118.22
ACTIVE(terms(z0)) → c1(SQR(z0))
381.42/118.22
ACTIVE(terms(z0)) → c1(S(z0))
381.42/118.22
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.42/118.22
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.42/118.22
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.22
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
381.42/118.22
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.22
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.22
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.22
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.22
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.22
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
381.42/118.22
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.42/118.22
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.22
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.22
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.22
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.22
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.22
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.42/118.22
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.22
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.42/118.22
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.42/118.22
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(dbl(0)))
381.42/118.22
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.42/118.22
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.42/118.22
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.42/118.22
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.42/118.22
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.22
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
381.42/118.22
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.42/118.22
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.42/118.22
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.42/118.22
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.42/118.22
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.42/118.22
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.42/118.22
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.42/118.22
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.42/118.22
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.42/118.22
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.22
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)), ACTIVE(dbl(0)))
381.42/118.22
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.22
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.22
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.22
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.22
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.22
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
381.42/118.22
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.42/118.22
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.22
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.22
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.22
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.22
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.22
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.42/118.22
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.22
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.42/118.22
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.22
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)), ACTIVE(dbl(0)))
381.42/118.22
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.22
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.22
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.22
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.22
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.22
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)), ACTIVE(half(0)))
381.42/118.22
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.42/118.22
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.22
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.22
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.22
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.22
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.22
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.42/118.22
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.22
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.42/118.22
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.42/118.22
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.22
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.42/118.22
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.42/118.22
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(s(sqr(0))) → c17(S(mark(0)), ACTIVE(sqr(0)))
381.42/118.22
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.22
ACTIVE(s(dbl(0))) → c17(S(mark(0)), ACTIVE(dbl(0)))
381.42/118.22
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.22
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.22
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.22
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.22
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.22
ACTIVE(s(half(0))) → c17(S(mark(0)), ACTIVE(half(0)))
381.42/118.22
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.42/118.22
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.22
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.22
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.22
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.22
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.22
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.42/118.22
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.22
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.42/118.22
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.42/118.22
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
381.42/118.22
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.42/118.22
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.42/118.22
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
381.42/118.22
TERMS(mark(z0)) → c24(TERMS(z0))
381.42/118.22
TERMS(ok(z0)) → c25(TERMS(z0))
381.42/118.22
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.42/118.22
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.42/118.22
RECIP(mark(z0)) → c28(RECIP(z0))
381.42/118.22
RECIP(ok(z0)) → c29(RECIP(z0))
381.42/118.22
SQR(mark(z0)) → c30(SQR(z0))
381.42/118.22
SQR(ok(z0)) → c31(SQR(z0))
381.42/118.22
S(mark(z0)) → c32(S(z0))
381.42/118.22
S(ok(z0)) → c33(S(z0))
381.42/118.22
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.42/118.22
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.42/118.22
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.42/118.22
DBL(mark(z0)) → c37(DBL(z0))
381.42/118.22
DBL(ok(z0)) → c38(DBL(z0))
381.42/118.22
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.42/118.22
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.42/118.22
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.42/118.22
HALF(mark(z0)) → c42(HALF(z0))
381.42/118.22
HALF(ok(z0)) → c43(HALF(z0))
381.42/118.22
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
381.42/118.22
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.22
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.42/118.22
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.42/118.22
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.42/118.22
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.22
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.42/118.22
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.22
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.42/118.22
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.42/118.22
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.42/118.22
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.42/118.22
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.42/118.22
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.42/118.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.42/118.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.42/118.22
ACTIVE(terms(z0)) → c1(SQR(z0))
381.42/118.22
ACTIVE(terms(z0)) → c1(S(z0))
381.42/118.22
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.42/118.22
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.42/118.22
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.22
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
381.42/118.22
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.22
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.22
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.22
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.22
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.22
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
381.42/118.22
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.42/118.22
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.22
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.22
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.22
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.22
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.22
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.42/118.22
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.22
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.42/118.22
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.42/118.22
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(dbl(0)))
381.42/118.22
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.42/118.22
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.42/118.22
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.42/118.22
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.42/118.22
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.22
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
381.42/118.22
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.42/118.22
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.42/118.22
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.42/118.22
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.42/118.22
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.42/118.22
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.42/118.22
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.42/118.22
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.42/118.22
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.42/118.22
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.22
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)), ACTIVE(dbl(0)))
381.42/118.22
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.22
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.22
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.22
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.22
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.22
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
381.42/118.22
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.42/118.22
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.22
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.22
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.22
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.22
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.22
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.42/118.22
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.22
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.42/118.22
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.22
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)), ACTIVE(dbl(0)))
381.42/118.22
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.22
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.22
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.22
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.22
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.22
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)), ACTIVE(half(0)))
381.42/118.22
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.42/118.22
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.22
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.22
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.22
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.22
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.22
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.42/118.22
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.22
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.22
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.22
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.42/118.22
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.42/118.22
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.22
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.42/118.22
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.42/118.22
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.22
ACTIVE(s(sqr(0))) → c17(S(mark(0)), ACTIVE(sqr(0)))
381.42/118.22
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.22
ACTIVE(s(dbl(0))) → c17(S(mark(0)), ACTIVE(dbl(0)))
381.42/118.22
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.22
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.22
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.22
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(s(half(0))) → c17(S(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
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, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17
381.42/118.25
381.42/118.25
(19) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing tuple parts
381.42/118.25
381.42/118.25
(20) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.42/118.25
active(sqr(0)) → mark(0)
381.42/118.25
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.42/118.25
active(dbl(0)) → mark(0)
381.42/118.25
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.42/118.25
active(add(0, z0)) → mark(z0)
381.42/118.25
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.42/118.25
active(first(0, z0)) → mark(nil)
381.42/118.25
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.42/118.25
active(half(0)) → mark(0)
381.42/118.25
active(half(s(0))) → mark(0)
381.42/118.25
active(half(s(s(z0)))) → mark(s(half(z0)))
381.42/118.25
active(half(dbl(z0))) → mark(z0)
381.42/118.25
active(terms(z0)) → terms(active(z0))
381.42/118.25
active(cons(z0, z1)) → cons(active(z0), z1)
381.42/118.25
active(recip(z0)) → recip(active(z0))
381.42/118.25
active(sqr(z0)) → sqr(active(z0))
381.42/118.25
active(s(z0)) → s(active(z0))
381.42/118.25
active(add(z0, z1)) → add(active(z0), z1)
381.42/118.25
active(add(z0, z1)) → add(z0, active(z1))
381.42/118.25
active(dbl(z0)) → dbl(active(z0))
381.42/118.25
active(first(z0, z1)) → first(active(z0), z1)
381.42/118.25
active(first(z0, z1)) → first(z0, active(z1))
381.42/118.25
active(half(z0)) → half(active(z0))
381.42/118.25
terms(mark(z0)) → mark(terms(z0))
381.42/118.25
terms(ok(z0)) → ok(terms(z0))
381.42/118.25
cons(mark(z0), z1) → mark(cons(z0, z1))
381.42/118.25
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.42/118.25
recip(mark(z0)) → mark(recip(z0))
381.42/118.25
recip(ok(z0)) → ok(recip(z0))
381.42/118.25
sqr(mark(z0)) → mark(sqr(z0))
381.42/118.25
sqr(ok(z0)) → ok(sqr(z0))
381.42/118.25
s(mark(z0)) → mark(s(z0))
381.42/118.25
s(ok(z0)) → ok(s(z0))
381.42/118.25
add(mark(z0), z1) → mark(add(z0, z1))
381.42/118.25
add(z0, mark(z1)) → mark(add(z0, z1))
381.42/118.25
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.42/118.25
dbl(mark(z0)) → mark(dbl(z0))
381.42/118.25
dbl(ok(z0)) → ok(dbl(z0))
381.42/118.25
first(mark(z0), z1) → mark(first(z0, z1))
381.42/118.25
first(z0, mark(z1)) → mark(first(z0, z1))
381.42/118.25
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.42/118.25
half(mark(z0)) → mark(half(z0))
381.42/118.25
half(ok(z0)) → ok(half(z0))
381.42/118.25
proper(terms(z0)) → terms(proper(z0))
381.42/118.25
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.42/118.25
proper(recip(z0)) → recip(proper(z0))
381.42/118.25
proper(sqr(z0)) → sqr(proper(z0))
381.42/118.25
proper(s(z0)) → s(proper(z0))
381.42/118.25
proper(0) → ok(0)
381.42/118.25
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.42/118.25
proper(dbl(z0)) → dbl(proper(z0))
381.42/118.25
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.42/118.25
proper(nil) → ok(nil)
381.42/118.25
proper(half(z0)) → half(proper(z0))
381.42/118.25
top(mark(z0)) → top(proper(z0))
381.42/118.25
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.42/118.25
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.42/118.25
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
381.42/118.25
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.42/118.25
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.42/118.25
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
381.42/118.25
TERMS(mark(z0)) → c24(TERMS(z0))
381.42/118.25
TERMS(ok(z0)) → c25(TERMS(z0))
381.42/118.25
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.42/118.25
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.42/118.25
RECIP(mark(z0)) → c28(RECIP(z0))
381.42/118.25
RECIP(ok(z0)) → c29(RECIP(z0))
381.42/118.25
SQR(mark(z0)) → c30(SQR(z0))
381.42/118.25
SQR(ok(z0)) → c31(SQR(z0))
381.42/118.25
S(mark(z0)) → c32(S(z0))
381.42/118.25
S(ok(z0)) → c33(S(z0))
381.42/118.25
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.42/118.25
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.42/118.25
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.42/118.25
DBL(mark(z0)) → c37(DBL(z0))
381.42/118.25
DBL(ok(z0)) → c38(DBL(z0))
381.42/118.25
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.42/118.25
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.42/118.25
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.42/118.25
HALF(mark(z0)) → c42(HALF(z0))
381.42/118.25
HALF(ok(z0)) → c43(HALF(z0))
381.42/118.25
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.25
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.25
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.25
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.42/118.25
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.42/118.25
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.42/118.25
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.42/118.25
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.42/118.25
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.42/118.25
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.42/118.25
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.42/118.25
ACTIVE(terms(z0)) → c1(SQR(z0))
381.42/118.25
ACTIVE(terms(z0)) → c1(S(z0))
381.42/118.25
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.42/118.25
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.42/118.25
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
381.42/118.25
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.42/118.25
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.25
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.42/118.25
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.42/118.25
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(s(dbl(0))) → c17(S(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(s(half(0))) → c17(S(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.42/118.25
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.42/118.25
ACTIVE(dbl(z0)) → c20(DBL(active(z0)), ACTIVE(z0))
381.42/118.25
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.42/118.25
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.42/118.25
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
381.42/118.25
TERMS(mark(z0)) → c24(TERMS(z0))
381.42/118.25
TERMS(ok(z0)) → c25(TERMS(z0))
381.42/118.25
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.42/118.25
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.42/118.25
RECIP(mark(z0)) → c28(RECIP(z0))
381.42/118.25
RECIP(ok(z0)) → c29(RECIP(z0))
381.42/118.25
SQR(mark(z0)) → c30(SQR(z0))
381.42/118.25
SQR(ok(z0)) → c31(SQR(z0))
381.42/118.25
S(mark(z0)) → c32(S(z0))
381.42/118.25
S(ok(z0)) → c33(S(z0))
381.42/118.25
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.42/118.25
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.42/118.25
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.42/118.25
DBL(mark(z0)) → c37(DBL(z0))
381.42/118.25
DBL(ok(z0)) → c38(DBL(z0))
381.42/118.25
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.42/118.25
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.42/118.25
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.42/118.25
HALF(mark(z0)) → c42(HALF(z0))
381.42/118.25
HALF(ok(z0)) → c43(HALF(z0))
381.42/118.25
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.25
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.25
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.25
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.42/118.25
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.42/118.25
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.42/118.25
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.42/118.25
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.42/118.25
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.42/118.25
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.42/118.25
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.42/118.25
ACTIVE(terms(z0)) → c1(SQR(z0))
381.42/118.25
ACTIVE(terms(z0)) → c1(S(z0))
381.42/118.25
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.42/118.25
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.42/118.25
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
381.42/118.25
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.42/118.25
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.25
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.42/118.25
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.42/118.25
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(s(dbl(0))) → c17(S(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(s(half(0))) → c17(S(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
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, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17
381.42/118.25
381.42/118.25
(21) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
dbl(
z0)) →
c20(
DBL(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)), ACTIVE(sqr(0)))
381.42/118.25
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
381.42/118.25
(22) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.42/118.25
active(sqr(0)) → mark(0)
381.42/118.25
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.42/118.25
active(dbl(0)) → mark(0)
381.42/118.25
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.42/118.25
active(add(0, z0)) → mark(z0)
381.42/118.25
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.42/118.25
active(first(0, z0)) → mark(nil)
381.42/118.25
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.42/118.25
active(half(0)) → mark(0)
381.42/118.25
active(half(s(0))) → mark(0)
381.42/118.25
active(half(s(s(z0)))) → mark(s(half(z0)))
381.42/118.25
active(half(dbl(z0))) → mark(z0)
381.42/118.25
active(terms(z0)) → terms(active(z0))
381.42/118.25
active(cons(z0, z1)) → cons(active(z0), z1)
381.42/118.25
active(recip(z0)) → recip(active(z0))
381.42/118.25
active(sqr(z0)) → sqr(active(z0))
381.42/118.25
active(s(z0)) → s(active(z0))
381.42/118.25
active(add(z0, z1)) → add(active(z0), z1)
381.42/118.25
active(add(z0, z1)) → add(z0, active(z1))
381.42/118.25
active(dbl(z0)) → dbl(active(z0))
381.42/118.25
active(first(z0, z1)) → first(active(z0), z1)
381.42/118.25
active(first(z0, z1)) → first(z0, active(z1))
381.42/118.25
active(half(z0)) → half(active(z0))
381.42/118.25
terms(mark(z0)) → mark(terms(z0))
381.42/118.25
terms(ok(z0)) → ok(terms(z0))
381.42/118.25
cons(mark(z0), z1) → mark(cons(z0, z1))
381.42/118.25
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.42/118.25
recip(mark(z0)) → mark(recip(z0))
381.42/118.25
recip(ok(z0)) → ok(recip(z0))
381.42/118.25
sqr(mark(z0)) → mark(sqr(z0))
381.42/118.25
sqr(ok(z0)) → ok(sqr(z0))
381.42/118.25
s(mark(z0)) → mark(s(z0))
381.42/118.25
s(ok(z0)) → ok(s(z0))
381.42/118.25
add(mark(z0), z1) → mark(add(z0, z1))
381.42/118.25
add(z0, mark(z1)) → mark(add(z0, z1))
381.42/118.25
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.42/118.25
dbl(mark(z0)) → mark(dbl(z0))
381.42/118.25
dbl(ok(z0)) → ok(dbl(z0))
381.42/118.25
first(mark(z0), z1) → mark(first(z0, z1))
381.42/118.25
first(z0, mark(z1)) → mark(first(z0, z1))
381.42/118.25
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.42/118.25
half(mark(z0)) → mark(half(z0))
381.42/118.25
half(ok(z0)) → ok(half(z0))
381.42/118.25
proper(terms(z0)) → terms(proper(z0))
381.42/118.25
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.42/118.25
proper(recip(z0)) → recip(proper(z0))
381.42/118.25
proper(sqr(z0)) → sqr(proper(z0))
381.42/118.25
proper(s(z0)) → s(proper(z0))
381.42/118.25
proper(0) → ok(0)
381.42/118.25
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.42/118.25
proper(dbl(z0)) → dbl(proper(z0))
381.42/118.25
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.42/118.25
proper(nil) → ok(nil)
381.42/118.25
proper(half(z0)) → half(proper(z0))
381.42/118.25
top(mark(z0)) → top(proper(z0))
381.42/118.25
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.42/118.25
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.42/118.25
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.42/118.25
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.42/118.25
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
381.42/118.25
TERMS(mark(z0)) → c24(TERMS(z0))
381.42/118.25
TERMS(ok(z0)) → c25(TERMS(z0))
381.42/118.25
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.42/118.25
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.42/118.25
RECIP(mark(z0)) → c28(RECIP(z0))
381.42/118.25
RECIP(ok(z0)) → c29(RECIP(z0))
381.42/118.25
SQR(mark(z0)) → c30(SQR(z0))
381.42/118.25
SQR(ok(z0)) → c31(SQR(z0))
381.42/118.25
S(mark(z0)) → c32(S(z0))
381.42/118.25
S(ok(z0)) → c33(S(z0))
381.42/118.25
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.42/118.25
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.42/118.25
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.42/118.25
DBL(mark(z0)) → c37(DBL(z0))
381.42/118.25
DBL(ok(z0)) → c38(DBL(z0))
381.42/118.25
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.42/118.25
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.42/118.25
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.42/118.25
HALF(mark(z0)) → c42(HALF(z0))
381.42/118.25
HALF(ok(z0)) → c43(HALF(z0))
381.42/118.25
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.25
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.25
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.25
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.42/118.25
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.42/118.25
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.42/118.25
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.42/118.25
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.42/118.25
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.42/118.25
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.42/118.25
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.42/118.25
ACTIVE(terms(z0)) → c1(SQR(z0))
381.42/118.25
ACTIVE(terms(z0)) → c1(S(z0))
381.42/118.25
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.42/118.25
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.42/118.25
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
381.42/118.25
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.42/118.25
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.25
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.42/118.25
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.42/118.25
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(s(dbl(0))) → c17(S(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(s(half(0))) → c17(S(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.42/118.25
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)), ACTIVE(sqr(0)))
381.42/118.25
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.42/118.25
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.42/118.25
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.42/118.25
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.42/118.25
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
381.42/118.25
TERMS(mark(z0)) → c24(TERMS(z0))
381.42/118.25
TERMS(ok(z0)) → c25(TERMS(z0))
381.42/118.25
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.42/118.25
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.42/118.25
RECIP(mark(z0)) → c28(RECIP(z0))
381.42/118.25
RECIP(ok(z0)) → c29(RECIP(z0))
381.42/118.25
SQR(mark(z0)) → c30(SQR(z0))
381.42/118.25
SQR(ok(z0)) → c31(SQR(z0))
381.42/118.25
S(mark(z0)) → c32(S(z0))
381.42/118.25
S(ok(z0)) → c33(S(z0))
381.42/118.25
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.42/118.25
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.42/118.25
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.42/118.25
DBL(mark(z0)) → c37(DBL(z0))
381.42/118.25
DBL(ok(z0)) → c38(DBL(z0))
381.42/118.25
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.42/118.25
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.42/118.25
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.42/118.25
HALF(mark(z0)) → c42(HALF(z0))
381.42/118.25
HALF(ok(z0)) → c43(HALF(z0))
381.42/118.25
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.25
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.25
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.25
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.42/118.25
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.42/118.25
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.42/118.25
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.42/118.25
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.42/118.25
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.42/118.25
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.42/118.25
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.42/118.25
ACTIVE(terms(z0)) → c1(SQR(z0))
381.42/118.25
ACTIVE(terms(z0)) → c1(S(z0))
381.42/118.25
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.42/118.25
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.42/118.25
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
381.42/118.25
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.42/118.25
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.25
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.42/118.25
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.42/118.25
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(s(dbl(0))) → c17(S(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(s(half(0))) → c17(S(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.42/118.25
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)), ACTIVE(sqr(0)))
381.42/118.25
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)), ACTIVE(dbl(0)))
381.42/118.25
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20
381.42/118.25
381.42/118.25
(23) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 7 trailing tuple parts
381.42/118.25
381.42/118.25
(24) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.42/118.25
active(sqr(0)) → mark(0)
381.42/118.25
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.42/118.25
active(dbl(0)) → mark(0)
381.42/118.25
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.42/118.25
active(add(0, z0)) → mark(z0)
381.42/118.25
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.42/118.25
active(first(0, z0)) → mark(nil)
381.42/118.25
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.42/118.25
active(half(0)) → mark(0)
381.42/118.25
active(half(s(0))) → mark(0)
381.42/118.25
active(half(s(s(z0)))) → mark(s(half(z0)))
381.42/118.25
active(half(dbl(z0))) → mark(z0)
381.42/118.25
active(terms(z0)) → terms(active(z0))
381.42/118.25
active(cons(z0, z1)) → cons(active(z0), z1)
381.42/118.25
active(recip(z0)) → recip(active(z0))
381.42/118.25
active(sqr(z0)) → sqr(active(z0))
381.42/118.25
active(s(z0)) → s(active(z0))
381.42/118.25
active(add(z0, z1)) → add(active(z0), z1)
381.42/118.25
active(add(z0, z1)) → add(z0, active(z1))
381.42/118.25
active(dbl(z0)) → dbl(active(z0))
381.42/118.25
active(first(z0, z1)) → first(active(z0), z1)
381.42/118.25
active(first(z0, z1)) → first(z0, active(z1))
381.42/118.25
active(half(z0)) → half(active(z0))
381.42/118.25
terms(mark(z0)) → mark(terms(z0))
381.42/118.25
terms(ok(z0)) → ok(terms(z0))
381.42/118.25
cons(mark(z0), z1) → mark(cons(z0, z1))
381.42/118.25
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.42/118.25
recip(mark(z0)) → mark(recip(z0))
381.42/118.25
recip(ok(z0)) → ok(recip(z0))
381.42/118.25
sqr(mark(z0)) → mark(sqr(z0))
381.42/118.25
sqr(ok(z0)) → ok(sqr(z0))
381.42/118.25
s(mark(z0)) → mark(s(z0))
381.42/118.25
s(ok(z0)) → ok(s(z0))
381.42/118.25
add(mark(z0), z1) → mark(add(z0, z1))
381.42/118.25
add(z0, mark(z1)) → mark(add(z0, z1))
381.42/118.25
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.42/118.25
dbl(mark(z0)) → mark(dbl(z0))
381.42/118.25
dbl(ok(z0)) → ok(dbl(z0))
381.42/118.25
first(mark(z0), z1) → mark(first(z0, z1))
381.42/118.25
first(z0, mark(z1)) → mark(first(z0, z1))
381.42/118.25
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.42/118.25
half(mark(z0)) → mark(half(z0))
381.42/118.25
half(ok(z0)) → ok(half(z0))
381.42/118.25
proper(terms(z0)) → terms(proper(z0))
381.42/118.25
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.42/118.25
proper(recip(z0)) → recip(proper(z0))
381.42/118.25
proper(sqr(z0)) → sqr(proper(z0))
381.42/118.25
proper(s(z0)) → s(proper(z0))
381.42/118.25
proper(0) → ok(0)
381.42/118.25
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.42/118.25
proper(dbl(z0)) → dbl(proper(z0))
381.42/118.25
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.42/118.25
proper(nil) → ok(nil)
381.42/118.25
proper(half(z0)) → half(proper(z0))
381.42/118.25
top(mark(z0)) → top(proper(z0))
381.42/118.25
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.42/118.25
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.42/118.25
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.42/118.25
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.42/118.25
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
381.42/118.25
TERMS(mark(z0)) → c24(TERMS(z0))
381.42/118.25
TERMS(ok(z0)) → c25(TERMS(z0))
381.42/118.25
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.42/118.25
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.42/118.25
RECIP(mark(z0)) → c28(RECIP(z0))
381.42/118.25
RECIP(ok(z0)) → c29(RECIP(z0))
381.42/118.25
SQR(mark(z0)) → c30(SQR(z0))
381.42/118.25
SQR(ok(z0)) → c31(SQR(z0))
381.42/118.25
S(mark(z0)) → c32(S(z0))
381.42/118.25
S(ok(z0)) → c33(S(z0))
381.42/118.25
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.42/118.25
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.42/118.25
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.42/118.25
DBL(mark(z0)) → c37(DBL(z0))
381.42/118.25
DBL(ok(z0)) → c38(DBL(z0))
381.42/118.25
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.42/118.25
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.42/118.25
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.42/118.25
HALF(mark(z0)) → c42(HALF(z0))
381.42/118.25
HALF(ok(z0)) → c43(HALF(z0))
381.42/118.25
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.25
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.25
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.42/118.25
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.25
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.42/118.25
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.42/118.25
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.42/118.25
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.42/118.25
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.42/118.25
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.42/118.25
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.42/118.25
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.42/118.25
ACTIVE(terms(z0)) → c1(SQR(z0))
381.42/118.25
ACTIVE(terms(z0)) → c1(S(z0))
381.42/118.25
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.42/118.25
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.42/118.25
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
381.42/118.25
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.42/118.25
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.25
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.42/118.25
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.42/118.25
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(s(half(0))) → c17(S(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.25
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.25
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.42/118.25
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.42/118.25
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.25
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.25
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.25
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.25
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.25
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.25
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)), ACTIVE(half(0)))
381.42/118.25
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.42/118.25
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.25
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.25
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.25
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.25
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.25
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.25
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.42/118.25
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.25
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.42/118.26
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.26
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.42/118.26
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.42/118.26
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.42/118.26
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.42/118.26
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.42/118.26
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.42/118.26
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.42/118.26
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.42/118.26
ACTIVE(half(z0)) → c23(HALF(active(z0)), ACTIVE(z0))
381.42/118.26
TERMS(mark(z0)) → c24(TERMS(z0))
381.42/118.26
TERMS(ok(z0)) → c25(TERMS(z0))
381.42/118.26
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.42/118.26
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.42/118.26
RECIP(mark(z0)) → c28(RECIP(z0))
381.42/118.26
RECIP(ok(z0)) → c29(RECIP(z0))
381.42/118.26
SQR(mark(z0)) → c30(SQR(z0))
381.42/118.26
SQR(ok(z0)) → c31(SQR(z0))
381.42/118.26
S(mark(z0)) → c32(S(z0))
381.42/118.26
S(ok(z0)) → c33(S(z0))
381.42/118.26
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.42/118.26
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.42/118.26
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.42/118.26
DBL(mark(z0)) → c37(DBL(z0))
381.42/118.26
DBL(ok(z0)) → c38(DBL(z0))
381.42/118.26
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.42/118.26
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.42/118.26
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.42/118.26
HALF(mark(z0)) → c42(HALF(z0))
381.42/118.26
HALF(ok(z0)) → c43(HALF(z0))
381.42/118.26
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.26
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.26
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.26
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.42/118.26
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.42/118.26
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.42/118.26
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.42/118.26
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.42/118.26
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.42/118.26
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.42/118.26
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.42/118.26
ACTIVE(terms(z0)) → c1(SQR(z0))
381.42/118.26
ACTIVE(terms(z0)) → c1(S(z0))
381.42/118.26
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.42/118.26
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.42/118.26
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
381.42/118.26
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.42/118.26
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.26
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.42/118.26
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.42/118.26
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(s(half(0))) → c17(S(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.42/118.26
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.42/118.26
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.26
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.42/118.26
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.42/118.26
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.42/118.26
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.42/118.26
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20
381.42/118.26
381.42/118.26
(25) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
half(
z0)) →
c23(
HALF(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)), ACTIVE(sqr(0)))
381.42/118.26
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)), ACTIVE(dbl(0)))
381.42/118.26
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(half(half(0))) → c23(HALF(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
381.42/118.26
(26) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.42/118.26
active(sqr(0)) → mark(0)
381.42/118.26
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.42/118.26
active(dbl(0)) → mark(0)
381.42/118.26
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.42/118.26
active(add(0, z0)) → mark(z0)
381.42/118.26
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.42/118.26
active(first(0, z0)) → mark(nil)
381.42/118.26
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.42/118.26
active(half(0)) → mark(0)
381.42/118.26
active(half(s(0))) → mark(0)
381.42/118.26
active(half(s(s(z0)))) → mark(s(half(z0)))
381.42/118.26
active(half(dbl(z0))) → mark(z0)
381.42/118.26
active(terms(z0)) → terms(active(z0))
381.42/118.26
active(cons(z0, z1)) → cons(active(z0), z1)
381.42/118.26
active(recip(z0)) → recip(active(z0))
381.42/118.26
active(sqr(z0)) → sqr(active(z0))
381.42/118.26
active(s(z0)) → s(active(z0))
381.42/118.26
active(add(z0, z1)) → add(active(z0), z1)
381.42/118.26
active(add(z0, z1)) → add(z0, active(z1))
381.42/118.26
active(dbl(z0)) → dbl(active(z0))
381.42/118.26
active(first(z0, z1)) → first(active(z0), z1)
381.42/118.26
active(first(z0, z1)) → first(z0, active(z1))
381.42/118.26
active(half(z0)) → half(active(z0))
381.42/118.26
terms(mark(z0)) → mark(terms(z0))
381.42/118.26
terms(ok(z0)) → ok(terms(z0))
381.42/118.26
cons(mark(z0), z1) → mark(cons(z0, z1))
381.42/118.26
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.42/118.26
recip(mark(z0)) → mark(recip(z0))
381.42/118.26
recip(ok(z0)) → ok(recip(z0))
381.42/118.26
sqr(mark(z0)) → mark(sqr(z0))
381.42/118.26
sqr(ok(z0)) → ok(sqr(z0))
381.42/118.26
s(mark(z0)) → mark(s(z0))
381.42/118.26
s(ok(z0)) → ok(s(z0))
381.42/118.26
add(mark(z0), z1) → mark(add(z0, z1))
381.42/118.26
add(z0, mark(z1)) → mark(add(z0, z1))
381.42/118.26
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.42/118.26
dbl(mark(z0)) → mark(dbl(z0))
381.42/118.26
dbl(ok(z0)) → ok(dbl(z0))
381.42/118.26
first(mark(z0), z1) → mark(first(z0, z1))
381.42/118.26
first(z0, mark(z1)) → mark(first(z0, z1))
381.42/118.26
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.42/118.26
half(mark(z0)) → mark(half(z0))
381.42/118.26
half(ok(z0)) → ok(half(z0))
381.42/118.26
proper(terms(z0)) → terms(proper(z0))
381.42/118.26
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.42/118.26
proper(recip(z0)) → recip(proper(z0))
381.42/118.26
proper(sqr(z0)) → sqr(proper(z0))
381.42/118.26
proper(s(z0)) → s(proper(z0))
381.42/118.26
proper(0) → ok(0)
381.42/118.26
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.42/118.26
proper(dbl(z0)) → dbl(proper(z0))
381.42/118.26
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.42/118.26
proper(nil) → ok(nil)
381.42/118.26
proper(half(z0)) → half(proper(z0))
381.42/118.26
top(mark(z0)) → top(proper(z0))
381.42/118.26
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.42/118.26
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.42/118.26
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.42/118.26
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.42/118.26
TERMS(mark(z0)) → c24(TERMS(z0))
381.42/118.26
TERMS(ok(z0)) → c25(TERMS(z0))
381.42/118.26
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.42/118.26
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.42/118.26
RECIP(mark(z0)) → c28(RECIP(z0))
381.42/118.26
RECIP(ok(z0)) → c29(RECIP(z0))
381.42/118.26
SQR(mark(z0)) → c30(SQR(z0))
381.42/118.26
SQR(ok(z0)) → c31(SQR(z0))
381.42/118.26
S(mark(z0)) → c32(S(z0))
381.42/118.26
S(ok(z0)) → c33(S(z0))
381.42/118.26
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.42/118.26
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.42/118.26
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.42/118.26
DBL(mark(z0)) → c37(DBL(z0))
381.42/118.26
DBL(ok(z0)) → c38(DBL(z0))
381.42/118.26
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.42/118.26
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.42/118.26
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.42/118.26
HALF(mark(z0)) → c42(HALF(z0))
381.42/118.26
HALF(ok(z0)) → c43(HALF(z0))
381.42/118.26
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.26
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.26
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.26
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.42/118.26
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.42/118.26
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.42/118.26
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.42/118.26
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.42/118.26
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.42/118.26
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.42/118.26
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.42/118.26
ACTIVE(terms(z0)) → c1(SQR(z0))
381.42/118.26
ACTIVE(terms(z0)) → c1(S(z0))
381.42/118.26
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.42/118.26
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.42/118.26
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
381.42/118.26
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.42/118.26
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.26
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.42/118.26
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.42/118.26
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(s(half(0))) → c17(S(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.42/118.26
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.42/118.26
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.26
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.42/118.26
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.42/118.26
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.42/118.26
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.42/118.26
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.42/118.26
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)), ACTIVE(sqr(0)))
381.42/118.26
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)), ACTIVE(dbl(0)))
381.42/118.26
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(half(half(0))) → c23(HALF(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.42/118.26
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.42/118.26
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.42/118.26
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.42/118.26
TERMS(mark(z0)) → c24(TERMS(z0))
381.42/118.26
TERMS(ok(z0)) → c25(TERMS(z0))
381.42/118.26
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.42/118.26
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.42/118.26
RECIP(mark(z0)) → c28(RECIP(z0))
381.42/118.26
RECIP(ok(z0)) → c29(RECIP(z0))
381.42/118.26
SQR(mark(z0)) → c30(SQR(z0))
381.42/118.26
SQR(ok(z0)) → c31(SQR(z0))
381.42/118.26
S(mark(z0)) → c32(S(z0))
381.42/118.26
S(ok(z0)) → c33(S(z0))
381.42/118.26
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.42/118.26
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.42/118.26
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.42/118.26
DBL(mark(z0)) → c37(DBL(z0))
381.42/118.26
DBL(ok(z0)) → c38(DBL(z0))
381.42/118.26
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.42/118.26
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.42/118.26
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.42/118.26
HALF(mark(z0)) → c42(HALF(z0))
381.42/118.26
HALF(ok(z0)) → c43(HALF(z0))
381.42/118.26
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.26
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.26
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.26
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.42/118.26
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.42/118.26
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.42/118.26
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.42/118.26
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.42/118.26
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.42/118.26
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.42/118.26
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.42/118.26
ACTIVE(terms(z0)) → c1(SQR(z0))
381.42/118.26
ACTIVE(terms(z0)) → c1(S(z0))
381.42/118.26
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.42/118.26
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.42/118.26
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(0)))
381.42/118.26
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.42/118.26
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.26
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.42/118.26
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.42/118.26
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(s(half(0))) → c17(S(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.42/118.26
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.42/118.26
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.26
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.42/118.26
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.42/118.26
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.42/118.26
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.42/118.26
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.42/118.26
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)), ACTIVE(sqr(0)))
381.42/118.26
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)), ACTIVE(dbl(0)))
381.42/118.26
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(half(half(0))) → c23(HALF(mark(0)), ACTIVE(half(0)))
381.42/118.26
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, 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, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23
381.42/118.26
381.42/118.26
(27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 9 trailing tuple parts
381.42/118.26
381.42/118.26
(28) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.42/118.26
active(sqr(0)) → mark(0)
381.42/118.26
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.42/118.26
active(dbl(0)) → mark(0)
381.42/118.26
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.42/118.26
active(add(0, z0)) → mark(z0)
381.42/118.26
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.42/118.26
active(first(0, z0)) → mark(nil)
381.42/118.26
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.42/118.26
active(half(0)) → mark(0)
381.42/118.26
active(half(s(0))) → mark(0)
381.42/118.26
active(half(s(s(z0)))) → mark(s(half(z0)))
381.42/118.26
active(half(dbl(z0))) → mark(z0)
381.42/118.26
active(terms(z0)) → terms(active(z0))
381.42/118.26
active(cons(z0, z1)) → cons(active(z0), z1)
381.42/118.26
active(recip(z0)) → recip(active(z0))
381.42/118.26
active(sqr(z0)) → sqr(active(z0))
381.42/118.26
active(s(z0)) → s(active(z0))
381.42/118.26
active(add(z0, z1)) → add(active(z0), z1)
381.42/118.26
active(add(z0, z1)) → add(z0, active(z1))
381.42/118.26
active(dbl(z0)) → dbl(active(z0))
381.42/118.26
active(first(z0, z1)) → first(active(z0), z1)
381.42/118.26
active(first(z0, z1)) → first(z0, active(z1))
381.42/118.26
active(half(z0)) → half(active(z0))
381.42/118.26
terms(mark(z0)) → mark(terms(z0))
381.42/118.26
terms(ok(z0)) → ok(terms(z0))
381.42/118.26
cons(mark(z0), z1) → mark(cons(z0, z1))
381.42/118.26
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.42/118.26
recip(mark(z0)) → mark(recip(z0))
381.42/118.26
recip(ok(z0)) → ok(recip(z0))
381.42/118.26
sqr(mark(z0)) → mark(sqr(z0))
381.42/118.26
sqr(ok(z0)) → ok(sqr(z0))
381.42/118.26
s(mark(z0)) → mark(s(z0))
381.42/118.26
s(ok(z0)) → ok(s(z0))
381.42/118.26
add(mark(z0), z1) → mark(add(z0, z1))
381.42/118.26
add(z0, mark(z1)) → mark(add(z0, z1))
381.42/118.26
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.42/118.26
dbl(mark(z0)) → mark(dbl(z0))
381.42/118.26
dbl(ok(z0)) → ok(dbl(z0))
381.42/118.26
first(mark(z0), z1) → mark(first(z0, z1))
381.42/118.26
first(z0, mark(z1)) → mark(first(z0, z1))
381.42/118.26
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.42/118.26
half(mark(z0)) → mark(half(z0))
381.42/118.26
half(ok(z0)) → ok(half(z0))
381.42/118.26
proper(terms(z0)) → terms(proper(z0))
381.42/118.26
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.42/118.26
proper(recip(z0)) → recip(proper(z0))
381.42/118.26
proper(sqr(z0)) → sqr(proper(z0))
381.42/118.26
proper(s(z0)) → s(proper(z0))
381.42/118.26
proper(0) → ok(0)
381.42/118.26
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.42/118.26
proper(dbl(z0)) → dbl(proper(z0))
381.42/118.26
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.42/118.26
proper(nil) → ok(nil)
381.42/118.26
proper(half(z0)) → half(proper(z0))
381.42/118.26
top(mark(z0)) → top(proper(z0))
381.42/118.26
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.42/118.26
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.42/118.26
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.42/118.26
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.42/118.26
TERMS(mark(z0)) → c24(TERMS(z0))
381.42/118.26
TERMS(ok(z0)) → c25(TERMS(z0))
381.42/118.26
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.42/118.26
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.42/118.26
RECIP(mark(z0)) → c28(RECIP(z0))
381.42/118.26
RECIP(ok(z0)) → c29(RECIP(z0))
381.42/118.26
SQR(mark(z0)) → c30(SQR(z0))
381.42/118.26
SQR(ok(z0)) → c31(SQR(z0))
381.42/118.26
S(mark(z0)) → c32(S(z0))
381.42/118.26
S(ok(z0)) → c33(S(z0))
381.42/118.26
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.42/118.26
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.42/118.26
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.42/118.26
DBL(mark(z0)) → c37(DBL(z0))
381.42/118.26
DBL(ok(z0)) → c38(DBL(z0))
381.42/118.26
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.42/118.26
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.42/118.26
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.42/118.26
HALF(mark(z0)) → c42(HALF(z0))
381.42/118.26
HALF(ok(z0)) → c43(HALF(z0))
381.42/118.26
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.26
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.26
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.26
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.42/118.26
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.42/118.26
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.42/118.26
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.42/118.26
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.42/118.26
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.42/118.26
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.42/118.26
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.42/118.26
ACTIVE(terms(z0)) → c1(SQR(z0))
381.42/118.26
ACTIVE(terms(z0)) → c1(S(z0))
381.42/118.26
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.42/118.26
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.42/118.26
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.42/118.26
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.26
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.42/118.26
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.42/118.26
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.42/118.26
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.42/118.26
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.26
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.42/118.26
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.42/118.26
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.42/118.26
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.42/118.26
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.42/118.26
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.42/118.26
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.26
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.42/118.26
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.42/118.26
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.42/118.26
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.42/118.26
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.42/118.26
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.42/118.26
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.42/118.26
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.42/118.26
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.42/118.26
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.42/118.26
TERMS(mark(z0)) → c24(TERMS(z0))
381.42/118.26
TERMS(ok(z0)) → c25(TERMS(z0))
381.42/118.26
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.42/118.26
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.42/118.26
RECIP(mark(z0)) → c28(RECIP(z0))
381.42/118.26
RECIP(ok(z0)) → c29(RECIP(z0))
381.42/118.26
SQR(mark(z0)) → c30(SQR(z0))
381.42/118.26
SQR(ok(z0)) → c31(SQR(z0))
381.42/118.26
S(mark(z0)) → c32(S(z0))
381.42/118.26
S(ok(z0)) → c33(S(z0))
381.42/118.26
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.42/118.26
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.42/118.26
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.42/118.26
DBL(mark(z0)) → c37(DBL(z0))
381.42/118.26
DBL(ok(z0)) → c38(DBL(z0))
381.42/118.26
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.42/118.26
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.42/118.26
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.42/118.26
HALF(mark(z0)) → c42(HALF(z0))
381.42/118.26
HALF(ok(z0)) → c43(HALF(z0))
381.42/118.26
PROPER(terms(z0)) → c44(TERMS(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.26
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.26
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.42/118.26
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.42/118.26
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.42/118.26
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.42/118.26
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.42/118.26
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.42/118.26
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.42/118.26
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.42/118.26
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.42/118.26
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.42/118.26
ACTIVE(terms(z0)) → c1(SQR(z0))
381.42/118.26
ACTIVE(terms(z0)) → c1(S(z0))
381.42/118.26
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.42/118.26
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.42/118.26
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.42/118.26
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.26
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.42/118.26
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.42/118.26
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.42/118.26
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.42/118.26
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.42/118.26
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.42/118.26
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.42/118.26
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.42/118.26
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.42/118.26
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.42/118.26
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.42/118.26
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.42/118.26
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.42/118.26
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.42/118.26
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.42/118.26
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.42/118.26
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.42/118.26
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.42/118.26
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.42/118.26
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.42/118.26
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.42/118.26
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.42/118.26
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.42/118.26
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.42/118.26
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.42/118.26
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.42/118.26
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.42/118.26
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.42/118.26
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.34
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.34
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.34
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.34
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.34
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.34
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.34
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.34
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, 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, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23
381.77/118.34
381.77/118.34
(29) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
terms(
z0)) →
c44(
TERMS(
proper(
z0)),
PROPER(
z0)) by
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.34
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.34
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.34
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.34
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.34
PROPER(terms(0)) → c44(TERMS(ok(0)), PROPER(0))
381.77/118.34
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.34
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.34
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.34
PROPER(terms(nil)) → c44(TERMS(ok(nil)), PROPER(nil))
381.77/118.34
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.34
381.77/118.34
(30) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.77/118.34
active(sqr(0)) → mark(0)
381.77/118.34
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.77/118.34
active(dbl(0)) → mark(0)
381.77/118.34
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.77/118.34
active(add(0, z0)) → mark(z0)
381.77/118.34
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.77/118.34
active(first(0, z0)) → mark(nil)
381.77/118.34
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.77/118.34
active(half(0)) → mark(0)
381.77/118.34
active(half(s(0))) → mark(0)
381.77/118.34
active(half(s(s(z0)))) → mark(s(half(z0)))
381.77/118.34
active(half(dbl(z0))) → mark(z0)
381.77/118.34
active(terms(z0)) → terms(active(z0))
381.77/118.34
active(cons(z0, z1)) → cons(active(z0), z1)
381.77/118.34
active(recip(z0)) → recip(active(z0))
381.77/118.34
active(sqr(z0)) → sqr(active(z0))
381.77/118.34
active(s(z0)) → s(active(z0))
381.77/118.34
active(add(z0, z1)) → add(active(z0), z1)
381.77/118.34
active(add(z0, z1)) → add(z0, active(z1))
381.77/118.34
active(dbl(z0)) → dbl(active(z0))
381.77/118.34
active(first(z0, z1)) → first(active(z0), z1)
381.77/118.34
active(first(z0, z1)) → first(z0, active(z1))
381.77/118.34
active(half(z0)) → half(active(z0))
381.77/118.34
terms(mark(z0)) → mark(terms(z0))
381.77/118.34
terms(ok(z0)) → ok(terms(z0))
381.77/118.34
cons(mark(z0), z1) → mark(cons(z0, z1))
381.77/118.34
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.77/118.34
recip(mark(z0)) → mark(recip(z0))
381.77/118.34
recip(ok(z0)) → ok(recip(z0))
381.77/118.34
sqr(mark(z0)) → mark(sqr(z0))
381.77/118.34
sqr(ok(z0)) → ok(sqr(z0))
381.77/118.34
s(mark(z0)) → mark(s(z0))
381.77/118.34
s(ok(z0)) → ok(s(z0))
381.77/118.34
add(mark(z0), z1) → mark(add(z0, z1))
381.77/118.34
add(z0, mark(z1)) → mark(add(z0, z1))
381.77/118.34
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.77/118.34
dbl(mark(z0)) → mark(dbl(z0))
381.77/118.34
dbl(ok(z0)) → ok(dbl(z0))
381.77/118.34
first(mark(z0), z1) → mark(first(z0, z1))
381.77/118.34
first(z0, mark(z1)) → mark(first(z0, z1))
381.77/118.34
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.77/118.34
half(mark(z0)) → mark(half(z0))
381.77/118.34
half(ok(z0)) → ok(half(z0))
381.77/118.34
proper(terms(z0)) → terms(proper(z0))
381.77/118.34
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.77/118.34
proper(recip(z0)) → recip(proper(z0))
381.77/118.34
proper(sqr(z0)) → sqr(proper(z0))
381.77/118.34
proper(s(z0)) → s(proper(z0))
381.77/118.34
proper(0) → ok(0)
381.77/118.34
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.77/118.34
proper(dbl(z0)) → dbl(proper(z0))
381.77/118.34
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.77/118.34
proper(nil) → ok(nil)
381.77/118.34
proper(half(z0)) → half(proper(z0))
381.77/118.34
top(mark(z0)) → top(proper(z0))
381.77/118.34
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.34
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.34
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.34
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.34
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.34
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.34
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.34
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.34
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.34
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.34
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.34
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.34
S(mark(z0)) → c32(S(z0))
381.77/118.34
S(ok(z0)) → c33(S(z0))
381.77/118.34
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.34
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.34
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.34
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.34
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.34
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.34
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.34
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.34
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.34
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.34
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.34
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.34
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.34
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.34
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.34
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.34
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.34
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.34
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.34
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.34
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.34
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.34
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.34
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.34
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.34
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.34
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.34
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.34
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.34
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.34
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.34
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.34
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.34
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.34
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.34
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.34
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.34
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.34
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.34
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.34
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.34
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.34
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.34
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.34
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.34
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.34
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.34
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.34
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.34
PROPER(terms(0)) → c44(TERMS(ok(0)), PROPER(0))
381.77/118.34
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.34
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.34
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.34
PROPER(terms(nil)) → c44(TERMS(ok(nil)), PROPER(nil))
381.77/118.34
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.34
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.34
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.34
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.34
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.34
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.34
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.34
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.34
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.34
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.34
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.34
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.34
S(mark(z0)) → c32(S(z0))
381.77/118.34
S(ok(z0)) → c33(S(z0))
381.77/118.34
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.34
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.34
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.34
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.34
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.34
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.34
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.34
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.34
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.34
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.34
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.34
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.34
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.34
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.34
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.34
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.34
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.34
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.34
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.34
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.34
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.34
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.34
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.34
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.34
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.34
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.34
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.34
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.34
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.34
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.34
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.34
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.34
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.34
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.34
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.34
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.34
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.34
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.34
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.34
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.34
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.34
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.34
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.34
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.34
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.34
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.34
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.34
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.34
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.34
PROPER(terms(0)) → c44(TERMS(ok(0)), PROPER(0))
381.77/118.34
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.34
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.34
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.34
PROPER(terms(nil)) → c44(TERMS(ok(nil)), PROPER(nil))
381.77/118.34
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c45, c46, c47, c48, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44
381.77/118.34
381.77/118.34
(31) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
381.77/118.34
381.77/118.34
(32) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.77/118.34
active(sqr(0)) → mark(0)
381.77/118.34
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.77/118.34
active(dbl(0)) → mark(0)
381.77/118.34
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.77/118.34
active(add(0, z0)) → mark(z0)
381.77/118.34
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.77/118.34
active(first(0, z0)) → mark(nil)
381.77/118.34
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.77/118.34
active(half(0)) → mark(0)
381.77/118.34
active(half(s(0))) → mark(0)
381.77/118.34
active(half(s(s(z0)))) → mark(s(half(z0)))
381.77/118.34
active(half(dbl(z0))) → mark(z0)
381.77/118.34
active(terms(z0)) → terms(active(z0))
381.77/118.34
active(cons(z0, z1)) → cons(active(z0), z1)
381.77/118.34
active(recip(z0)) → recip(active(z0))
381.77/118.34
active(sqr(z0)) → sqr(active(z0))
381.77/118.34
active(s(z0)) → s(active(z0))
381.77/118.34
active(add(z0, z1)) → add(active(z0), z1)
381.77/118.34
active(add(z0, z1)) → add(z0, active(z1))
381.77/118.34
active(dbl(z0)) → dbl(active(z0))
381.77/118.34
active(first(z0, z1)) → first(active(z0), z1)
381.77/118.34
active(first(z0, z1)) → first(z0, active(z1))
381.77/118.34
active(half(z0)) → half(active(z0))
381.77/118.34
terms(mark(z0)) → mark(terms(z0))
381.77/118.34
terms(ok(z0)) → ok(terms(z0))
381.77/118.34
cons(mark(z0), z1) → mark(cons(z0, z1))
381.77/118.34
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.77/118.34
recip(mark(z0)) → mark(recip(z0))
381.77/118.34
recip(ok(z0)) → ok(recip(z0))
381.77/118.34
sqr(mark(z0)) → mark(sqr(z0))
381.77/118.34
sqr(ok(z0)) → ok(sqr(z0))
381.77/118.34
s(mark(z0)) → mark(s(z0))
381.77/118.34
s(ok(z0)) → ok(s(z0))
381.77/118.34
add(mark(z0), z1) → mark(add(z0, z1))
381.77/118.34
add(z0, mark(z1)) → mark(add(z0, z1))
381.77/118.34
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.77/118.34
dbl(mark(z0)) → mark(dbl(z0))
381.77/118.34
dbl(ok(z0)) → ok(dbl(z0))
381.77/118.34
first(mark(z0), z1) → mark(first(z0, z1))
381.77/118.34
first(z0, mark(z1)) → mark(first(z0, z1))
381.77/118.34
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.77/118.34
half(mark(z0)) → mark(half(z0))
381.77/118.34
half(ok(z0)) → ok(half(z0))
381.77/118.34
proper(terms(z0)) → terms(proper(z0))
381.77/118.34
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.77/118.34
proper(recip(z0)) → recip(proper(z0))
381.77/118.34
proper(sqr(z0)) → sqr(proper(z0))
381.77/118.34
proper(s(z0)) → s(proper(z0))
381.77/118.34
proper(0) → ok(0)
381.77/118.34
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.77/118.34
proper(dbl(z0)) → dbl(proper(z0))
381.77/118.34
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.77/118.34
proper(nil) → ok(nil)
381.77/118.34
proper(half(z0)) → half(proper(z0))
381.77/118.34
top(mark(z0)) → top(proper(z0))
381.77/118.34
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.34
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.34
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.34
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.34
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.34
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.34
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.34
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.34
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.34
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.34
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.34
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.34
S(mark(z0)) → c32(S(z0))
381.77/118.34
S(ok(z0)) → c33(S(z0))
381.77/118.34
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.34
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.34
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.34
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.34
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.34
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.34
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.34
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.34
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.34
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.34
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.34
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.34
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.34
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.34
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.34
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.34
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.34
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.34
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.34
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.34
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.34
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.34
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.34
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.34
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.34
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.34
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.34
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.34
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.34
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.34
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.34
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.34
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.34
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.34
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.34
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.34
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.34
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.34
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.34
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.34
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.34
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.34
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.34
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.34
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.34
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.34
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.34
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.34
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.34
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.34
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.34
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.34
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.34
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.34
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.34
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.34
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.34
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.34
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.34
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.34
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.34
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.34
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.34
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.34
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.34
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.34
S(mark(z0)) → c32(S(z0))
381.77/118.34
S(ok(z0)) → c33(S(z0))
381.77/118.34
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.34
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.34
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.34
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.34
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.34
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.34
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.34
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.34
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.34
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.34
PROPER(cons(z0, z1)) → c45(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.34
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.34
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.34
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.34
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.34
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.34
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.34
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.34
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.34
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.34
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.34
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.34
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.34
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.34
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.34
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.34
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.34
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.34
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.34
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.34
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.34
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.34
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.34
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.34
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.34
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.34
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.34
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.34
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.34
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.34
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.34
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.34
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.35
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.35
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.35
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.35
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.35
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.35
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.35
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.35
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.35
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.35
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.35
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.35
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.35
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.35
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.35
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.35
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.35
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.35
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.35
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.35
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.35
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.35
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.35
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.35
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.35
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.35
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.35
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.35
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.35
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.35
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.35
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c45, c46, c47, c48, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44
381.77/118.35
381.77/118.35
(33) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
cons(
z0,
z1)) →
c45(
CONS(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.35
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.35
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.35
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.35
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.35
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
381.77/118.35
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.35
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.35
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.35
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
381.77/118.35
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.35
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.35
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
381.77/118.35
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.35
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.35
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
381.77/118.35
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.35
381.77/118.35
(34) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.77/118.35
active(sqr(0)) → mark(0)
381.77/118.35
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.77/118.35
active(dbl(0)) → mark(0)
381.77/118.35
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.77/118.35
active(add(0, z0)) → mark(z0)
381.77/118.35
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.77/118.35
active(first(0, z0)) → mark(nil)
381.77/118.35
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.77/118.35
active(half(0)) → mark(0)
381.77/118.35
active(half(s(0))) → mark(0)
381.77/118.35
active(half(s(s(z0)))) → mark(s(half(z0)))
381.77/118.35
active(half(dbl(z0))) → mark(z0)
381.77/118.35
active(terms(z0)) → terms(active(z0))
381.77/118.35
active(cons(z0, z1)) → cons(active(z0), z1)
381.77/118.35
active(recip(z0)) → recip(active(z0))
381.77/118.35
active(sqr(z0)) → sqr(active(z0))
381.77/118.35
active(s(z0)) → s(active(z0))
381.77/118.35
active(add(z0, z1)) → add(active(z0), z1)
381.77/118.35
active(add(z0, z1)) → add(z0, active(z1))
381.77/118.35
active(dbl(z0)) → dbl(active(z0))
381.77/118.35
active(first(z0, z1)) → first(active(z0), z1)
381.77/118.35
active(first(z0, z1)) → first(z0, active(z1))
381.77/118.35
active(half(z0)) → half(active(z0))
381.77/118.35
terms(mark(z0)) → mark(terms(z0))
381.77/118.35
terms(ok(z0)) → ok(terms(z0))
381.77/118.35
cons(mark(z0), z1) → mark(cons(z0, z1))
381.77/118.35
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.77/118.35
recip(mark(z0)) → mark(recip(z0))
381.77/118.35
recip(ok(z0)) → ok(recip(z0))
381.77/118.35
sqr(mark(z0)) → mark(sqr(z0))
381.77/118.35
sqr(ok(z0)) → ok(sqr(z0))
381.77/118.35
s(mark(z0)) → mark(s(z0))
381.77/118.35
s(ok(z0)) → ok(s(z0))
381.77/118.35
add(mark(z0), z1) → mark(add(z0, z1))
381.77/118.35
add(z0, mark(z1)) → mark(add(z0, z1))
381.77/118.35
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.77/118.35
dbl(mark(z0)) → mark(dbl(z0))
381.77/118.35
dbl(ok(z0)) → ok(dbl(z0))
381.77/118.35
first(mark(z0), z1) → mark(first(z0, z1))
381.77/118.35
first(z0, mark(z1)) → mark(first(z0, z1))
381.77/118.35
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.77/118.35
half(mark(z0)) → mark(half(z0))
381.77/118.35
half(ok(z0)) → ok(half(z0))
381.77/118.35
proper(terms(z0)) → terms(proper(z0))
381.77/118.35
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.77/118.35
proper(recip(z0)) → recip(proper(z0))
381.77/118.35
proper(sqr(z0)) → sqr(proper(z0))
381.77/118.35
proper(s(z0)) → s(proper(z0))
381.77/118.35
proper(0) → ok(0)
381.77/118.35
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.77/118.35
proper(dbl(z0)) → dbl(proper(z0))
381.77/118.35
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.77/118.35
proper(nil) → ok(nil)
381.77/118.35
proper(half(z0)) → half(proper(z0))
381.77/118.35
top(mark(z0)) → top(proper(z0))
381.77/118.35
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.35
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.35
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.35
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.35
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.35
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.35
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.35
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.35
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.35
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.35
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.35
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.35
S(mark(z0)) → c32(S(z0))
381.77/118.35
S(ok(z0)) → c33(S(z0))
381.77/118.35
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.35
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.35
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.35
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.35
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.35
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.35
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.35
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.35
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.35
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.35
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.35
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.35
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.35
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.35
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.35
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.35
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.35
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.35
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.35
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.35
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.35
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.35
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.35
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.35
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.35
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.35
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.35
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.35
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.35
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.35
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.35
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.35
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.35
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.35
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.35
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.35
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.35
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.35
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.35
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.35
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.35
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.35
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.35
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.35
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.35
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.35
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.35
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.35
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.35
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.35
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.35
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.35
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.35
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.35
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.35
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.35
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.35
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.35
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.35
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
381.77/118.35
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.35
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.35
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.35
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
381.77/118.35
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.35
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.35
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
381.77/118.35
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.35
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.35
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
381.77/118.35
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.35
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.35
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.35
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.35
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.35
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.35
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.35
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.35
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.35
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.35
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.35
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.35
S(mark(z0)) → c32(S(z0))
381.77/118.35
S(ok(z0)) → c33(S(z0))
381.77/118.35
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.35
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.35
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.35
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.35
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.35
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.35
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.35
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.35
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.35
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.35
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.35
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.35
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.35
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.35
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.35
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.35
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.35
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.35
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.35
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.35
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.35
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.35
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.35
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.35
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.35
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.35
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.35
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.35
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.35
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.35
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.35
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.35
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.35
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.35
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.35
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.35
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.35
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.35
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.35
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.35
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.35
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.35
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.35
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.35
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.35
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.35
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.35
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.35
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.35
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.35
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.35
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.35
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.35
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.35
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.35
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.35
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.35
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.35
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.35
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
381.77/118.35
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.35
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.35
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.35
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
381.77/118.35
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.35
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.35
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
381.77/118.35
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.35
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.35
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
381.77/118.35
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c46, c47, c48, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45
381.77/118.35
381.77/118.35
(35) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
381.77/118.35
381.77/118.35
(36) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.77/118.35
active(sqr(0)) → mark(0)
381.77/118.35
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.77/118.35
active(dbl(0)) → mark(0)
381.77/118.35
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.77/118.35
active(add(0, z0)) → mark(z0)
381.77/118.35
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.77/118.35
active(first(0, z0)) → mark(nil)
381.77/118.35
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.77/118.35
active(half(0)) → mark(0)
381.77/118.35
active(half(s(0))) → mark(0)
381.77/118.35
active(half(s(s(z0)))) → mark(s(half(z0)))
381.77/118.35
active(half(dbl(z0))) → mark(z0)
381.77/118.35
active(terms(z0)) → terms(active(z0))
381.77/118.35
active(cons(z0, z1)) → cons(active(z0), z1)
381.77/118.35
active(recip(z0)) → recip(active(z0))
381.77/118.35
active(sqr(z0)) → sqr(active(z0))
381.77/118.35
active(s(z0)) → s(active(z0))
381.77/118.35
active(add(z0, z1)) → add(active(z0), z1)
381.77/118.35
active(add(z0, z1)) → add(z0, active(z1))
381.77/118.35
active(dbl(z0)) → dbl(active(z0))
381.77/118.35
active(first(z0, z1)) → first(active(z0), z1)
381.77/118.35
active(first(z0, z1)) → first(z0, active(z1))
381.77/118.35
active(half(z0)) → half(active(z0))
381.77/118.35
terms(mark(z0)) → mark(terms(z0))
381.77/118.35
terms(ok(z0)) → ok(terms(z0))
381.77/118.35
cons(mark(z0), z1) → mark(cons(z0, z1))
381.77/118.35
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.77/118.35
recip(mark(z0)) → mark(recip(z0))
381.77/118.35
recip(ok(z0)) → ok(recip(z0))
381.77/118.35
sqr(mark(z0)) → mark(sqr(z0))
381.77/118.35
sqr(ok(z0)) → ok(sqr(z0))
381.77/118.35
s(mark(z0)) → mark(s(z0))
381.77/118.35
s(ok(z0)) → ok(s(z0))
381.77/118.35
add(mark(z0), z1) → mark(add(z0, z1))
381.77/118.35
add(z0, mark(z1)) → mark(add(z0, z1))
381.77/118.35
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.77/118.35
dbl(mark(z0)) → mark(dbl(z0))
381.77/118.35
dbl(ok(z0)) → ok(dbl(z0))
381.77/118.35
first(mark(z0), z1) → mark(first(z0, z1))
381.77/118.35
first(z0, mark(z1)) → mark(first(z0, z1))
381.77/118.35
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.77/118.35
half(mark(z0)) → mark(half(z0))
381.77/118.35
half(ok(z0)) → ok(half(z0))
381.77/118.35
proper(terms(z0)) → terms(proper(z0))
381.77/118.35
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.77/118.35
proper(recip(z0)) → recip(proper(z0))
381.77/118.35
proper(sqr(z0)) → sqr(proper(z0))
381.77/118.35
proper(s(z0)) → s(proper(z0))
381.77/118.35
proper(0) → ok(0)
381.77/118.35
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.77/118.35
proper(dbl(z0)) → dbl(proper(z0))
381.77/118.35
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.77/118.35
proper(nil) → ok(nil)
381.77/118.35
proper(half(z0)) → half(proper(z0))
381.77/118.35
top(mark(z0)) → top(proper(z0))
381.77/118.35
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.35
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.35
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.35
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.35
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.35
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.35
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.35
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.35
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.35
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.35
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.35
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.35
S(mark(z0)) → c32(S(z0))
381.77/118.35
S(ok(z0)) → c33(S(z0))
381.77/118.35
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.35
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.35
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.35
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.35
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.35
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.35
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.35
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.35
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.35
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.35
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.35
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.35
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.35
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.35
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.35
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.35
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.35
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.35
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.35
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.35
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.35
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.35
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.35
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.35
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.35
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.35
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.35
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.35
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.35
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.35
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.35
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.35
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.35
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.35
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.35
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.35
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.35
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.35
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.35
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.35
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.35
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.35
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.35
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.35
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.35
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.35
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.35
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.35
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.35
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.35
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.35
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.35
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.35
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.35
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.35
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.35
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.35
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.35
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.35
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.35
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.35
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.35
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.35
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.35
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.35
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.35
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.35
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.35
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.35
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.35
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.35
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.35
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.35
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.35
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.35
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.35
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.35
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.35
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.35
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.35
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.35
S(mark(z0)) → c32(S(z0))
381.77/118.35
S(ok(z0)) → c33(S(z0))
381.77/118.35
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.35
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.35
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.35
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.35
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.35
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.35
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.35
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.35
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.35
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.35
PROPER(recip(z0)) → c46(RECIP(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.35
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.35
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.35
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.35
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.35
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.35
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.35
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.35
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.35
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.35
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.35
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.35
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.35
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.35
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.35
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.35
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.35
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.35
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.35
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.35
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.35
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.35
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.35
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.35
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.35
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.35
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.35
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.35
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.35
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.35
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.35
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.35
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.35
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.35
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.35
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.35
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.35
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.35
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.35
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.35
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.35
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.35
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.35
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.35
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.35
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.35
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.35
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.35
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.35
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.35
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.35
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.35
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.35
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.35
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.35
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.35
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.35
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.35
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.35
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.35
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.35
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.35
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.35
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.35
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.35
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.35
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.35
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.35
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.35
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.35
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.35
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.35
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.35
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.35
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.35
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.35
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.35
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.35
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.35
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c46, c47, c48, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45
381.77/118.35
381.77/118.35
(37) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
recip(
z0)) →
c46(
RECIP(
proper(
z0)),
PROPER(
z0)) by
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.35
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.35
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.35
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.35
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.35
PROPER(recip(0)) → c46(RECIP(ok(0)), PROPER(0))
381.77/118.35
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.35
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.35
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.35
PROPER(recip(nil)) → c46(RECIP(ok(nil)), PROPER(nil))
381.77/118.35
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.35
381.77/118.35
(38) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.77/118.35
active(sqr(0)) → mark(0)
381.77/118.35
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.77/118.35
active(dbl(0)) → mark(0)
381.77/118.35
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.77/118.35
active(add(0, z0)) → mark(z0)
381.77/118.35
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.77/118.35
active(first(0, z0)) → mark(nil)
381.77/118.35
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.77/118.35
active(half(0)) → mark(0)
381.77/118.35
active(half(s(0))) → mark(0)
381.77/118.35
active(half(s(s(z0)))) → mark(s(half(z0)))
381.77/118.35
active(half(dbl(z0))) → mark(z0)
381.77/118.35
active(terms(z0)) → terms(active(z0))
381.77/118.35
active(cons(z0, z1)) → cons(active(z0), z1)
381.77/118.35
active(recip(z0)) → recip(active(z0))
381.77/118.35
active(sqr(z0)) → sqr(active(z0))
381.77/118.35
active(s(z0)) → s(active(z0))
381.77/118.35
active(add(z0, z1)) → add(active(z0), z1)
381.77/118.35
active(add(z0, z1)) → add(z0, active(z1))
381.77/118.35
active(dbl(z0)) → dbl(active(z0))
381.77/118.35
active(first(z0, z1)) → first(active(z0), z1)
381.77/118.35
active(first(z0, z1)) → first(z0, active(z1))
381.77/118.35
active(half(z0)) → half(active(z0))
381.77/118.35
terms(mark(z0)) → mark(terms(z0))
381.77/118.35
terms(ok(z0)) → ok(terms(z0))
381.77/118.35
cons(mark(z0), z1) → mark(cons(z0, z1))
381.77/118.35
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.77/118.35
recip(mark(z0)) → mark(recip(z0))
381.77/118.35
recip(ok(z0)) → ok(recip(z0))
381.77/118.35
sqr(mark(z0)) → mark(sqr(z0))
381.77/118.35
sqr(ok(z0)) → ok(sqr(z0))
381.77/118.35
s(mark(z0)) → mark(s(z0))
381.77/118.35
s(ok(z0)) → ok(s(z0))
381.77/118.35
add(mark(z0), z1) → mark(add(z0, z1))
381.77/118.35
add(z0, mark(z1)) → mark(add(z0, z1))
381.77/118.35
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.77/118.35
dbl(mark(z0)) → mark(dbl(z0))
381.77/118.35
dbl(ok(z0)) → ok(dbl(z0))
381.77/118.35
first(mark(z0), z1) → mark(first(z0, z1))
381.77/118.35
first(z0, mark(z1)) → mark(first(z0, z1))
381.77/118.36
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.77/118.36
half(mark(z0)) → mark(half(z0))
381.77/118.36
half(ok(z0)) → ok(half(z0))
381.77/118.36
proper(terms(z0)) → terms(proper(z0))
381.77/118.36
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.77/118.36
proper(recip(z0)) → recip(proper(z0))
381.77/118.36
proper(sqr(z0)) → sqr(proper(z0))
381.77/118.36
proper(s(z0)) → s(proper(z0))
381.77/118.36
proper(0) → ok(0)
381.77/118.36
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.77/118.36
proper(dbl(z0)) → dbl(proper(z0))
381.77/118.36
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.77/118.36
proper(nil) → ok(nil)
381.77/118.36
proper(half(z0)) → half(proper(z0))
381.77/118.36
top(mark(z0)) → top(proper(z0))
381.77/118.36
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.36
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.36
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.36
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.36
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.36
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.36
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.36
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.36
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.36
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.36
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.36
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.36
S(mark(z0)) → c32(S(z0))
381.77/118.36
S(ok(z0)) → c33(S(z0))
381.77/118.36
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.36
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.36
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.36
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.36
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.36
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.36
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.36
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.36
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.36
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.36
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.36
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.36
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.36
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.36
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.36
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.36
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.36
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.36
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.36
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.36
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.36
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.36
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.36
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.36
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.36
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.36
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.36
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.36
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.36
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.36
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.36
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.36
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.36
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.36
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.36
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.36
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.36
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.36
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.36
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.36
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.36
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.36
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.36
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.36
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.36
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.36
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.36
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.36
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.36
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.36
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.36
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.36
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.36
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.36
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.36
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.36
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.36
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.36
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.36
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.36
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.36
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.36
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.36
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.36
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.36
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.36
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.36
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.36
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.36
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.36
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.36
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.36
PROPER(recip(0)) → c46(RECIP(ok(0)), PROPER(0))
381.77/118.36
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.36
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.36
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.36
PROPER(recip(nil)) → c46(RECIP(ok(nil)), PROPER(nil))
381.77/118.36
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.36
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.36
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.36
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.36
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.36
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.36
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.36
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.36
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.36
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.36
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.36
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.36
S(mark(z0)) → c32(S(z0))
381.77/118.36
S(ok(z0)) → c33(S(z0))
381.77/118.36
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.36
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.36
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.36
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.36
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.36
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.36
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.36
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.36
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.36
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.36
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.36
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.36
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.36
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.36
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.36
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.36
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.36
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.36
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.36
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.36
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.36
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.36
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.36
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.36
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.36
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.36
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.36
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.36
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.36
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.36
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.36
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.36
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.36
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.36
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.36
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.36
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.36
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.36
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.36
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.36
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.36
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.36
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.36
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.36
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.36
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.36
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.36
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.36
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.36
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.36
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.36
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.36
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.36
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.36
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.36
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.36
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.36
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.36
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.36
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.36
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.36
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.36
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.36
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.36
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.36
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.36
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.36
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.36
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.36
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.36
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.36
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.36
PROPER(recip(0)) → c46(RECIP(ok(0)), PROPER(0))
381.77/118.36
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.36
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.36
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.36
PROPER(recip(nil)) → c46(RECIP(ok(nil)), PROPER(nil))
381.77/118.36
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c47, c48, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46
381.77/118.36
381.77/118.36
(39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
381.77/118.36
381.77/118.36
(40) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.77/118.36
active(sqr(0)) → mark(0)
381.77/118.36
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.77/118.36
active(dbl(0)) → mark(0)
381.77/118.36
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.77/118.36
active(add(0, z0)) → mark(z0)
381.77/118.36
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.77/118.36
active(first(0, z0)) → mark(nil)
381.77/118.36
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.77/118.36
active(half(0)) → mark(0)
381.77/118.36
active(half(s(0))) → mark(0)
381.77/118.36
active(half(s(s(z0)))) → mark(s(half(z0)))
381.77/118.36
active(half(dbl(z0))) → mark(z0)
381.77/118.36
active(terms(z0)) → terms(active(z0))
381.77/118.36
active(cons(z0, z1)) → cons(active(z0), z1)
381.77/118.36
active(recip(z0)) → recip(active(z0))
381.77/118.36
active(sqr(z0)) → sqr(active(z0))
381.77/118.36
active(s(z0)) → s(active(z0))
381.77/118.36
active(add(z0, z1)) → add(active(z0), z1)
381.77/118.36
active(add(z0, z1)) → add(z0, active(z1))
381.77/118.36
active(dbl(z0)) → dbl(active(z0))
381.77/118.36
active(first(z0, z1)) → first(active(z0), z1)
381.77/118.36
active(first(z0, z1)) → first(z0, active(z1))
381.77/118.36
active(half(z0)) → half(active(z0))
381.77/118.36
terms(mark(z0)) → mark(terms(z0))
381.77/118.36
terms(ok(z0)) → ok(terms(z0))
381.77/118.36
cons(mark(z0), z1) → mark(cons(z0, z1))
381.77/118.36
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.77/118.36
recip(mark(z0)) → mark(recip(z0))
381.77/118.36
recip(ok(z0)) → ok(recip(z0))
381.77/118.36
sqr(mark(z0)) → mark(sqr(z0))
381.77/118.36
sqr(ok(z0)) → ok(sqr(z0))
381.77/118.36
s(mark(z0)) → mark(s(z0))
381.77/118.36
s(ok(z0)) → ok(s(z0))
381.77/118.36
add(mark(z0), z1) → mark(add(z0, z1))
381.77/118.36
add(z0, mark(z1)) → mark(add(z0, z1))
381.77/118.36
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.77/118.36
dbl(mark(z0)) → mark(dbl(z0))
381.77/118.36
dbl(ok(z0)) → ok(dbl(z0))
381.77/118.36
first(mark(z0), z1) → mark(first(z0, z1))
381.77/118.36
first(z0, mark(z1)) → mark(first(z0, z1))
381.77/118.36
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.77/118.36
half(mark(z0)) → mark(half(z0))
381.77/118.36
half(ok(z0)) → ok(half(z0))
381.77/118.36
proper(terms(z0)) → terms(proper(z0))
381.77/118.36
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.77/118.36
proper(recip(z0)) → recip(proper(z0))
381.77/118.36
proper(sqr(z0)) → sqr(proper(z0))
381.77/118.36
proper(s(z0)) → s(proper(z0))
381.77/118.36
proper(0) → ok(0)
381.77/118.36
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.77/118.36
proper(dbl(z0)) → dbl(proper(z0))
381.77/118.36
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.77/118.36
proper(nil) → ok(nil)
381.77/118.36
proper(half(z0)) → half(proper(z0))
381.77/118.36
top(mark(z0)) → top(proper(z0))
381.77/118.36
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.36
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.36
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.36
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.36
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.36
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.36
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.36
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.36
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.36
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.36
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.36
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.36
S(mark(z0)) → c32(S(z0))
381.77/118.36
S(ok(z0)) → c33(S(z0))
381.77/118.36
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.36
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.36
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.36
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.36
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.36
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.36
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.36
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.36
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.36
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.36
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.36
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.36
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.36
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.36
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.36
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.36
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.36
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.36
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.36
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.36
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.36
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.36
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.36
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.36
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.36
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.36
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.36
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.36
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.36
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.36
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.36
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.36
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.36
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.36
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.36
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.36
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.36
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.36
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.36
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.36
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.36
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.36
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.36
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.36
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.36
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.36
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.36
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.36
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.36
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.36
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.36
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.36
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.36
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.36
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.36
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.36
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.36
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.36
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.36
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.36
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.36
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.36
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.36
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.36
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.36
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.36
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.36
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.36
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.36
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.36
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.36
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.36
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.36
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.36
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.36
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.36
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.36
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.36
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.36
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.36
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.36
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.36
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.36
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.36
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.36
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.36
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.36
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.36
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.36
S(mark(z0)) → c32(S(z0))
381.77/118.36
S(ok(z0)) → c33(S(z0))
381.77/118.36
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.36
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.36
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.36
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.36
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.36
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.36
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.36
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.36
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.36
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.36
PROPER(sqr(z0)) → c47(SQR(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.36
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.36
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.36
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.36
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.36
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.36
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.36
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.36
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.36
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.36
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.36
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.36
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.36
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.36
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.36
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.36
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.36
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.36
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.36
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.36
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.36
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.36
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.36
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.36
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.36
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.36
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.36
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.36
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.36
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.36
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.36
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.36
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.36
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.36
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.36
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.36
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.36
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.36
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.36
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.36
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.36
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.36
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.36
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.36
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.36
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.36
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.36
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.36
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.36
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.36
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.36
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.36
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.36
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.36
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.36
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.36
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.36
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.36
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.36
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.36
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.36
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.36
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.36
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.36
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.36
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.36
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.36
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c47, c48, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46
381.77/118.36
381.77/118.36
(41) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
sqr(
z0)) →
c47(
SQR(
proper(
z0)),
PROPER(
z0)) by
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.36
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.36
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.36
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.36
PROPER(sqr(0)) → c47(SQR(ok(0)), PROPER(0))
381.77/118.36
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.36
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.36
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.36
PROPER(sqr(nil)) → c47(SQR(ok(nil)), PROPER(nil))
381.77/118.36
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
381.77/118.36
381.77/118.36
(42) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.77/118.36
active(sqr(0)) → mark(0)
381.77/118.36
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.77/118.36
active(dbl(0)) → mark(0)
381.77/118.36
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.77/118.36
active(add(0, z0)) → mark(z0)
381.77/118.36
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.77/118.36
active(first(0, z0)) → mark(nil)
381.77/118.36
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.77/118.36
active(half(0)) → mark(0)
381.77/118.36
active(half(s(0))) → mark(0)
381.77/118.36
active(half(s(s(z0)))) → mark(s(half(z0)))
381.77/118.36
active(half(dbl(z0))) → mark(z0)
381.77/118.36
active(terms(z0)) → terms(active(z0))
381.77/118.36
active(cons(z0, z1)) → cons(active(z0), z1)
381.77/118.36
active(recip(z0)) → recip(active(z0))
381.77/118.36
active(sqr(z0)) → sqr(active(z0))
381.77/118.36
active(s(z0)) → s(active(z0))
381.77/118.36
active(add(z0, z1)) → add(active(z0), z1)
381.77/118.36
active(add(z0, z1)) → add(z0, active(z1))
381.77/118.36
active(dbl(z0)) → dbl(active(z0))
381.77/118.36
active(first(z0, z1)) → first(active(z0), z1)
381.77/118.36
active(first(z0, z1)) → first(z0, active(z1))
381.77/118.36
active(half(z0)) → half(active(z0))
381.77/118.36
terms(mark(z0)) → mark(terms(z0))
381.77/118.36
terms(ok(z0)) → ok(terms(z0))
381.77/118.36
cons(mark(z0), z1) → mark(cons(z0, z1))
381.77/118.36
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.77/118.36
recip(mark(z0)) → mark(recip(z0))
381.77/118.36
recip(ok(z0)) → ok(recip(z0))
381.77/118.36
sqr(mark(z0)) → mark(sqr(z0))
381.77/118.36
sqr(ok(z0)) → ok(sqr(z0))
381.77/118.36
s(mark(z0)) → mark(s(z0))
381.77/118.36
s(ok(z0)) → ok(s(z0))
381.77/118.36
add(mark(z0), z1) → mark(add(z0, z1))
381.77/118.36
add(z0, mark(z1)) → mark(add(z0, z1))
381.77/118.36
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.77/118.36
dbl(mark(z0)) → mark(dbl(z0))
381.77/118.36
dbl(ok(z0)) → ok(dbl(z0))
381.77/118.36
first(mark(z0), z1) → mark(first(z0, z1))
381.77/118.36
first(z0, mark(z1)) → mark(first(z0, z1))
381.77/118.36
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.77/118.36
half(mark(z0)) → mark(half(z0))
381.77/118.36
half(ok(z0)) → ok(half(z0))
381.77/118.36
proper(terms(z0)) → terms(proper(z0))
381.77/118.36
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.77/118.36
proper(recip(z0)) → recip(proper(z0))
381.77/118.36
proper(sqr(z0)) → sqr(proper(z0))
381.77/118.36
proper(s(z0)) → s(proper(z0))
381.77/118.36
proper(0) → ok(0)
381.77/118.36
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.77/118.36
proper(dbl(z0)) → dbl(proper(z0))
381.77/118.36
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.77/118.36
proper(nil) → ok(nil)
381.77/118.36
proper(half(z0)) → half(proper(z0))
381.77/118.36
top(mark(z0)) → top(proper(z0))
381.77/118.36
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.36
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.36
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.36
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.36
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.36
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.36
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.36
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.36
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.36
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.36
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.36
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.36
S(mark(z0)) → c32(S(z0))
381.77/118.36
S(ok(z0)) → c33(S(z0))
381.77/118.36
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.36
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.36
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.36
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.36
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.36
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.36
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.36
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.36
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.36
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.36
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.36
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.36
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.36
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.36
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.36
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.36
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.36
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.36
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.36
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.36
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.36
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.36
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.36
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.36
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.36
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.36
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.36
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.36
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.36
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.36
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.36
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.36
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.36
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.36
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.36
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.36
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.36
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.36
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.36
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.36
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.36
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.36
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.36
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.36
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.36
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.36
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.36
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.36
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.36
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.36
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.36
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.36
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.36
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.36
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.36
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.36
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.36
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.36
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.36
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.36
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.36
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.36
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.36
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.36
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.36
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.36
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.36
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.36
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.36
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.36
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.36
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.36
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.36
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.36
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.36
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.36
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.36
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.36
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.36
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.36
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.36
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.36
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.36
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.36
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.36
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.36
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.36
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.36
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.36
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.36
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.36
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.36
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.36
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.36
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.36
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.36
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.36
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.36
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.36
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.36
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.36
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.36
PROPER(sqr(0)) → c47(SQR(ok(0)), PROPER(0))
381.77/118.36
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.36
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.36
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.36
PROPER(sqr(nil)) → c47(SQR(ok(nil)), PROPER(nil))
381.77/118.36
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.36
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.36
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.36
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.36
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.36
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.36
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.36
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.36
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.36
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.36
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.36
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.36
S(mark(z0)) → c32(S(z0))
381.77/118.36
S(ok(z0)) → c33(S(z0))
381.77/118.36
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.36
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.36
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.36
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.36
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.36
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.36
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.36
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.36
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.36
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.36
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.36
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.36
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.36
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.36
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.36
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.36
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.36
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.36
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.36
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.36
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.36
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.36
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.37
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.37
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.37
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.37
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.37
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.37
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.37
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.37
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.37
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.37
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.37
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.37
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.37
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.37
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.37
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.37
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.37
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.37
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.37
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.37
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.37
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.37
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.37
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.37
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.37
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.37
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.37
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.37
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.37
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.37
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.37
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.37
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.37
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.37
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.37
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.37
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.37
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.37
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.37
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.37
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.37
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.37
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.37
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(sqr(0)) → c47(SQR(ok(0)), PROPER(0))
381.77/118.37
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(sqr(nil)) → c47(SQR(ok(nil)), PROPER(nil))
381.77/118.37
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c48, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46, c47
381.77/118.37
381.77/118.37
(43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
381.77/118.37
381.77/118.37
(44) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.77/118.37
active(sqr(0)) → mark(0)
381.77/118.37
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.77/118.37
active(dbl(0)) → mark(0)
381.77/118.37
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.77/118.37
active(add(0, z0)) → mark(z0)
381.77/118.37
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.77/118.37
active(first(0, z0)) → mark(nil)
381.77/118.37
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.77/118.37
active(half(0)) → mark(0)
381.77/118.37
active(half(s(0))) → mark(0)
381.77/118.37
active(half(s(s(z0)))) → mark(s(half(z0)))
381.77/118.37
active(half(dbl(z0))) → mark(z0)
381.77/118.37
active(terms(z0)) → terms(active(z0))
381.77/118.37
active(cons(z0, z1)) → cons(active(z0), z1)
381.77/118.37
active(recip(z0)) → recip(active(z0))
381.77/118.37
active(sqr(z0)) → sqr(active(z0))
381.77/118.37
active(s(z0)) → s(active(z0))
381.77/118.37
active(add(z0, z1)) → add(active(z0), z1)
381.77/118.37
active(add(z0, z1)) → add(z0, active(z1))
381.77/118.37
active(dbl(z0)) → dbl(active(z0))
381.77/118.37
active(first(z0, z1)) → first(active(z0), z1)
381.77/118.37
active(first(z0, z1)) → first(z0, active(z1))
381.77/118.37
active(half(z0)) → half(active(z0))
381.77/118.37
terms(mark(z0)) → mark(terms(z0))
381.77/118.37
terms(ok(z0)) → ok(terms(z0))
381.77/118.37
cons(mark(z0), z1) → mark(cons(z0, z1))
381.77/118.37
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.77/118.37
recip(mark(z0)) → mark(recip(z0))
381.77/118.37
recip(ok(z0)) → ok(recip(z0))
381.77/118.37
sqr(mark(z0)) → mark(sqr(z0))
381.77/118.37
sqr(ok(z0)) → ok(sqr(z0))
381.77/118.37
s(mark(z0)) → mark(s(z0))
381.77/118.37
s(ok(z0)) → ok(s(z0))
381.77/118.37
add(mark(z0), z1) → mark(add(z0, z1))
381.77/118.37
add(z0, mark(z1)) → mark(add(z0, z1))
381.77/118.37
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.77/118.37
dbl(mark(z0)) → mark(dbl(z0))
381.77/118.37
dbl(ok(z0)) → ok(dbl(z0))
381.77/118.37
first(mark(z0), z1) → mark(first(z0, z1))
381.77/118.37
first(z0, mark(z1)) → mark(first(z0, z1))
381.77/118.37
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.77/118.37
half(mark(z0)) → mark(half(z0))
381.77/118.37
half(ok(z0)) → ok(half(z0))
381.77/118.37
proper(terms(z0)) → terms(proper(z0))
381.77/118.37
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.77/118.37
proper(recip(z0)) → recip(proper(z0))
381.77/118.37
proper(sqr(z0)) → sqr(proper(z0))
381.77/118.37
proper(s(z0)) → s(proper(z0))
381.77/118.37
proper(0) → ok(0)
381.77/118.37
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.77/118.37
proper(dbl(z0)) → dbl(proper(z0))
381.77/118.37
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.77/118.37
proper(nil) → ok(nil)
381.77/118.37
proper(half(z0)) → half(proper(z0))
381.77/118.37
top(mark(z0)) → top(proper(z0))
381.77/118.37
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.37
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.37
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.37
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.37
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.37
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.37
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.37
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.37
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.37
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.37
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.37
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.37
S(mark(z0)) → c32(S(z0))
381.77/118.37
S(ok(z0)) → c33(S(z0))
381.77/118.37
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.37
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.37
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.37
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.37
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.37
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.37
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.37
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.37
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.37
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.37
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.37
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.37
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.37
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.37
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.37
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.37
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.37
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.37
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.37
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.37
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.37
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.37
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.37
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.37
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.37
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.37
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.37
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.37
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.37
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.37
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.37
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.37
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.37
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.37
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.37
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.37
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.37
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.37
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.37
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.37
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.37
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.37
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.37
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.37
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.37
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.37
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.37
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.37
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.37
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.37
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.37
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.37
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.37
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.37
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.37
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.37
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.37
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.37
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.37
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.37
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.37
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.37
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.37
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.37
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.37
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.37
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
381.77/118.37
PROPER(sqr(0)) → c47(SQR(ok(0)))
381.77/118.37
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.37
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.37
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.37
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.37
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.37
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.37
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.37
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.37
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.37
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.37
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.37
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.37
S(mark(z0)) → c32(S(z0))
381.77/118.37
S(ok(z0)) → c33(S(z0))
381.77/118.37
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.37
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.37
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.37
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.37
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.37
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.37
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.37
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.37
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.37
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.37
PROPER(s(z0)) → c48(S(proper(z0)), PROPER(z0))
381.77/118.37
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.37
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.37
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.37
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.37
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.37
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.37
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.37
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.37
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.37
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.37
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.37
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.37
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.37
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.37
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.37
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.37
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.37
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.37
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.37
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.37
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.37
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.37
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.37
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.37
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.37
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.37
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.37
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.37
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.37
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.37
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.37
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.37
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.37
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.37
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.37
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.37
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.37
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.37
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.37
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.37
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.37
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.37
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.37
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.37
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.37
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.37
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.37
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.37
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.37
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.37
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.37
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.37
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.37
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.37
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.37
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
381.77/118.37
PROPER(sqr(0)) → c47(SQR(ok(0)))
381.77/118.37
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c48, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46, c47, c47
381.77/118.37
381.77/118.37
(45) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
s(
z0)) →
c48(
S(
proper(
z0)),
PROPER(
z0)) by
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(s(0)) → c48(S(ok(0)), PROPER(0))
381.77/118.37
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(s(nil)) → c48(S(ok(nil)), PROPER(nil))
381.77/118.37
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
381.77/118.37
381.77/118.37
(46) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.77/118.37
active(sqr(0)) → mark(0)
381.77/118.37
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.77/118.37
active(dbl(0)) → mark(0)
381.77/118.37
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.77/118.37
active(add(0, z0)) → mark(z0)
381.77/118.37
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.77/118.37
active(first(0, z0)) → mark(nil)
381.77/118.37
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.77/118.37
active(half(0)) → mark(0)
381.77/118.37
active(half(s(0))) → mark(0)
381.77/118.37
active(half(s(s(z0)))) → mark(s(half(z0)))
381.77/118.37
active(half(dbl(z0))) → mark(z0)
381.77/118.37
active(terms(z0)) → terms(active(z0))
381.77/118.37
active(cons(z0, z1)) → cons(active(z0), z1)
381.77/118.37
active(recip(z0)) → recip(active(z0))
381.77/118.37
active(sqr(z0)) → sqr(active(z0))
381.77/118.37
active(s(z0)) → s(active(z0))
381.77/118.37
active(add(z0, z1)) → add(active(z0), z1)
381.77/118.37
active(add(z0, z1)) → add(z0, active(z1))
381.77/118.37
active(dbl(z0)) → dbl(active(z0))
381.77/118.37
active(first(z0, z1)) → first(active(z0), z1)
381.77/118.37
active(first(z0, z1)) → first(z0, active(z1))
381.77/118.37
active(half(z0)) → half(active(z0))
381.77/118.37
terms(mark(z0)) → mark(terms(z0))
381.77/118.37
terms(ok(z0)) → ok(terms(z0))
381.77/118.37
cons(mark(z0), z1) → mark(cons(z0, z1))
381.77/118.37
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.77/118.37
recip(mark(z0)) → mark(recip(z0))
381.77/118.37
recip(ok(z0)) → ok(recip(z0))
381.77/118.37
sqr(mark(z0)) → mark(sqr(z0))
381.77/118.37
sqr(ok(z0)) → ok(sqr(z0))
381.77/118.37
s(mark(z0)) → mark(s(z0))
381.77/118.37
s(ok(z0)) → ok(s(z0))
381.77/118.37
add(mark(z0), z1) → mark(add(z0, z1))
381.77/118.37
add(z0, mark(z1)) → mark(add(z0, z1))
381.77/118.37
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.77/118.37
dbl(mark(z0)) → mark(dbl(z0))
381.77/118.37
dbl(ok(z0)) → ok(dbl(z0))
381.77/118.37
first(mark(z0), z1) → mark(first(z0, z1))
381.77/118.37
first(z0, mark(z1)) → mark(first(z0, z1))
381.77/118.37
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.77/118.37
half(mark(z0)) → mark(half(z0))
381.77/118.37
half(ok(z0)) → ok(half(z0))
381.77/118.37
proper(terms(z0)) → terms(proper(z0))
381.77/118.37
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.77/118.37
proper(recip(z0)) → recip(proper(z0))
381.77/118.37
proper(sqr(z0)) → sqr(proper(z0))
381.77/118.37
proper(s(z0)) → s(proper(z0))
381.77/118.37
proper(0) → ok(0)
381.77/118.37
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.77/118.37
proper(dbl(z0)) → dbl(proper(z0))
381.77/118.37
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.77/118.37
proper(nil) → ok(nil)
381.77/118.37
proper(half(z0)) → half(proper(z0))
381.77/118.37
top(mark(z0)) → top(proper(z0))
381.77/118.37
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.37
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.37
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.37
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.37
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.37
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.37
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.37
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.37
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.37
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.37
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.37
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.37
S(mark(z0)) → c32(S(z0))
381.77/118.37
S(ok(z0)) → c33(S(z0))
381.77/118.37
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.37
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.37
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.37
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.37
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.37
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.37
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.37
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.37
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.37
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.37
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.37
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.37
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.37
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.37
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.37
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.37
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.37
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.37
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.37
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.37
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.37
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.37
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.37
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.37
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.37
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.37
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.37
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.37
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.37
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.37
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.37
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.37
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.37
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.37
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.37
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.37
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.37
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.37
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.37
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.37
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.37
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.37
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.37
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.37
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.37
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.37
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.37
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.37
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.37
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.37
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.37
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.37
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.37
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.37
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.37
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.37
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.37
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.37
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.37
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.37
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.37
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.37
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.37
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.37
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.37
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
381.77/118.37
PROPER(sqr(0)) → c47(SQR(ok(0)))
381.77/118.37
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
381.77/118.37
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(s(0)) → c48(S(ok(0)), PROPER(0))
381.77/118.37
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(s(nil)) → c48(S(ok(nil)), PROPER(nil))
381.77/118.37
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.37
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.37
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.37
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.37
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.37
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.37
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.37
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.37
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.37
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.37
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.37
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.37
S(mark(z0)) → c32(S(z0))
381.77/118.37
S(ok(z0)) → c33(S(z0))
381.77/118.37
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.37
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.37
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.37
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.37
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.37
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.37
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.37
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.37
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.37
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.37
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.37
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.37
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.37
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.37
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.37
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.37
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.37
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.37
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.37
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.37
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.37
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.37
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.37
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.37
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.37
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.37
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.37
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.37
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.37
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.37
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.37
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.37
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.37
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.37
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.37
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.37
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.37
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.37
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.37
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.37
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.37
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.37
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.37
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.37
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.37
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.37
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.37
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.37
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.37
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.37
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.37
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.37
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.37
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.37
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.37
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.37
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.37
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.37
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.37
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.37
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.37
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.37
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.37
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.37
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.37
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.37
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
381.77/118.37
PROPER(sqr(0)) → c47(SQR(ok(0)))
381.77/118.37
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
381.77/118.37
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.37
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.37
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.37
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.37
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
381.77/118.37
PROPER(s(0)) → c48(S(ok(0)), PROPER(0))
381.77/118.37
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.37
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.37
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.37
PROPER(s(nil)) → c48(S(ok(nil)), PROPER(nil))
381.77/118.37
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46, c47, c47, c48
381.77/118.37
381.77/118.37
(47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
381.77/118.37
381.77/118.37
(48) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.77/118.37
active(sqr(0)) → mark(0)
381.77/118.37
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.77/118.37
active(dbl(0)) → mark(0)
381.77/118.37
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.77/118.37
active(add(0, z0)) → mark(z0)
381.77/118.37
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.77/118.37
active(first(0, z0)) → mark(nil)
381.77/118.37
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.77/118.37
active(half(0)) → mark(0)
381.77/118.37
active(half(s(0))) → mark(0)
381.77/118.37
active(half(s(s(z0)))) → mark(s(half(z0)))
381.77/118.37
active(half(dbl(z0))) → mark(z0)
381.77/118.37
active(terms(z0)) → terms(active(z0))
381.77/118.37
active(cons(z0, z1)) → cons(active(z0), z1)
381.77/118.37
active(recip(z0)) → recip(active(z0))
381.77/118.37
active(sqr(z0)) → sqr(active(z0))
381.77/118.37
active(s(z0)) → s(active(z0))
381.77/118.37
active(add(z0, z1)) → add(active(z0), z1)
381.77/118.37
active(add(z0, z1)) → add(z0, active(z1))
381.77/118.37
active(dbl(z0)) → dbl(active(z0))
381.77/118.37
active(first(z0, z1)) → first(active(z0), z1)
381.77/118.37
active(first(z0, z1)) → first(z0, active(z1))
381.77/118.37
active(half(z0)) → half(active(z0))
381.77/118.37
terms(mark(z0)) → mark(terms(z0))
381.77/118.37
terms(ok(z0)) → ok(terms(z0))
381.77/118.37
cons(mark(z0), z1) → mark(cons(z0, z1))
381.77/118.37
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.77/118.37
recip(mark(z0)) → mark(recip(z0))
381.77/118.37
recip(ok(z0)) → ok(recip(z0))
381.77/118.37
sqr(mark(z0)) → mark(sqr(z0))
381.77/118.37
sqr(ok(z0)) → ok(sqr(z0))
381.77/118.37
s(mark(z0)) → mark(s(z0))
381.77/118.37
s(ok(z0)) → ok(s(z0))
381.77/118.37
add(mark(z0), z1) → mark(add(z0, z1))
381.77/118.37
add(z0, mark(z1)) → mark(add(z0, z1))
381.77/118.37
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.77/118.37
dbl(mark(z0)) → mark(dbl(z0))
381.77/118.37
dbl(ok(z0)) → ok(dbl(z0))
381.77/118.37
first(mark(z0), z1) → mark(first(z0, z1))
381.77/118.37
first(z0, mark(z1)) → mark(first(z0, z1))
381.77/118.37
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.77/118.37
half(mark(z0)) → mark(half(z0))
381.77/118.37
half(ok(z0)) → ok(half(z0))
381.77/118.37
proper(terms(z0)) → terms(proper(z0))
381.77/118.37
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.77/118.37
proper(recip(z0)) → recip(proper(z0))
381.77/118.37
proper(sqr(z0)) → sqr(proper(z0))
381.77/118.37
proper(s(z0)) → s(proper(z0))
381.77/118.37
proper(0) → ok(0)
381.77/118.37
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.77/118.37
proper(dbl(z0)) → dbl(proper(z0))
381.77/118.37
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.77/118.37
proper(nil) → ok(nil)
381.77/118.37
proper(half(z0)) → half(proper(z0))
381.77/118.37
top(mark(z0)) → top(proper(z0))
381.77/118.37
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.37
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.37
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.37
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.37
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.37
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.37
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.37
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.37
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.37
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.37
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.37
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.37
S(mark(z0)) → c32(S(z0))
381.77/118.37
S(ok(z0)) → c33(S(z0))
381.77/118.37
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.37
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.37
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.37
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.37
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.37
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.37
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.37
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.37
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.37
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.37
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.37
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.37
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.37
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.37
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.37
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.37
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.37
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.37
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.37
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.37
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.37
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.37
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.37
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.37
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.37
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.37
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.37
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.37
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.37
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.37
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.37
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.37
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.37
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.37
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.37
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.37
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.37
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.37
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.37
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.37
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.37
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.38
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.38
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.38
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.38
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.38
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.38
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.38
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.38
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.38
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.38
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.38
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.38
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.38
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.38
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.38
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.38
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.38
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.38
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.38
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.38
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.38
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.38
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.38
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.38
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.38
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.38
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.38
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.38
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.38
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.38
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.38
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.38
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.38
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.38
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.38
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.38
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.38
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(sqr(0)) → c47(SQR(ok(0)))
381.77/118.38
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
381.77/118.38
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(s(0)) → c48(S(ok(0)))
381.77/118.38
PROPER(s(nil)) → c48(S(ok(nil)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.38
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.38
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.38
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.38
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.38
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.38
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.38
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.38
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.38
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.38
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.38
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.38
S(mark(z0)) → c32(S(z0))
381.77/118.38
S(ok(z0)) → c33(S(z0))
381.77/118.38
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.38
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.38
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.38
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.38
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.38
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.38
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.38
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.38
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.38
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.38
PROPER(add(z0, z1)) → c50(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.38
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.38
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.38
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.38
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.38
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.38
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.38
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.38
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.38
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.38
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.38
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.38
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.38
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.38
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.38
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.38
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.38
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.38
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.38
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.38
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.38
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.38
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.38
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.38
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.38
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.38
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.38
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.38
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.38
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.38
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.38
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.38
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.38
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.38
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.38
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.38
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.38
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.38
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.38
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.38
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.38
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.38
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.38
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.38
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.38
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.38
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.38
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.38
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.38
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.38
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(sqr(0)) → c47(SQR(ok(0)))
381.77/118.38
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
381.77/118.38
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(s(0)) → c48(S(ok(0)))
381.77/118.38
PROPER(s(nil)) → c48(S(ok(nil)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c50, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46, c47, c47, c48, c48
381.77/118.38
381.77/118.38
(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
add(
z0,
z1)) →
c50(
ADD(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.38
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.38
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.38
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.38
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0), PROPER(0))
381.77/118.38
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.38
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.38
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.38
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
381.77/118.38
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.38
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.38
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.38
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.38
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.38
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(0), PROPER(x1))
381.77/118.38
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.38
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
381.77/118.38
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.38
381.77/118.38
(50) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.77/118.38
active(sqr(0)) → mark(0)
381.77/118.38
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.77/118.38
active(dbl(0)) → mark(0)
381.77/118.38
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.77/118.38
active(add(0, z0)) → mark(z0)
381.77/118.38
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.77/118.38
active(first(0, z0)) → mark(nil)
381.77/118.38
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.77/118.38
active(half(0)) → mark(0)
381.77/118.38
active(half(s(0))) → mark(0)
381.77/118.38
active(half(s(s(z0)))) → mark(s(half(z0)))
381.77/118.38
active(half(dbl(z0))) → mark(z0)
381.77/118.38
active(terms(z0)) → terms(active(z0))
381.77/118.38
active(cons(z0, z1)) → cons(active(z0), z1)
381.77/118.38
active(recip(z0)) → recip(active(z0))
381.77/118.38
active(sqr(z0)) → sqr(active(z0))
381.77/118.38
active(s(z0)) → s(active(z0))
381.77/118.38
active(add(z0, z1)) → add(active(z0), z1)
381.77/118.38
active(add(z0, z1)) → add(z0, active(z1))
381.77/118.38
active(dbl(z0)) → dbl(active(z0))
381.77/118.38
active(first(z0, z1)) → first(active(z0), z1)
381.77/118.38
active(first(z0, z1)) → first(z0, active(z1))
381.77/118.38
active(half(z0)) → half(active(z0))
381.77/118.38
terms(mark(z0)) → mark(terms(z0))
381.77/118.38
terms(ok(z0)) → ok(terms(z0))
381.77/118.38
cons(mark(z0), z1) → mark(cons(z0, z1))
381.77/118.38
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.77/118.38
recip(mark(z0)) → mark(recip(z0))
381.77/118.38
recip(ok(z0)) → ok(recip(z0))
381.77/118.38
sqr(mark(z0)) → mark(sqr(z0))
381.77/118.38
sqr(ok(z0)) → ok(sqr(z0))
381.77/118.38
s(mark(z0)) → mark(s(z0))
381.77/118.38
s(ok(z0)) → ok(s(z0))
381.77/118.38
add(mark(z0), z1) → mark(add(z0, z1))
381.77/118.38
add(z0, mark(z1)) → mark(add(z0, z1))
381.77/118.38
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.77/118.38
dbl(mark(z0)) → mark(dbl(z0))
381.77/118.38
dbl(ok(z0)) → ok(dbl(z0))
381.77/118.38
first(mark(z0), z1) → mark(first(z0, z1))
381.77/118.38
first(z0, mark(z1)) → mark(first(z0, z1))
381.77/118.38
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.77/118.38
half(mark(z0)) → mark(half(z0))
381.77/118.38
half(ok(z0)) → ok(half(z0))
381.77/118.38
proper(terms(z0)) → terms(proper(z0))
381.77/118.38
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.77/118.38
proper(recip(z0)) → recip(proper(z0))
381.77/118.38
proper(sqr(z0)) → sqr(proper(z0))
381.77/118.38
proper(s(z0)) → s(proper(z0))
381.77/118.38
proper(0) → ok(0)
381.77/118.38
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.77/118.38
proper(dbl(z0)) → dbl(proper(z0))
381.77/118.38
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.77/118.38
proper(nil) → ok(nil)
381.77/118.38
proper(half(z0)) → half(proper(z0))
381.77/118.38
top(mark(z0)) → top(proper(z0))
381.77/118.38
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.38
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.38
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.38
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.38
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.38
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.38
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.38
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.38
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.38
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.38
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.38
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.38
S(mark(z0)) → c32(S(z0))
381.77/118.38
S(ok(z0)) → c33(S(z0))
381.77/118.38
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.38
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.38
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.38
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.38
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.38
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.38
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.38
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.38
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.38
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.38
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.38
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.38
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.38
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.38
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.38
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.38
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.38
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.38
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.38
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.38
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.38
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.38
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.38
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.38
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.38
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.38
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.38
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.38
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.38
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.38
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.38
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.38
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.38
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.38
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.38
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.38
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.38
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.38
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.38
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.38
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.38
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.38
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.38
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.38
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.38
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.38
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.38
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.38
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.38
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.38
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.38
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.38
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.38
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.38
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.38
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.38
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.38
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.38
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.38
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(sqr(0)) → c47(SQR(ok(0)))
381.77/118.38
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
381.77/118.38
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(s(0)) → c48(S(ok(0)))
381.77/118.38
PROPER(s(nil)) → c48(S(ok(nil)))
381.77/118.38
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.38
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.38
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.38
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.38
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0), PROPER(0))
381.77/118.38
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.38
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.38
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.38
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
381.77/118.38
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.38
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.38
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.38
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.38
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.38
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(0), PROPER(x1))
381.77/118.38
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.38
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
381.77/118.38
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.38
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.38
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.38
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.38
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.38
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.38
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.38
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.38
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.38
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.38
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.38
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.38
S(mark(z0)) → c32(S(z0))
381.77/118.38
S(ok(z0)) → c33(S(z0))
381.77/118.38
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.38
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.38
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.38
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.38
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.38
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.38
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.38
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.38
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.38
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.38
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.38
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.38
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.38
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.38
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.38
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.38
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.38
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.38
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.38
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.38
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.38
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.38
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.38
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.38
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.38
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.38
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.38
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.38
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.38
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.38
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.38
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.38
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.38
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.38
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.38
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.38
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.38
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.38
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.38
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.38
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.38
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.38
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.38
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.38
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.38
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.38
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.38
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.38
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.38
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.38
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.38
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.38
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.38
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.38
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.38
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.38
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.38
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.38
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.38
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(sqr(0)) → c47(SQR(ok(0)))
381.77/118.38
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
381.77/118.38
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(s(0)) → c48(S(ok(0)))
381.77/118.38
PROPER(s(nil)) → c48(S(ok(nil)))
381.77/118.38
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.38
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.38
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.38
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.38
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0), PROPER(0))
381.77/118.38
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.38
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.38
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.38
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
381.77/118.38
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.38
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.38
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.38
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.38
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.38
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(0), PROPER(x1))
381.77/118.38
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.38
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
381.77/118.38
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46, c47, c47, c48, c48, c50
381.77/118.38
381.77/118.38
(51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
381.77/118.38
381.77/118.38
(52) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.77/118.38
active(sqr(0)) → mark(0)
381.77/118.38
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.77/118.38
active(dbl(0)) → mark(0)
381.77/118.38
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.77/118.38
active(add(0, z0)) → mark(z0)
381.77/118.38
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.77/118.38
active(first(0, z0)) → mark(nil)
381.77/118.38
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.77/118.38
active(half(0)) → mark(0)
381.77/118.38
active(half(s(0))) → mark(0)
381.77/118.38
active(half(s(s(z0)))) → mark(s(half(z0)))
381.77/118.38
active(half(dbl(z0))) → mark(z0)
381.77/118.38
active(terms(z0)) → terms(active(z0))
381.77/118.38
active(cons(z0, z1)) → cons(active(z0), z1)
381.77/118.38
active(recip(z0)) → recip(active(z0))
381.77/118.38
active(sqr(z0)) → sqr(active(z0))
381.77/118.38
active(s(z0)) → s(active(z0))
381.77/118.38
active(add(z0, z1)) → add(active(z0), z1)
381.77/118.38
active(add(z0, z1)) → add(z0, active(z1))
381.77/118.38
active(dbl(z0)) → dbl(active(z0))
381.77/118.38
active(first(z0, z1)) → first(active(z0), z1)
381.77/118.38
active(first(z0, z1)) → first(z0, active(z1))
381.77/118.38
active(half(z0)) → half(active(z0))
381.77/118.38
terms(mark(z0)) → mark(terms(z0))
381.77/118.38
terms(ok(z0)) → ok(terms(z0))
381.77/118.38
cons(mark(z0), z1) → mark(cons(z0, z1))
381.77/118.38
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.77/118.38
recip(mark(z0)) → mark(recip(z0))
381.77/118.38
recip(ok(z0)) → ok(recip(z0))
381.77/118.38
sqr(mark(z0)) → mark(sqr(z0))
381.77/118.38
sqr(ok(z0)) → ok(sqr(z0))
381.77/118.38
s(mark(z0)) → mark(s(z0))
381.77/118.38
s(ok(z0)) → ok(s(z0))
381.77/118.38
add(mark(z0), z1) → mark(add(z0, z1))
381.77/118.38
add(z0, mark(z1)) → mark(add(z0, z1))
381.77/118.38
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.77/118.38
dbl(mark(z0)) → mark(dbl(z0))
381.77/118.38
dbl(ok(z0)) → ok(dbl(z0))
381.77/118.38
first(mark(z0), z1) → mark(first(z0, z1))
381.77/118.38
first(z0, mark(z1)) → mark(first(z0, z1))
381.77/118.38
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.77/118.38
half(mark(z0)) → mark(half(z0))
381.77/118.38
half(ok(z0)) → ok(half(z0))
381.77/118.38
proper(terms(z0)) → terms(proper(z0))
381.77/118.38
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.77/118.38
proper(recip(z0)) → recip(proper(z0))
381.77/118.38
proper(sqr(z0)) → sqr(proper(z0))
381.77/118.38
proper(s(z0)) → s(proper(z0))
381.77/118.38
proper(0) → ok(0)
381.77/118.38
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.77/118.38
proper(dbl(z0)) → dbl(proper(z0))
381.77/118.38
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.77/118.38
proper(nil) → ok(nil)
381.77/118.38
proper(half(z0)) → half(proper(z0))
381.77/118.38
top(mark(z0)) → top(proper(z0))
381.77/118.38
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.38
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.38
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.38
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.38
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.38
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.38
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.38
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.38
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.38
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.38
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.38
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.38
S(mark(z0)) → c32(S(z0))
381.77/118.38
S(ok(z0)) → c33(S(z0))
381.77/118.38
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.38
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.38
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.38
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.38
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.38
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.38
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.38
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.38
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.38
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.38
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.38
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.38
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.38
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.38
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.38
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.38
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.38
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.38
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.38
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.38
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.38
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.38
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.38
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.38
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.38
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.38
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.38
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.38
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.38
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.38
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.38
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.38
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.38
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.38
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.38
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.38
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.38
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.38
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.38
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.38
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.38
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.38
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.38
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.38
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.38
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.38
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.38
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.38
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.38
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.38
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.38
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.38
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.38
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.38
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.38
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.38
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.38
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.38
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.38
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.38
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.38
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.38
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.38
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(sqr(0)) → c47(SQR(ok(0)))
381.77/118.38
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
381.77/118.38
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.38
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.38
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.38
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
381.77/118.38
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.38
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.38
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.38
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
381.77/118.38
PROPER(s(0)) → c48(S(ok(0)))
381.77/118.38
PROPER(s(nil)) → c48(S(ok(nil)))
381.77/118.38
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.38
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.38
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.38
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.38
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.38
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.38
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.38
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.38
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.38
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.38
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.38
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.38
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.38
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.38
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.38
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.38
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
381.77/118.38
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
381.77/118.38
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
381.77/118.38
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.38
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.38
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.38
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.38
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.38
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.38
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.38
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.38
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.38
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.38
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.38
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.38
S(mark(z0)) → c32(S(z0))
381.77/118.38
S(ok(z0)) → c33(S(z0))
381.77/118.38
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.38
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.38
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.38
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.38
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.38
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.38
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.38
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.38
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.38
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.38
PROPER(dbl(z0)) → c51(DBL(proper(z0)), PROPER(z0))
381.77/118.38
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.38
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.38
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.38
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.38
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.38
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.38
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.38
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.38
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.38
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.38
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.38
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.38
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.38
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.38
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.38
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.38
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.38
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.38
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.38
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.38
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.38
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.38
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.38
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.38
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.38
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.38
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.39
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.39
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.39
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.39
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.39
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.39
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.39
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.39
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.39
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.39
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.39
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.39
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.39
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.39
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.39
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.39
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.39
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.39
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.39
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.39
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.39
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.39
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.39
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.39
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.39
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.39
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.39
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.39
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.39
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.39
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.39
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.39
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.39
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.39
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.39
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(sqr(0)) → c47(SQR(ok(0)))
381.77/118.39
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
381.77/118.39
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(s(0)) → c48(S(ok(0)))
381.77/118.39
PROPER(s(nil)) → c48(S(ok(nil)))
381.77/118.39
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.39
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.39
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.39
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.39
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.39
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.39
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.39
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.39
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.39
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.39
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.39
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.39
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.39
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.39
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
381.77/118.39
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
381.77/118.39
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c51, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46, c47, c47, c48, c48, c50, c50
381.77/118.39
381.77/118.39
(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
dbl(
z0)) →
c51(
DBL(
proper(
z0)),
PROPER(
z0)) by
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(dbl(0)) → c51(DBL(ok(0)), PROPER(0))
381.77/118.39
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(dbl(nil)) → c51(DBL(ok(nil)), PROPER(nil))
381.77/118.39
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
381.77/118.39
(54) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.77/118.39
active(sqr(0)) → mark(0)
381.77/118.39
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.77/118.39
active(dbl(0)) → mark(0)
381.77/118.39
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.77/118.39
active(add(0, z0)) → mark(z0)
381.77/118.39
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.77/118.39
active(first(0, z0)) → mark(nil)
381.77/118.39
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.77/118.39
active(half(0)) → mark(0)
381.77/118.39
active(half(s(0))) → mark(0)
381.77/118.39
active(half(s(s(z0)))) → mark(s(half(z0)))
381.77/118.39
active(half(dbl(z0))) → mark(z0)
381.77/118.39
active(terms(z0)) → terms(active(z0))
381.77/118.39
active(cons(z0, z1)) → cons(active(z0), z1)
381.77/118.39
active(recip(z0)) → recip(active(z0))
381.77/118.39
active(sqr(z0)) → sqr(active(z0))
381.77/118.39
active(s(z0)) → s(active(z0))
381.77/118.39
active(add(z0, z1)) → add(active(z0), z1)
381.77/118.39
active(add(z0, z1)) → add(z0, active(z1))
381.77/118.39
active(dbl(z0)) → dbl(active(z0))
381.77/118.39
active(first(z0, z1)) → first(active(z0), z1)
381.77/118.39
active(first(z0, z1)) → first(z0, active(z1))
381.77/118.39
active(half(z0)) → half(active(z0))
381.77/118.39
terms(mark(z0)) → mark(terms(z0))
381.77/118.39
terms(ok(z0)) → ok(terms(z0))
381.77/118.39
cons(mark(z0), z1) → mark(cons(z0, z1))
381.77/118.39
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.77/118.39
recip(mark(z0)) → mark(recip(z0))
381.77/118.39
recip(ok(z0)) → ok(recip(z0))
381.77/118.39
sqr(mark(z0)) → mark(sqr(z0))
381.77/118.39
sqr(ok(z0)) → ok(sqr(z0))
381.77/118.39
s(mark(z0)) → mark(s(z0))
381.77/118.39
s(ok(z0)) → ok(s(z0))
381.77/118.39
add(mark(z0), z1) → mark(add(z0, z1))
381.77/118.39
add(z0, mark(z1)) → mark(add(z0, z1))
381.77/118.39
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.77/118.39
dbl(mark(z0)) → mark(dbl(z0))
381.77/118.39
dbl(ok(z0)) → ok(dbl(z0))
381.77/118.39
first(mark(z0), z1) → mark(first(z0, z1))
381.77/118.39
first(z0, mark(z1)) → mark(first(z0, z1))
381.77/118.39
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.77/118.39
half(mark(z0)) → mark(half(z0))
381.77/118.39
half(ok(z0)) → ok(half(z0))
381.77/118.39
proper(terms(z0)) → terms(proper(z0))
381.77/118.39
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.77/118.39
proper(recip(z0)) → recip(proper(z0))
381.77/118.39
proper(sqr(z0)) → sqr(proper(z0))
381.77/118.39
proper(s(z0)) → s(proper(z0))
381.77/118.39
proper(0) → ok(0)
381.77/118.39
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.77/118.39
proper(dbl(z0)) → dbl(proper(z0))
381.77/118.39
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.77/118.39
proper(nil) → ok(nil)
381.77/118.39
proper(half(z0)) → half(proper(z0))
381.77/118.39
top(mark(z0)) → top(proper(z0))
381.77/118.39
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.39
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.39
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.39
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.39
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.39
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.39
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.39
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.39
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.39
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.39
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.39
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.39
S(mark(z0)) → c32(S(z0))
381.77/118.39
S(ok(z0)) → c33(S(z0))
381.77/118.39
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.39
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.39
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.39
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.39
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.39
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.39
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.39
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.39
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.39
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.39
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.39
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.39
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.39
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.39
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.39
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.39
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.39
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.39
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.39
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.39
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.39
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.39
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.39
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.39
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.39
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.39
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.39
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.39
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.39
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.39
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.39
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.39
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.39
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.39
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.39
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.39
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.39
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.39
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.39
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.39
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.39
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.39
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.39
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.39
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.39
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.39
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.39
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.39
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.39
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.39
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.39
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.39
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.39
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.39
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.39
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.39
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(sqr(0)) → c47(SQR(ok(0)))
381.77/118.39
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
381.77/118.39
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(s(0)) → c48(S(ok(0)))
381.77/118.39
PROPER(s(nil)) → c48(S(ok(nil)))
381.77/118.39
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.39
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.39
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.39
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.39
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.39
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.39
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.39
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.39
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.39
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.39
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.39
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.39
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.39
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.39
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
381.77/118.39
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
381.77/118.39
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(dbl(0)) → c51(DBL(ok(0)), PROPER(0))
381.77/118.39
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(dbl(nil)) → c51(DBL(ok(nil)), PROPER(nil))
381.77/118.39
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.39
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.39
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.39
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.39
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.39
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.39
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.39
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.39
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.39
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.39
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.39
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.39
S(mark(z0)) → c32(S(z0))
381.77/118.39
S(ok(z0)) → c33(S(z0))
381.77/118.39
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.39
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.39
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.39
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.39
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.39
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.39
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.39
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.39
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.39
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.39
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.39
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.39
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.39
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.39
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.39
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.39
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.39
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.39
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.39
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.39
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.39
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.39
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.39
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.39
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.39
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.39
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.39
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.39
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.39
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.39
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.39
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.39
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.39
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.39
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.39
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.39
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.39
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.39
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.39
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.39
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.39
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.39
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.39
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.39
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.39
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.39
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.39
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.39
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.39
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.39
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.39
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.39
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.39
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.39
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.39
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.39
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(sqr(0)) → c47(SQR(ok(0)))
381.77/118.39
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
381.77/118.39
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(s(0)) → c48(S(ok(0)))
381.77/118.39
PROPER(s(nil)) → c48(S(ok(nil)))
381.77/118.39
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.39
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.39
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.39
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.39
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.39
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.39
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.39
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.39
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.39
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.39
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.39
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.39
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.39
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.39
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
381.77/118.39
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
381.77/118.39
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(dbl(0)) → c51(DBL(ok(0)), PROPER(0))
381.77/118.39
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(dbl(nil)) → c51(DBL(ok(nil)), PROPER(nil))
381.77/118.39
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46, c47, c47, c48, c48, c50, c50, c51
381.77/118.39
381.77/118.39
(55) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
381.77/118.39
381.77/118.39
(56) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.77/118.39
active(sqr(0)) → mark(0)
381.77/118.39
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.77/118.39
active(dbl(0)) → mark(0)
381.77/118.39
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.77/118.39
active(add(0, z0)) → mark(z0)
381.77/118.39
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.77/118.39
active(first(0, z0)) → mark(nil)
381.77/118.39
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.77/118.39
active(half(0)) → mark(0)
381.77/118.39
active(half(s(0))) → mark(0)
381.77/118.39
active(half(s(s(z0)))) → mark(s(half(z0)))
381.77/118.39
active(half(dbl(z0))) → mark(z0)
381.77/118.39
active(terms(z0)) → terms(active(z0))
381.77/118.39
active(cons(z0, z1)) → cons(active(z0), z1)
381.77/118.39
active(recip(z0)) → recip(active(z0))
381.77/118.39
active(sqr(z0)) → sqr(active(z0))
381.77/118.39
active(s(z0)) → s(active(z0))
381.77/118.39
active(add(z0, z1)) → add(active(z0), z1)
381.77/118.39
active(add(z0, z1)) → add(z0, active(z1))
381.77/118.39
active(dbl(z0)) → dbl(active(z0))
381.77/118.39
active(first(z0, z1)) → first(active(z0), z1)
381.77/118.39
active(first(z0, z1)) → first(z0, active(z1))
381.77/118.39
active(half(z0)) → half(active(z0))
381.77/118.39
terms(mark(z0)) → mark(terms(z0))
381.77/118.39
terms(ok(z0)) → ok(terms(z0))
381.77/118.39
cons(mark(z0), z1) → mark(cons(z0, z1))
381.77/118.39
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.77/118.39
recip(mark(z0)) → mark(recip(z0))
381.77/118.39
recip(ok(z0)) → ok(recip(z0))
381.77/118.39
sqr(mark(z0)) → mark(sqr(z0))
381.77/118.39
sqr(ok(z0)) → ok(sqr(z0))
381.77/118.39
s(mark(z0)) → mark(s(z0))
381.77/118.39
s(ok(z0)) → ok(s(z0))
381.77/118.39
add(mark(z0), z1) → mark(add(z0, z1))
381.77/118.39
add(z0, mark(z1)) → mark(add(z0, z1))
381.77/118.39
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.77/118.39
dbl(mark(z0)) → mark(dbl(z0))
381.77/118.39
dbl(ok(z0)) → ok(dbl(z0))
381.77/118.39
first(mark(z0), z1) → mark(first(z0, z1))
381.77/118.39
first(z0, mark(z1)) → mark(first(z0, z1))
381.77/118.39
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.77/118.39
half(mark(z0)) → mark(half(z0))
381.77/118.39
half(ok(z0)) → ok(half(z0))
381.77/118.39
proper(terms(z0)) → terms(proper(z0))
381.77/118.39
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.77/118.39
proper(recip(z0)) → recip(proper(z0))
381.77/118.39
proper(sqr(z0)) → sqr(proper(z0))
381.77/118.39
proper(s(z0)) → s(proper(z0))
381.77/118.39
proper(0) → ok(0)
381.77/118.39
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.77/118.39
proper(dbl(z0)) → dbl(proper(z0))
381.77/118.39
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.77/118.39
proper(nil) → ok(nil)
381.77/118.39
proper(half(z0)) → half(proper(z0))
381.77/118.39
top(mark(z0)) → top(proper(z0))
381.77/118.39
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.39
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.39
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.39
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.39
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.39
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.39
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.39
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.39
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.39
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.39
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.39
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.39
S(mark(z0)) → c32(S(z0))
381.77/118.39
S(ok(z0)) → c33(S(z0))
381.77/118.39
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.39
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.39
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.39
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.39
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.39
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.39
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.39
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.39
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.39
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.39
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.39
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.39
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.39
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.39
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.39
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.39
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.39
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.39
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.39
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.39
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.39
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.39
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.39
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.39
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.39
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.39
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.39
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.39
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.39
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.39
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.39
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.39
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.39
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.39
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.39
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.39
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.39
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.39
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.39
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.39
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.39
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.39
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.39
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.39
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.39
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.39
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.39
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.39
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.39
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.39
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.39
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.39
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.39
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.39
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.39
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.39
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(sqr(0)) → c47(SQR(ok(0)))
381.77/118.39
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
381.77/118.39
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(s(0)) → c48(S(ok(0)))
381.77/118.39
PROPER(s(nil)) → c48(S(ok(nil)))
381.77/118.39
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.39
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.39
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.39
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.39
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.39
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.39
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.39
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.39
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.39
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.39
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.39
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.39
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.39
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.39
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
381.77/118.39
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
381.77/118.39
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(dbl(0)) → c51(DBL(ok(0)))
381.77/118.39
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.39
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.39
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.39
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.39
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.39
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.39
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.39
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.39
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.39
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.39
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.39
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.39
S(mark(z0)) → c32(S(z0))
381.77/118.39
S(ok(z0)) → c33(S(z0))
381.77/118.39
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.39
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.39
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.39
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.39
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.39
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.39
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.39
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.39
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.39
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.39
PROPER(first(z0, z1)) → c52(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
381.77/118.39
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.39
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.39
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.39
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.39
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.39
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.39
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.39
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.39
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.39
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.39
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.39
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.39
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.39
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.39
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.39
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.39
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.39
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.39
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.39
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.39
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.39
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.39
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.39
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.39
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.39
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.39
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.39
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.39
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.39
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.39
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.39
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.39
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.39
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.39
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.39
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.39
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.39
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.39
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.39
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.39
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.39
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.39
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.39
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.39
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.39
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.39
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.39
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.39
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.39
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.39
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.39
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.39
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.39
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.39
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.39
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.39
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.39
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.39
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.39
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.39
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.39
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.39
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.39
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.39
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(recip(0)) → c46(RECIP(ok(0)))
381.77/118.39
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
381.77/118.39
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.39
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.39
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.39
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
381.77/118.39
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.39
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.39
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.39
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
381.77/118.39
PROPER(sqr(0)) → c47(SQR(ok(0)))
381.77/118.39
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
381.77/118.39
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.39
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.40
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.40
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.40
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
381.77/118.40
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.40
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.40
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.40
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
381.77/118.40
PROPER(s(0)) → c48(S(ok(0)))
381.77/118.40
PROPER(s(nil)) → c48(S(ok(nil)))
381.77/118.40
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.40
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.40
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.40
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.40
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.40
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.40
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.40
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.40
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.40
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.40
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.40
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.40
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.40
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.40
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.40
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.40
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.40
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.40
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
381.77/118.40
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
381.77/118.40
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
381.77/118.40
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
381.77/118.40
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.40
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.40
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.40
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.40
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
381.77/118.40
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.40
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.40
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.40
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
381.77/118.40
PROPER(dbl(0)) → c51(DBL(ok(0)))
381.77/118.40
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c52, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46, c47, c47, c48, c48, c50, c50, c51, c51
381.77/118.40
381.77/118.40
(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
first(
z0,
z1)) →
c52(
FIRST(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.40
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.40
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.40
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.40
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.40
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0), PROPER(0))
381.77/118.40
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.40
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.40
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.40
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
381.77/118.40
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.40
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.40
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.40
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.40
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.40
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.40
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(0), PROPER(x1))
381.77/118.40
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.40
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.40
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.40
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
381.77/118.40
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.40
381.77/118.40
(58) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
381.77/118.40
active(sqr(0)) → mark(0)
381.77/118.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
381.77/118.40
active(dbl(0)) → mark(0)
381.77/118.40
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
381.77/118.40
active(add(0, z0)) → mark(z0)
381.77/118.40
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
381.77/118.40
active(first(0, z0)) → mark(nil)
381.77/118.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
381.77/118.40
active(half(0)) → mark(0)
381.77/118.40
active(half(s(0))) → mark(0)
381.77/118.40
active(half(s(s(z0)))) → mark(s(half(z0)))
381.77/118.40
active(half(dbl(z0))) → mark(z0)
381.77/118.40
active(terms(z0)) → terms(active(z0))
381.77/118.40
active(cons(z0, z1)) → cons(active(z0), z1)
381.77/118.40
active(recip(z0)) → recip(active(z0))
381.77/118.40
active(sqr(z0)) → sqr(active(z0))
381.77/118.40
active(s(z0)) → s(active(z0))
381.77/118.40
active(add(z0, z1)) → add(active(z0), z1)
381.77/118.40
active(add(z0, z1)) → add(z0, active(z1))
381.77/118.40
active(dbl(z0)) → dbl(active(z0))
381.77/118.40
active(first(z0, z1)) → first(active(z0), z1)
381.77/118.40
active(first(z0, z1)) → first(z0, active(z1))
381.77/118.40
active(half(z0)) → half(active(z0))
381.77/118.40
terms(mark(z0)) → mark(terms(z0))
381.77/118.40
terms(ok(z0)) → ok(terms(z0))
381.77/118.40
cons(mark(z0), z1) → mark(cons(z0, z1))
381.77/118.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
381.77/118.40
recip(mark(z0)) → mark(recip(z0))
381.77/118.40
recip(ok(z0)) → ok(recip(z0))
381.77/118.40
sqr(mark(z0)) → mark(sqr(z0))
381.77/118.40
sqr(ok(z0)) → ok(sqr(z0))
381.77/118.40
s(mark(z0)) → mark(s(z0))
381.77/118.40
s(ok(z0)) → ok(s(z0))
381.77/118.40
add(mark(z0), z1) → mark(add(z0, z1))
381.77/118.40
add(z0, mark(z1)) → mark(add(z0, z1))
381.77/118.40
add(ok(z0), ok(z1)) → ok(add(z0, z1))
381.77/118.40
dbl(mark(z0)) → mark(dbl(z0))
381.77/118.40
dbl(ok(z0)) → ok(dbl(z0))
381.77/118.40
first(mark(z0), z1) → mark(first(z0, z1))
381.77/118.40
first(z0, mark(z1)) → mark(first(z0, z1))
381.77/118.40
first(ok(z0), ok(z1)) → ok(first(z0, z1))
381.77/118.40
half(mark(z0)) → mark(half(z0))
381.77/118.40
half(ok(z0)) → ok(half(z0))
381.77/118.40
proper(terms(z0)) → terms(proper(z0))
381.77/118.40
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
381.77/118.40
proper(recip(z0)) → recip(proper(z0))
381.77/118.40
proper(sqr(z0)) → sqr(proper(z0))
381.77/118.40
proper(s(z0)) → s(proper(z0))
381.77/118.40
proper(0) → ok(0)
381.77/118.40
proper(add(z0, z1)) → add(proper(z0), proper(z1))
381.77/118.40
proper(dbl(z0)) → dbl(proper(z0))
381.77/118.40
proper(first(z0, z1)) → first(proper(z0), proper(z1))
381.77/118.40
proper(nil) → ok(nil)
381.77/118.40
proper(half(z0)) → half(proper(z0))
381.77/118.40
top(mark(z0)) → top(proper(z0))
381.77/118.40
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
381.77/118.40
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
381.77/118.40
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
381.77/118.40
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
381.77/118.40
TERMS(mark(z0)) → c24(TERMS(z0))
381.77/118.40
TERMS(ok(z0)) → c25(TERMS(z0))
381.77/118.40
CONS(mark(z0), z1) → c26(CONS(z0, z1))
381.77/118.40
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
381.77/118.40
RECIP(mark(z0)) → c28(RECIP(z0))
381.77/118.40
RECIP(ok(z0)) → c29(RECIP(z0))
381.77/118.40
SQR(mark(z0)) → c30(SQR(z0))
381.77/118.40
SQR(ok(z0)) → c31(SQR(z0))
381.77/118.40
S(mark(z0)) → c32(S(z0))
381.77/118.40
S(ok(z0)) → c33(S(z0))
381.77/118.40
ADD(mark(z0), z1) → c34(ADD(z0, z1))
381.77/118.40
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
381.77/118.40
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
381.77/118.40
DBL(mark(z0)) → c37(DBL(z0))
381.77/118.40
DBL(ok(z0)) → c38(DBL(z0))
381.77/118.40
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
381.77/118.40
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
381.77/118.40
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
381.77/118.40
HALF(mark(z0)) → c42(HALF(z0))
381.77/118.40
HALF(ok(z0)) → c43(HALF(z0))
381.77/118.40
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
381.77/118.40
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
381.77/118.40
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
381.77/118.40
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
381.77/118.40
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
381.77/118.40
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
381.77/118.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
381.77/118.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
381.77/118.40
ACTIVE(terms(z0)) → c1(SQR(z0))
381.77/118.40
ACTIVE(terms(z0)) → c1(S(z0))
381.77/118.40
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
381.77/118.40
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
381.77/118.40
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.40
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.40
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.40
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.40
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.40
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.40
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.40
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
381.77/118.40
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.40
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.40
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.40
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.40
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.40
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.40
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
381.77/118.40
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.40
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.40
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.40
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.40
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.40
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
381.77/118.40
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
381.77/118.40
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
381.77/118.40
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
381.77/118.40
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
381.77/118.40
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
381.77/118.40
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
381.77/118.40
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.40
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
381.77/118.40
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
381.77/118.40
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
381.77/118.40
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
381.77/118.40
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
381.77/118.40
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
381.77/118.40
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
381.77/118.40
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
381.77/118.40
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
381.77/118.40
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
381.77/118.40
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
381.77/118.40
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
381.77/118.40
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
381.77/118.40
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
381.77/118.40
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.40
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.40
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.40
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.40
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.40
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.40
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.40
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
381.77/118.40
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.40
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.40
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.40
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.40
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.40
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.40
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
381.77/118.40
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.40
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.40
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.40
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.40
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.40
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
381.77/118.40
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.40
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.40
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.40
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.40
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.40
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.40
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.40
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
381.77/118.40
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.40
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.40
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.40
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.40
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.40
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.40
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
381.77/118.40
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.40
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.40
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.40
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.40
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.40
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
381.77/118.40
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
381.77/118.40
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.40
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
381.77/118.40
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
381.77/118.40
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.40
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.40
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.40
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.40
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.40
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.40
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.40
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
381.77/118.40
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.40
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.40
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.40
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.40
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.40
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.40
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
381.77/118.40
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.40
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.40
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.40
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.40
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.40
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
381.77/118.40
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
381.77/118.40
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.40
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.40
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.40
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.40
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.40
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.40
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.40
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
381.77/118.40
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.40
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.40
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.40
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.40
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.40
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.40
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
381.77/118.40
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.40
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.40
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.40
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.40
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.40
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
381.77/118.40
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
381.77/118.40
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.40
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
381.77/118.40
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
381.77/118.40
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
381.77/118.40
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
381.77/118.40
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
381.77/118.40
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
381.77/118.40
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
381.77/118.40
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
381.77/118.40
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
381.77/118.40
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
381.77/118.40
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
381.77/118.40
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
381.77/118.40
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
381.77/118.40
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
381.77/118.40
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
381.77/118.40
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
381.77/118.40
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
381.77/118.40
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
381.77/118.40
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
381.77/118.40
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
381.77/118.40
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
381.77/118.40
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
381.77/118.40
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
381.77/118.40
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
381.77/118.40
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
381.77/118.40
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
381.77/118.40
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
381.77/118.40
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
381.77/118.40
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
381.77/118.40
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
381.77/118.40
ACTIVE(s(half(0))) → c17(S(mark(0)))
381.77/118.40
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
381.77/118.40
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
381.77/118.40
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
381.77/118.40
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
381.77/118.40
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.40
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.40
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.40
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.40
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
381.77/118.40
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
381.77/118.40
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
381.77/118.40
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
381.77/118.40
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
381.77/118.40
PROPER(terms(0)) → c44(TERMS(ok(0)))
381.77/118.40
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
381.77/118.40
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
381.77/118.40
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
381.77/118.40
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
381.77/118.40
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
381.77/118.40
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
381.77/118.40
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
381.77/118.40
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
381.77/118.40
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
381.77/118.40
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
381.77/118.40
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
381.77/118.40
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
381.77/118.40
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
381.77/118.40
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
381.77/118.40
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
381.77/118.40
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
381.77/118.40
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
381.77/118.40
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
381.77/118.40
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
381.77/118.40
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
381.77/118.40
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
381.77/118.40
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
381.77/118.40
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
381.77/118.40
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
381.77/118.40
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
381.77/118.40
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
381.77/118.40
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
381.77/118.40
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
381.77/118.40
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(recip(0)) → c46(RECIP(ok(0)))
382.08/118.40
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
382.08/118.40
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(sqr(0)) → c47(SQR(ok(0)))
382.08/118.40
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
382.08/118.40
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(s(0)) → c48(S(ok(0)))
382.08/118.40
PROPER(s(nil)) → c48(S(ok(nil)))
382.08/118.40
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.40
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.40
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.40
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.40
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.40
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.40
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.40
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.40
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.40
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.40
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.40
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.40
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.40
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.40
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
382.08/118.40
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
382.08/118.40
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(dbl(0)) → c51(DBL(ok(0)))
382.08/118.40
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
382.08/118.40
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.40
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.40
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.40
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.40
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0), PROPER(0))
382.08/118.40
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.40
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.40
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.40
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
382.08/118.40
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.40
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.40
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.40
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.40
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.40
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(0), PROPER(x1))
382.08/118.40
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.40
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
382.08/118.40
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
382.08/118.40
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
382.08/118.40
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
382.08/118.40
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
382.08/118.40
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.40
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.40
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.40
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.40
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.40
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.40
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.40
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.40
S(mark(z0)) → c32(S(z0))
382.08/118.40
S(ok(z0)) → c33(S(z0))
382.08/118.40
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.40
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.40
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.40
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.40
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.40
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.40
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.40
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.40
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.40
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.40
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
382.08/118.40
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
382.08/118.40
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
382.08/118.40
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
382.08/118.40
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
382.08/118.40
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
382.08/118.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
382.08/118.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
382.08/118.40
ACTIVE(terms(z0)) → c1(SQR(z0))
382.08/118.40
ACTIVE(terms(z0)) → c1(S(z0))
382.08/118.40
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
382.08/118.40
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
382.08/118.40
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
382.08/118.40
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.40
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
382.08/118.40
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
382.08/118.40
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
382.08/118.40
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
382.08/118.40
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.40
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
382.08/118.40
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
382.08/118.40
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
382.08/118.40
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
382.08/118.40
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
382.08/118.40
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
382.08/118.40
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.40
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
382.08/118.40
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
382.08/118.40
ACTIVE(s(half(0))) → c17(S(mark(0)))
382.08/118.40
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
382.08/118.40
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
382.08/118.40
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
382.08/118.40
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
382.08/118.40
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(terms(0)) → c44(TERMS(ok(0)))
382.08/118.40
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
382.08/118.40
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.40
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.40
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.40
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.40
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.40
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.40
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.40
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.40
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
382.08/118.40
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
382.08/118.40
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(recip(0)) → c46(RECIP(ok(0)))
382.08/118.40
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
382.08/118.40
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(sqr(0)) → c47(SQR(ok(0)))
382.08/118.40
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
382.08/118.40
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(s(0)) → c48(S(ok(0)))
382.08/118.40
PROPER(s(nil)) → c48(S(ok(nil)))
382.08/118.40
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.40
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.40
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.40
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.40
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.40
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.40
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.40
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.40
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.40
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.40
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.40
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.40
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.40
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.40
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
382.08/118.40
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
382.08/118.40
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(dbl(0)) → c51(DBL(ok(0)))
382.08/118.40
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
382.08/118.40
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.40
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.40
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.40
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.40
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0), PROPER(0))
382.08/118.40
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.40
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.40
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.40
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
382.08/118.40
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.40
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.40
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.40
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.40
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.40
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(0), PROPER(x1))
382.08/118.40
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.40
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
382.08/118.40
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46, c47, c47, c48, c48, c50, c50, c51, c51, c52
382.08/118.40
382.08/118.40
(59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
382.08/118.40
382.08/118.40
(60) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.40
active(sqr(0)) → mark(0)
382.08/118.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.40
active(dbl(0)) → mark(0)
382.08/118.40
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.40
active(add(0, z0)) → mark(z0)
382.08/118.40
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.40
active(first(0, z0)) → mark(nil)
382.08/118.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.40
active(half(0)) → mark(0)
382.08/118.40
active(half(s(0))) → mark(0)
382.08/118.40
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.40
active(half(dbl(z0))) → mark(z0)
382.08/118.40
active(terms(z0)) → terms(active(z0))
382.08/118.40
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.40
active(recip(z0)) → recip(active(z0))
382.08/118.40
active(sqr(z0)) → sqr(active(z0))
382.08/118.40
active(s(z0)) → s(active(z0))
382.08/118.40
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.40
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.40
active(dbl(z0)) → dbl(active(z0))
382.08/118.40
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.40
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.40
active(half(z0)) → half(active(z0))
382.08/118.40
terms(mark(z0)) → mark(terms(z0))
382.08/118.40
terms(ok(z0)) → ok(terms(z0))
382.08/118.40
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.40
recip(mark(z0)) → mark(recip(z0))
382.08/118.40
recip(ok(z0)) → ok(recip(z0))
382.08/118.40
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.40
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.40
s(mark(z0)) → mark(s(z0))
382.08/118.40
s(ok(z0)) → ok(s(z0))
382.08/118.40
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.40
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.40
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.40
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.40
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.40
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.40
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.40
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.40
half(mark(z0)) → mark(half(z0))
382.08/118.40
half(ok(z0)) → ok(half(z0))
382.08/118.40
proper(terms(z0)) → terms(proper(z0))
382.08/118.40
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.40
proper(recip(z0)) → recip(proper(z0))
382.08/118.40
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.40
proper(s(z0)) → s(proper(z0))
382.08/118.40
proper(0) → ok(0)
382.08/118.40
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.40
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.40
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.40
proper(nil) → ok(nil)
382.08/118.40
proper(half(z0)) → half(proper(z0))
382.08/118.40
top(mark(z0)) → top(proper(z0))
382.08/118.40
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
382.08/118.40
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
382.08/118.40
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
382.08/118.40
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
382.08/118.40
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.40
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.40
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.40
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.40
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.40
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.40
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.40
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.40
S(mark(z0)) → c32(S(z0))
382.08/118.40
S(ok(z0)) → c33(S(z0))
382.08/118.40
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.40
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.40
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.40
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.40
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.40
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.40
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.40
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.40
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.40
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.40
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
382.08/118.40
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
382.08/118.40
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
382.08/118.40
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
382.08/118.40
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
382.08/118.40
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
382.08/118.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
382.08/118.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
382.08/118.40
ACTIVE(terms(z0)) → c1(SQR(z0))
382.08/118.40
ACTIVE(terms(z0)) → c1(S(z0))
382.08/118.40
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
382.08/118.40
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
382.08/118.40
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
382.08/118.40
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.40
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
382.08/118.40
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
382.08/118.40
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
382.08/118.40
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
382.08/118.40
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.40
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
382.08/118.40
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
382.08/118.40
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
382.08/118.40
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
382.08/118.40
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
382.08/118.40
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
382.08/118.40
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.40
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
382.08/118.40
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
382.08/118.40
ACTIVE(s(half(0))) → c17(S(mark(0)))
382.08/118.40
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
382.08/118.40
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
382.08/118.40
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
382.08/118.40
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
382.08/118.40
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(terms(0)) → c44(TERMS(ok(0)))
382.08/118.40
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
382.08/118.40
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.40
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.40
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.40
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.40
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.40
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.40
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.40
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.40
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
382.08/118.40
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
382.08/118.40
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(recip(0)) → c46(RECIP(ok(0)))
382.08/118.40
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
382.08/118.40
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(sqr(0)) → c47(SQR(ok(0)))
382.08/118.40
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
382.08/118.40
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(s(0)) → c48(S(ok(0)))
382.08/118.40
PROPER(s(nil)) → c48(S(ok(nil)))
382.08/118.40
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.40
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.40
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.40
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.40
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.40
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.40
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.40
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.40
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.40
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.40
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.40
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.40
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.40
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.40
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
382.08/118.40
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
382.08/118.40
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(dbl(0)) → c51(DBL(ok(0)))
382.08/118.40
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
382.08/118.40
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.40
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.40
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.40
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.40
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.40
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.40
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.40
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.40
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.40
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.40
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.40
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.40
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.40
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.40
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0))
382.08/118.40
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0))
382.08/118.40
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
382.08/118.40
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
382.08/118.40
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
382.08/118.40
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
382.08/118.40
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.40
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.40
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.40
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.40
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.40
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.40
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.40
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.40
S(mark(z0)) → c32(S(z0))
382.08/118.40
S(ok(z0)) → c33(S(z0))
382.08/118.40
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.40
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.40
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.40
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.40
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.40
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.40
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.40
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.40
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.40
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.40
PROPER(half(z0)) → c54(HALF(proper(z0)), PROPER(z0))
382.08/118.40
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
382.08/118.40
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
382.08/118.40
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
382.08/118.40
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
382.08/118.40
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
382.08/118.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
382.08/118.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
382.08/118.40
ACTIVE(terms(z0)) → c1(SQR(z0))
382.08/118.40
ACTIVE(terms(z0)) → c1(S(z0))
382.08/118.40
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
382.08/118.40
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
382.08/118.40
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
382.08/118.40
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.40
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
382.08/118.40
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
382.08/118.40
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
382.08/118.40
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
382.08/118.40
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.40
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
382.08/118.40
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
382.08/118.40
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
382.08/118.40
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
382.08/118.40
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
382.08/118.40
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.40
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.40
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.40
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.40
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.40
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.40
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
382.08/118.40
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.40
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.40
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.40
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.40
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.40
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.40
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
382.08/118.40
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.40
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.40
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.40
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
382.08/118.40
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
382.08/118.40
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.40
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
382.08/118.40
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
382.08/118.40
ACTIVE(s(half(0))) → c17(S(mark(0)))
382.08/118.40
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
382.08/118.40
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
382.08/118.40
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
382.08/118.40
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
382.08/118.40
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(terms(0)) → c44(TERMS(ok(0)))
382.08/118.40
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
382.08/118.40
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.40
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.40
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.40
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.40
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.40
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.40
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.40
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.40
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.40
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
382.08/118.40
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
382.08/118.40
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(recip(0)) → c46(RECIP(ok(0)))
382.08/118.40
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
382.08/118.40
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(sqr(0)) → c47(SQR(ok(0)))
382.08/118.40
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
382.08/118.40
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(s(0)) → c48(S(ok(0)))
382.08/118.40
PROPER(s(nil)) → c48(S(ok(nil)))
382.08/118.40
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.40
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.40
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.40
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.40
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.40
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.40
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.40
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.40
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.40
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.40
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.40
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.40
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.40
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.40
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
382.08/118.40
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
382.08/118.40
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
PROPER(dbl(0)) → c51(DBL(ok(0)))
382.08/118.40
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
382.08/118.40
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.40
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.40
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.40
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.40
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.40
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.40
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.40
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.40
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.40
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.40
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.40
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.40
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.40
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.40
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.40
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0))
382.08/118.40
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0))
382.08/118.40
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(x1))
382.08/118.40
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c54, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52
382.08/118.40
382.08/118.40
(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
half(
z0)) →
c54(
HALF(
proper(
z0)),
PROPER(
z0)) by
PROPER(half(terms(z0))) → c54(HALF(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.40
PROPER(half(cons(z0, z1))) → c54(HALF(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.40
PROPER(half(recip(z0))) → c54(HALF(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.40
PROPER(half(sqr(z0))) → c54(HALF(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.40
PROPER(half(s(z0))) → c54(HALF(s(proper(z0))), PROPER(s(z0)))
382.08/118.40
PROPER(half(0)) → c54(HALF(ok(0)), PROPER(0))
382.08/118.40
PROPER(half(add(z0, z1))) → c54(HALF(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.40
PROPER(half(dbl(z0))) → c54(HALF(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.40
PROPER(half(first(z0, z1))) → c54(HALF(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.40
PROPER(half(nil)) → c54(HALF(ok(nil)), PROPER(nil))
382.08/118.40
PROPER(half(half(z0))) → c54(HALF(half(proper(z0))), PROPER(half(z0)))
382.08/118.40
382.08/118.40
(62) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.40
active(sqr(0)) → mark(0)
382.08/118.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.40
active(dbl(0)) → mark(0)
382.08/118.40
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.40
active(add(0, z0)) → mark(z0)
382.08/118.40
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.40
active(first(0, z0)) → mark(nil)
382.08/118.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.40
active(half(0)) → mark(0)
382.08/118.40
active(half(s(0))) → mark(0)
382.08/118.40
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.40
active(half(dbl(z0))) → mark(z0)
382.08/118.40
active(terms(z0)) → terms(active(z0))
382.08/118.40
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.40
active(recip(z0)) → recip(active(z0))
382.08/118.40
active(sqr(z0)) → sqr(active(z0))
382.08/118.40
active(s(z0)) → s(active(z0))
382.08/118.40
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.40
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.40
active(dbl(z0)) → dbl(active(z0))
382.08/118.40
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.40
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.40
active(half(z0)) → half(active(z0))
382.08/118.40
terms(mark(z0)) → mark(terms(z0))
382.08/118.40
terms(ok(z0)) → ok(terms(z0))
382.08/118.40
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.40
recip(mark(z0)) → mark(recip(z0))
382.08/118.40
recip(ok(z0)) → ok(recip(z0))
382.08/118.40
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.40
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.40
s(mark(z0)) → mark(s(z0))
382.08/118.40
s(ok(z0)) → ok(s(z0))
382.08/118.40
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.41
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.41
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.41
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.41
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.41
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.41
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.41
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.41
half(mark(z0)) → mark(half(z0))
382.08/118.41
half(ok(z0)) → ok(half(z0))
382.08/118.41
proper(terms(z0)) → terms(proper(z0))
382.08/118.41
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.41
proper(recip(z0)) → recip(proper(z0))
382.08/118.41
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.41
proper(s(z0)) → s(proper(z0))
382.08/118.41
proper(0) → ok(0)
382.08/118.41
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.41
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.41
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.41
proper(nil) → ok(nil)
382.08/118.41
proper(half(z0)) → half(proper(z0))
382.08/118.41
top(mark(z0)) → top(proper(z0))
382.08/118.41
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
382.08/118.41
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
382.08/118.41
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
382.08/118.41
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
382.08/118.41
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.41
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.41
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.41
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.41
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.41
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.41
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.41
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.41
S(mark(z0)) → c32(S(z0))
382.08/118.41
S(ok(z0)) → c33(S(z0))
382.08/118.41
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.41
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.41
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.41
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.41
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.41
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.41
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.41
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.41
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.41
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.41
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
382.08/118.41
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
382.08/118.41
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
382.08/118.41
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
382.08/118.41
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
382.08/118.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
382.08/118.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
382.08/118.41
ACTIVE(terms(z0)) → c1(SQR(z0))
382.08/118.41
ACTIVE(terms(z0)) → c1(S(z0))
382.08/118.41
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
382.08/118.41
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
382.08/118.41
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
382.08/118.41
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.41
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
382.08/118.41
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
382.08/118.41
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
382.08/118.41
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
382.08/118.41
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.41
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
382.08/118.41
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
382.08/118.41
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
382.08/118.41
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
382.08/118.41
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
382.08/118.41
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
382.08/118.41
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.41
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
382.08/118.41
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
382.08/118.41
ACTIVE(s(half(0))) → c17(S(mark(0)))
382.08/118.41
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
382.08/118.41
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
382.08/118.41
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
382.08/118.41
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
382.08/118.41
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(terms(0)) → c44(TERMS(ok(0)))
382.08/118.41
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
382.08/118.41
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.41
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.41
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.41
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.41
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.41
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.41
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.41
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.41
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
382.08/118.41
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
382.08/118.41
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(recip(0)) → c46(RECIP(ok(0)))
382.08/118.41
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
382.08/118.41
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(sqr(0)) → c47(SQR(ok(0)))
382.08/118.41
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
382.08/118.41
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(s(0)) → c48(S(ok(0)))
382.08/118.41
PROPER(s(nil)) → c48(S(ok(nil)))
382.08/118.41
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.41
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.41
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.41
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.41
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.41
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.41
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.41
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.41
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.41
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.41
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.41
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.41
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.41
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.41
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
382.08/118.41
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
382.08/118.41
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(dbl(0)) → c51(DBL(ok(0)))
382.08/118.41
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
382.08/118.41
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.41
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.41
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.41
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.41
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.41
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.41
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.41
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.41
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.41
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.41
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.41
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.41
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.41
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.41
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0))
382.08/118.41
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0))
382.08/118.41
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(half(terms(z0))) → c54(HALF(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(half(cons(z0, z1))) → c54(HALF(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(half(recip(z0))) → c54(HALF(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(half(sqr(z0))) → c54(HALF(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(half(s(z0))) → c54(HALF(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(half(0)) → c54(HALF(ok(0)), PROPER(0))
382.08/118.41
PROPER(half(add(z0, z1))) → c54(HALF(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(half(dbl(z0))) → c54(HALF(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(half(first(z0, z1))) → c54(HALF(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(half(nil)) → c54(HALF(ok(nil)), PROPER(nil))
382.08/118.41
PROPER(half(half(z0))) → c54(HALF(half(proper(z0))), PROPER(half(z0)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
382.08/118.41
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
382.08/118.41
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
382.08/118.41
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
382.08/118.41
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.41
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.41
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.41
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.41
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.41
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.41
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.41
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.41
S(mark(z0)) → c32(S(z0))
382.08/118.41
S(ok(z0)) → c33(S(z0))
382.08/118.41
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.41
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.41
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.41
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.41
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.41
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.41
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.41
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.41
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.41
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.41
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
382.08/118.41
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
382.08/118.41
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
382.08/118.41
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
382.08/118.41
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
382.08/118.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
382.08/118.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
382.08/118.41
ACTIVE(terms(z0)) → c1(SQR(z0))
382.08/118.41
ACTIVE(terms(z0)) → c1(S(z0))
382.08/118.41
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
382.08/118.41
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
382.08/118.41
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
382.08/118.41
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.41
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
382.08/118.41
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
382.08/118.41
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
382.08/118.41
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
382.08/118.41
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.41
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
382.08/118.41
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
382.08/118.41
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
382.08/118.41
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
382.08/118.41
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
382.08/118.41
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
382.08/118.41
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.41
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
382.08/118.41
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
382.08/118.41
ACTIVE(s(half(0))) → c17(S(mark(0)))
382.08/118.41
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
382.08/118.41
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
382.08/118.41
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
382.08/118.41
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
382.08/118.41
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(terms(0)) → c44(TERMS(ok(0)))
382.08/118.41
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
382.08/118.41
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.41
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.41
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.41
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.41
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.41
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.41
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.41
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.41
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
382.08/118.41
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
382.08/118.41
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(recip(0)) → c46(RECIP(ok(0)))
382.08/118.41
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
382.08/118.41
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(sqr(0)) → c47(SQR(ok(0)))
382.08/118.41
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
382.08/118.41
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(s(0)) → c48(S(ok(0)))
382.08/118.41
PROPER(s(nil)) → c48(S(ok(nil)))
382.08/118.41
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.41
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.41
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.41
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.41
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.41
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.41
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.41
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.41
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.41
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.41
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.41
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.41
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.41
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.41
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
382.08/118.41
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
382.08/118.41
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(dbl(0)) → c51(DBL(ok(0)))
382.08/118.41
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
382.08/118.41
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.41
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.41
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.41
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.41
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.41
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.41
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.41
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.41
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.41
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.41
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.41
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.41
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.41
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.41
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0))
382.08/118.41
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0))
382.08/118.41
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(half(terms(z0))) → c54(HALF(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(half(cons(z0, z1))) → c54(HALF(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(half(recip(z0))) → c54(HALF(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(half(sqr(z0))) → c54(HALF(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(half(s(z0))) → c54(HALF(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(half(0)) → c54(HALF(ok(0)), PROPER(0))
382.08/118.41
PROPER(half(add(z0, z1))) → c54(HALF(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(half(dbl(z0))) → c54(HALF(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(half(first(z0, z1))) → c54(HALF(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(half(nil)) → c54(HALF(ok(nil)), PROPER(nil))
382.08/118.41
PROPER(half(half(z0))) → c54(HALF(half(proper(z0))), PROPER(half(z0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, TOP, PROPER
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c54
382.08/118.41
382.08/118.41
(63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
382.08/118.41
382.08/118.41
(64) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.41
active(sqr(0)) → mark(0)
382.08/118.41
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.41
active(dbl(0)) → mark(0)
382.08/118.41
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.41
active(add(0, z0)) → mark(z0)
382.08/118.41
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.41
active(first(0, z0)) → mark(nil)
382.08/118.41
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.41
active(half(0)) → mark(0)
382.08/118.41
active(half(s(0))) → mark(0)
382.08/118.41
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.41
active(half(dbl(z0))) → mark(z0)
382.08/118.41
active(terms(z0)) → terms(active(z0))
382.08/118.41
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.41
active(recip(z0)) → recip(active(z0))
382.08/118.41
active(sqr(z0)) → sqr(active(z0))
382.08/118.41
active(s(z0)) → s(active(z0))
382.08/118.41
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.41
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.41
active(dbl(z0)) → dbl(active(z0))
382.08/118.41
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.41
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.41
active(half(z0)) → half(active(z0))
382.08/118.41
terms(mark(z0)) → mark(terms(z0))
382.08/118.41
terms(ok(z0)) → ok(terms(z0))
382.08/118.41
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.41
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.41
recip(mark(z0)) → mark(recip(z0))
382.08/118.41
recip(ok(z0)) → ok(recip(z0))
382.08/118.41
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.41
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.41
s(mark(z0)) → mark(s(z0))
382.08/118.41
s(ok(z0)) → ok(s(z0))
382.08/118.41
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.41
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.41
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.41
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.41
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.41
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.41
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.41
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.41
half(mark(z0)) → mark(half(z0))
382.08/118.41
half(ok(z0)) → ok(half(z0))
382.08/118.41
proper(terms(z0)) → terms(proper(z0))
382.08/118.41
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.41
proper(recip(z0)) → recip(proper(z0))
382.08/118.41
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.41
proper(s(z0)) → s(proper(z0))
382.08/118.41
proper(0) → ok(0)
382.08/118.41
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.41
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.41
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.41
proper(nil) → ok(nil)
382.08/118.41
proper(half(z0)) → half(proper(z0))
382.08/118.41
top(mark(z0)) → top(proper(z0))
382.08/118.41
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
382.08/118.41
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
382.08/118.41
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
382.08/118.41
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
382.08/118.41
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.41
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.41
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.41
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.41
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.41
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.41
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.41
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.41
S(mark(z0)) → c32(S(z0))
382.08/118.41
S(ok(z0)) → c33(S(z0))
382.08/118.41
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.41
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.41
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.41
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.41
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.41
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.41
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.41
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.41
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.41
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.41
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
382.08/118.41
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
382.08/118.41
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
382.08/118.41
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
382.08/118.41
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
382.08/118.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
382.08/118.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
382.08/118.41
ACTIVE(terms(z0)) → c1(SQR(z0))
382.08/118.41
ACTIVE(terms(z0)) → c1(S(z0))
382.08/118.41
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
382.08/118.41
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
382.08/118.41
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
382.08/118.41
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.41
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
382.08/118.41
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
382.08/118.41
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
382.08/118.41
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
382.08/118.41
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.41
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
382.08/118.41
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
382.08/118.41
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
382.08/118.41
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
382.08/118.41
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
382.08/118.41
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
382.08/118.41
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.41
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
382.08/118.41
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
382.08/118.41
ACTIVE(s(half(0))) → c17(S(mark(0)))
382.08/118.41
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
382.08/118.41
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
382.08/118.41
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
382.08/118.41
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
382.08/118.41
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(terms(0)) → c44(TERMS(ok(0)))
382.08/118.41
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
382.08/118.41
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.41
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.41
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.41
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.41
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.41
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.41
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.41
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.41
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
382.08/118.41
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
382.08/118.41
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(recip(0)) → c46(RECIP(ok(0)))
382.08/118.41
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
382.08/118.41
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(sqr(0)) → c47(SQR(ok(0)))
382.08/118.41
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
382.08/118.41
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(s(0)) → c48(S(ok(0)))
382.08/118.41
PROPER(s(nil)) → c48(S(ok(nil)))
382.08/118.41
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.41
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.41
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.41
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.41
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.41
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.41
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.41
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.41
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.41
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.41
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.41
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.41
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.41
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.41
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
382.08/118.41
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
382.08/118.41
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(dbl(0)) → c51(DBL(ok(0)))
382.08/118.41
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
382.08/118.41
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.41
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.41
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.41
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.41
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.41
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.41
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.41
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.41
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.41
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.41
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.41
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.41
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.41
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.41
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0))
382.08/118.41
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0))
382.08/118.41
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(half(terms(z0))) → c54(HALF(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(half(cons(z0, z1))) → c54(HALF(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(half(recip(z0))) → c54(HALF(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(half(sqr(z0))) → c54(HALF(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(half(s(z0))) → c54(HALF(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(half(add(z0, z1))) → c54(HALF(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(half(dbl(z0))) → c54(HALF(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(half(first(z0, z1))) → c54(HALF(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(half(half(z0))) → c54(HALF(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(half(0)) → c54(HALF(ok(0)))
382.08/118.41
PROPER(half(nil)) → c54(HALF(ok(nil)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
382.08/118.41
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
382.08/118.41
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
382.08/118.41
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
382.08/118.41
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.41
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.41
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.41
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.41
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.41
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.41
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.41
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.41
S(mark(z0)) → c32(S(z0))
382.08/118.41
S(ok(z0)) → c33(S(z0))
382.08/118.41
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.41
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.41
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.41
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.41
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.41
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.41
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.41
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.41
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.41
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.41
TOP(mark(z0)) → c55(TOP(proper(z0)), PROPER(z0))
382.08/118.41
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
382.08/118.41
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
382.08/118.41
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
382.08/118.41
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
382.08/118.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
382.08/118.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
382.08/118.41
ACTIVE(terms(z0)) → c1(SQR(z0))
382.08/118.41
ACTIVE(terms(z0)) → c1(S(z0))
382.08/118.41
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
382.08/118.41
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
382.08/118.41
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
382.08/118.41
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.41
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
382.08/118.41
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
382.08/118.41
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
382.08/118.41
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
382.08/118.41
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.41
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
382.08/118.41
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
382.08/118.41
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
382.08/118.41
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
382.08/118.41
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
382.08/118.41
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.41
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.41
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.41
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
382.08/118.41
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
382.08/118.41
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.41
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
382.08/118.41
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
382.08/118.41
ACTIVE(s(half(0))) → c17(S(mark(0)))
382.08/118.41
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
382.08/118.41
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
382.08/118.41
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
382.08/118.41
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
382.08/118.41
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(terms(0)) → c44(TERMS(ok(0)))
382.08/118.41
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
382.08/118.41
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.41
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.41
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.41
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.41
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.41
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.41
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.41
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.41
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.41
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
382.08/118.41
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
382.08/118.41
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(recip(0)) → c46(RECIP(ok(0)))
382.08/118.41
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
382.08/118.41
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(sqr(0)) → c47(SQR(ok(0)))
382.08/118.41
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
382.08/118.41
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(s(0)) → c48(S(ok(0)))
382.08/118.41
PROPER(s(nil)) → c48(S(ok(nil)))
382.08/118.41
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.41
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.41
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.41
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.41
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.41
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.41
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.41
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.41
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.41
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.41
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.41
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.41
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.41
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.41
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
382.08/118.41
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
382.08/118.41
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(dbl(0)) → c51(DBL(ok(0)))
382.08/118.41
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
382.08/118.41
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.41
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.41
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.41
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.41
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.41
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.41
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.41
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.41
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.41
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.41
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.41
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.41
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.41
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.41
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.41
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0))
382.08/118.41
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0))
382.08/118.41
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(x1))
382.08/118.41
PROPER(half(terms(z0))) → c54(HALF(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
PROPER(half(cons(z0, z1))) → c54(HALF(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
PROPER(half(recip(z0))) → c54(HALF(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
PROPER(half(sqr(z0))) → c54(HALF(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
PROPER(half(s(z0))) → c54(HALF(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
PROPER(half(add(z0, z1))) → c54(HALF(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
PROPER(half(dbl(z0))) → c54(HALF(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
PROPER(half(first(z0, z1))) → c54(HALF(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
PROPER(half(half(z0))) → c54(HALF(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
PROPER(half(0)) → c54(HALF(ok(0)))
382.08/118.41
PROPER(half(nil)) → c54(HALF(ok(nil)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, TOP, PROPER
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c55, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c54, c54
382.08/118.41
382.08/118.41
(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
TOP(
mark(
z0)) →
c55(
TOP(
proper(
z0)),
PROPER(
z0)) by
TOP(mark(terms(z0))) → c55(TOP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.41
TOP(mark(cons(z0, z1))) → c55(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.41
TOP(mark(recip(z0))) → c55(TOP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.41
TOP(mark(sqr(z0))) → c55(TOP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.41
TOP(mark(s(z0))) → c55(TOP(s(proper(z0))), PROPER(s(z0)))
382.08/118.41
TOP(mark(0)) → c55(TOP(ok(0)), PROPER(0))
382.08/118.41
TOP(mark(add(z0, z1))) → c55(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.41
TOP(mark(dbl(z0))) → c55(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.41
TOP(mark(first(z0, z1))) → c55(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.41
TOP(mark(nil)) → c55(TOP(ok(nil)), PROPER(nil))
382.08/118.41
TOP(mark(half(z0))) → c55(TOP(half(proper(z0))), PROPER(half(z0)))
382.08/118.41
382.08/118.41
(66) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.41
active(sqr(0)) → mark(0)
382.08/118.41
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.41
active(dbl(0)) → mark(0)
382.08/118.41
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.41
active(add(0, z0)) → mark(z0)
382.08/118.41
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.41
active(first(0, z0)) → mark(nil)
382.08/118.41
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.41
active(half(0)) → mark(0)
382.08/118.41
active(half(s(0))) → mark(0)
382.08/118.41
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.41
active(half(dbl(z0))) → mark(z0)
382.08/118.41
active(terms(z0)) → terms(active(z0))
382.08/118.41
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.41
active(recip(z0)) → recip(active(z0))
382.08/118.41
active(sqr(z0)) → sqr(active(z0))
382.08/118.41
active(s(z0)) → s(active(z0))
382.08/118.41
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.41
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.41
active(dbl(z0)) → dbl(active(z0))
382.08/118.41
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.41
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.41
active(half(z0)) → half(active(z0))
382.08/118.41
terms(mark(z0)) → mark(terms(z0))
382.08/118.41
terms(ok(z0)) → ok(terms(z0))
382.08/118.41
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.41
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.41
recip(mark(z0)) → mark(recip(z0))
382.08/118.41
recip(ok(z0)) → ok(recip(z0))
382.08/118.41
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.41
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.41
s(mark(z0)) → mark(s(z0))
382.08/118.41
s(ok(z0)) → ok(s(z0))
382.08/118.41
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.41
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.41
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.41
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.41
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.41
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.41
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.41
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.41
half(mark(z0)) → mark(half(z0))
382.08/118.41
half(ok(z0)) → ok(half(z0))
382.08/118.41
proper(terms(z0)) → terms(proper(z0))
382.08/118.41
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.41
proper(recip(z0)) → recip(proper(z0))
382.08/118.41
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.41
proper(s(z0)) → s(proper(z0))
382.08/118.41
proper(0) → ok(0)
382.08/118.41
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.41
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.41
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.41
proper(nil) → ok(nil)
382.08/118.41
proper(half(z0)) → half(proper(z0))
382.08/118.41
top(mark(z0)) → top(proper(z0))
382.08/118.41
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
382.08/118.41
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
382.08/118.41
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
382.08/118.41
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
382.08/118.41
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.41
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.41
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.41
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.41
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.41
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.41
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.41
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.41
S(mark(z0)) → c32(S(z0))
382.08/118.41
S(ok(z0)) → c33(S(z0))
382.08/118.41
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.41
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.41
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.41
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.41
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.41
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.41
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.41
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.41
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.41
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.41
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
382.08/118.41
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
382.08/118.41
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
382.08/118.41
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
382.08/118.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
382.08/118.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
382.08/118.41
ACTIVE(terms(z0)) → c1(SQR(z0))
382.08/118.41
ACTIVE(terms(z0)) → c1(S(z0))
382.08/118.41
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
382.08/118.41
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
382.08/118.41
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.41
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.41
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.41
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.41
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.41
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.41
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
382.08/118.41
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.41
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.41
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.41
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.41
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.41
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.41
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
382.08/118.41
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
382.08/118.42
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.42
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
382.08/118.42
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
382.08/118.42
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
382.08/118.42
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
382.08/118.42
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.42
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
382.08/118.42
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
382.08/118.42
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
382.08/118.42
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
382.08/118.42
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
382.08/118.42
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
382.08/118.42
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.42
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
382.08/118.42
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
382.08/118.42
ACTIVE(s(half(0))) → c17(S(mark(0)))
382.08/118.42
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
382.08/118.42
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
382.08/118.42
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
382.08/118.42
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
382.08/118.42
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(terms(0)) → c44(TERMS(ok(0)))
382.08/118.42
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
382.08/118.42
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.42
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.42
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.42
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.42
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.42
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.42
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.42
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.42
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
382.08/118.42
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
382.08/118.42
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(recip(0)) → c46(RECIP(ok(0)))
382.08/118.42
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
382.08/118.42
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(sqr(0)) → c47(SQR(ok(0)))
382.08/118.42
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
382.08/118.42
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(s(0)) → c48(S(ok(0)))
382.08/118.42
PROPER(s(nil)) → c48(S(ok(nil)))
382.08/118.42
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.42
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.42
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.42
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.42
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.42
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.42
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.42
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.42
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.42
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.42
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.42
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.42
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.42
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.42
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
382.08/118.42
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
382.08/118.42
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(dbl(0)) → c51(DBL(ok(0)))
382.08/118.42
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
382.08/118.42
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.42
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.42
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.42
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.42
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.42
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.42
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.42
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.42
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.42
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.42
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.42
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.42
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.42
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.42
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0))
382.08/118.42
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0))
382.08/118.42
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(half(terms(z0))) → c54(HALF(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(half(cons(z0, z1))) → c54(HALF(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(half(recip(z0))) → c54(HALF(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(half(sqr(z0))) → c54(HALF(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(half(s(z0))) → c54(HALF(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(half(add(z0, z1))) → c54(HALF(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(half(dbl(z0))) → c54(HALF(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(half(first(z0, z1))) → c54(HALF(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(half(half(z0))) → c54(HALF(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(half(0)) → c54(HALF(ok(0)))
382.08/118.42
PROPER(half(nil)) → c54(HALF(ok(nil)))
382.08/118.42
TOP(mark(terms(z0))) → c55(TOP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
TOP(mark(cons(z0, z1))) → c55(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
TOP(mark(recip(z0))) → c55(TOP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
TOP(mark(sqr(z0))) → c55(TOP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
TOP(mark(s(z0))) → c55(TOP(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
TOP(mark(0)) → c55(TOP(ok(0)), PROPER(0))
382.08/118.42
TOP(mark(add(z0, z1))) → c55(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
TOP(mark(dbl(z0))) → c55(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
TOP(mark(first(z0, z1))) → c55(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
TOP(mark(nil)) → c55(TOP(ok(nil)), PROPER(nil))
382.08/118.42
TOP(mark(half(z0))) → c55(TOP(half(proper(z0))), PROPER(half(z0)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
382.08/118.42
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
382.08/118.42
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
382.08/118.42
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
382.08/118.42
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.42
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.42
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.42
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.42
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.42
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.42
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.42
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.42
S(mark(z0)) → c32(S(z0))
382.08/118.42
S(ok(z0)) → c33(S(z0))
382.08/118.42
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.42
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.42
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.42
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.42
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.42
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.42
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.42
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.42
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.42
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.42
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
382.08/118.42
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
382.08/118.42
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
382.08/118.42
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
382.08/118.42
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
382.08/118.42
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
382.08/118.42
ACTIVE(terms(z0)) → c1(SQR(z0))
382.08/118.42
ACTIVE(terms(z0)) → c1(S(z0))
382.08/118.42
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
382.08/118.42
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
382.08/118.42
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
382.08/118.42
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.42
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
382.08/118.42
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
382.08/118.42
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
382.08/118.42
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
382.08/118.42
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.42
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
382.08/118.42
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
382.08/118.42
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
382.08/118.42
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
382.08/118.42
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
382.08/118.42
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
382.08/118.42
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.42
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
382.08/118.42
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
382.08/118.42
ACTIVE(s(half(0))) → c17(S(mark(0)))
382.08/118.42
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
382.08/118.42
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
382.08/118.42
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
382.08/118.42
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
382.08/118.42
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(terms(0)) → c44(TERMS(ok(0)))
382.08/118.42
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
382.08/118.42
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.42
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.42
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.42
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.42
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.42
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.42
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.42
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.42
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
382.08/118.42
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
382.08/118.42
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(recip(0)) → c46(RECIP(ok(0)))
382.08/118.42
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
382.08/118.42
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(sqr(0)) → c47(SQR(ok(0)))
382.08/118.42
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
382.08/118.42
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(s(0)) → c48(S(ok(0)))
382.08/118.42
PROPER(s(nil)) → c48(S(ok(nil)))
382.08/118.42
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.42
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.42
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.42
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.42
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.42
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.42
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.42
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.42
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.42
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.42
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.42
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.42
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.42
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.42
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
382.08/118.42
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
382.08/118.42
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(dbl(0)) → c51(DBL(ok(0)))
382.08/118.42
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
382.08/118.42
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.42
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.42
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.42
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.42
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.42
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.42
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.42
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.42
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.42
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.42
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.42
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.42
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.42
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.42
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0))
382.08/118.42
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0))
382.08/118.42
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(half(terms(z0))) → c54(HALF(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(half(cons(z0, z1))) → c54(HALF(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(half(recip(z0))) → c54(HALF(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(half(sqr(z0))) → c54(HALF(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(half(s(z0))) → c54(HALF(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(half(add(z0, z1))) → c54(HALF(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(half(dbl(z0))) → c54(HALF(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(half(first(z0, z1))) → c54(HALF(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(half(half(z0))) → c54(HALF(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(half(0)) → c54(HALF(ok(0)))
382.08/118.42
PROPER(half(nil)) → c54(HALF(ok(nil)))
382.08/118.42
TOP(mark(terms(z0))) → c55(TOP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
TOP(mark(cons(z0, z1))) → c55(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
TOP(mark(recip(z0))) → c55(TOP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
TOP(mark(sqr(z0))) → c55(TOP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
TOP(mark(s(z0))) → c55(TOP(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
TOP(mark(0)) → c55(TOP(ok(0)), PROPER(0))
382.08/118.42
TOP(mark(add(z0, z1))) → c55(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
TOP(mark(dbl(z0))) → c55(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
TOP(mark(first(z0, z1))) → c55(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
TOP(mark(nil)) → c55(TOP(ok(nil)), PROPER(nil))
382.08/118.42
TOP(mark(half(z0))) → c55(TOP(half(proper(z0))), PROPER(half(z0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, TOP, PROPER
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c54, c54, c55
382.08/118.42
382.08/118.42
(67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
382.08/118.42
382.08/118.42
(68) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.42
active(sqr(0)) → mark(0)
382.08/118.42
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.42
active(dbl(0)) → mark(0)
382.08/118.42
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.42
active(add(0, z0)) → mark(z0)
382.08/118.42
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.42
active(first(0, z0)) → mark(nil)
382.08/118.42
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.42
active(half(0)) → mark(0)
382.08/118.42
active(half(s(0))) → mark(0)
382.08/118.42
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.42
active(half(dbl(z0))) → mark(z0)
382.08/118.42
active(terms(z0)) → terms(active(z0))
382.08/118.42
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.42
active(recip(z0)) → recip(active(z0))
382.08/118.42
active(sqr(z0)) → sqr(active(z0))
382.08/118.42
active(s(z0)) → s(active(z0))
382.08/118.42
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.42
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.42
active(dbl(z0)) → dbl(active(z0))
382.08/118.42
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.42
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.42
active(half(z0)) → half(active(z0))
382.08/118.42
terms(mark(z0)) → mark(terms(z0))
382.08/118.42
terms(ok(z0)) → ok(terms(z0))
382.08/118.42
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.42
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.42
recip(mark(z0)) → mark(recip(z0))
382.08/118.42
recip(ok(z0)) → ok(recip(z0))
382.08/118.42
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.42
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.42
s(mark(z0)) → mark(s(z0))
382.08/118.42
s(ok(z0)) → ok(s(z0))
382.08/118.42
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.42
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.42
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.42
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.42
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.42
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.42
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.42
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.42
half(mark(z0)) → mark(half(z0))
382.08/118.42
half(ok(z0)) → ok(half(z0))
382.08/118.42
proper(terms(z0)) → terms(proper(z0))
382.08/118.42
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.42
proper(recip(z0)) → recip(proper(z0))
382.08/118.42
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.42
proper(s(z0)) → s(proper(z0))
382.08/118.42
proper(0) → ok(0)
382.08/118.42
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.42
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.42
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.42
proper(nil) → ok(nil)
382.08/118.42
proper(half(z0)) → half(proper(z0))
382.08/118.42
top(mark(z0)) → top(proper(z0))
382.08/118.42
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
382.08/118.42
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
382.08/118.42
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
382.08/118.42
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
382.08/118.42
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.42
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.42
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.42
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.42
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.42
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.42
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.42
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.42
S(mark(z0)) → c32(S(z0))
382.08/118.42
S(ok(z0)) → c33(S(z0))
382.08/118.42
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.42
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.42
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.42
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.42
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.42
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.42
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.42
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.42
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.42
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.42
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
382.08/118.42
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
382.08/118.42
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
382.08/118.42
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
382.08/118.42
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
382.08/118.42
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
382.08/118.42
ACTIVE(terms(z0)) → c1(SQR(z0))
382.08/118.42
ACTIVE(terms(z0)) → c1(S(z0))
382.08/118.42
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
382.08/118.42
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
382.08/118.42
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
382.08/118.42
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.42
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
382.08/118.42
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
382.08/118.42
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
382.08/118.42
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
382.08/118.42
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.42
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
382.08/118.42
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
382.08/118.42
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
382.08/118.42
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
382.08/118.42
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
382.08/118.42
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
382.08/118.42
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.42
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
382.08/118.42
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
382.08/118.42
ACTIVE(s(half(0))) → c17(S(mark(0)))
382.08/118.42
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
382.08/118.42
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
382.08/118.42
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
382.08/118.42
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
382.08/118.42
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(terms(0)) → c44(TERMS(ok(0)))
382.08/118.42
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
382.08/118.42
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.42
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.42
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.42
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.42
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.42
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.42
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.42
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.42
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
382.08/118.42
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
382.08/118.42
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(recip(0)) → c46(RECIP(ok(0)))
382.08/118.42
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
382.08/118.42
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(sqr(0)) → c47(SQR(ok(0)))
382.08/118.42
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
382.08/118.42
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(s(0)) → c48(S(ok(0)))
382.08/118.42
PROPER(s(nil)) → c48(S(ok(nil)))
382.08/118.42
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.42
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.42
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.42
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.42
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.42
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.42
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.42
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.42
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.42
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.42
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.42
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.42
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.42
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.42
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
382.08/118.42
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
382.08/118.42
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(dbl(0)) → c51(DBL(ok(0)))
382.08/118.42
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
382.08/118.42
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.42
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.42
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.42
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.42
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.42
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.42
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.42
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.42
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.42
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.42
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.42
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.42
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.42
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.42
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0))
382.08/118.42
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0))
382.08/118.42
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(half(terms(z0))) → c54(HALF(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(half(cons(z0, z1))) → c54(HALF(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(half(recip(z0))) → c54(HALF(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(half(sqr(z0))) → c54(HALF(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(half(s(z0))) → c54(HALF(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(half(add(z0, z1))) → c54(HALF(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(half(dbl(z0))) → c54(HALF(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(half(first(z0, z1))) → c54(HALF(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(half(half(z0))) → c54(HALF(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(half(0)) → c54(HALF(ok(0)))
382.08/118.42
PROPER(half(nil)) → c54(HALF(ok(nil)))
382.08/118.42
TOP(mark(terms(z0))) → c55(TOP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
TOP(mark(cons(z0, z1))) → c55(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
TOP(mark(recip(z0))) → c55(TOP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
TOP(mark(sqr(z0))) → c55(TOP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
TOP(mark(s(z0))) → c55(TOP(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
TOP(mark(add(z0, z1))) → c55(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
TOP(mark(dbl(z0))) → c55(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
TOP(mark(first(z0, z1))) → c55(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
TOP(mark(half(z0))) → c55(TOP(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
TOP(mark(0)) → c55(TOP(ok(0)))
382.08/118.42
TOP(mark(nil)) → c55(TOP(ok(nil)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
382.08/118.42
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
382.08/118.42
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
382.08/118.42
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
382.08/118.42
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.42
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.42
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.42
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.42
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.42
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.42
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.42
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.42
S(mark(z0)) → c32(S(z0))
382.08/118.42
S(ok(z0)) → c33(S(z0))
382.08/118.42
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.42
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.42
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.42
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.42
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.42
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.42
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.42
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.42
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.42
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.42
TOP(ok(z0)) → c56(TOP(active(z0)), ACTIVE(z0))
382.08/118.42
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
382.08/118.42
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
382.08/118.42
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
382.08/118.42
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
382.08/118.42
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
382.08/118.42
ACTIVE(terms(z0)) → c1(SQR(z0))
382.08/118.42
ACTIVE(terms(z0)) → c1(S(z0))
382.08/118.42
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
382.08/118.42
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
382.08/118.42
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
382.08/118.42
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.42
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
382.08/118.42
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
382.08/118.42
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
382.08/118.42
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
382.08/118.42
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.42
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
382.08/118.42
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
382.08/118.42
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
382.08/118.42
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
382.08/118.42
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
382.08/118.42
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
382.08/118.42
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.42
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
382.08/118.42
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
382.08/118.42
ACTIVE(s(half(0))) → c17(S(mark(0)))
382.08/118.42
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
382.08/118.42
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
382.08/118.42
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
382.08/118.42
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
382.08/118.42
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(terms(0)) → c44(TERMS(ok(0)))
382.08/118.42
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
382.08/118.42
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.42
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.42
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.42
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.42
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.42
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.42
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.42
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.42
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.42
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
382.08/118.42
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
382.08/118.42
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(recip(0)) → c46(RECIP(ok(0)))
382.08/118.42
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
382.08/118.42
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(sqr(0)) → c47(SQR(ok(0)))
382.08/118.42
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
382.08/118.42
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(s(0)) → c48(S(ok(0)))
382.08/118.42
PROPER(s(nil)) → c48(S(ok(nil)))
382.08/118.42
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.42
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.42
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.42
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.42
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.42
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.42
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.42
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.42
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.42
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.42
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.42
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.42
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.42
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.42
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
382.08/118.42
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
382.08/118.42
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(dbl(0)) → c51(DBL(ok(0)))
382.08/118.42
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
382.08/118.42
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.42
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.42
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.42
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.42
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.42
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.42
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.42
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.42
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.42
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.42
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.42
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.42
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.42
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.42
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.42
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0))
382.08/118.42
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0))
382.08/118.42
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(x1))
382.08/118.42
PROPER(half(terms(z0))) → c54(HALF(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
PROPER(half(cons(z0, z1))) → c54(HALF(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
PROPER(half(recip(z0))) → c54(HALF(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
PROPER(half(sqr(z0))) → c54(HALF(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
PROPER(half(s(z0))) → c54(HALF(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
PROPER(half(add(z0, z1))) → c54(HALF(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
PROPER(half(dbl(z0))) → c54(HALF(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
PROPER(half(first(z0, z1))) → c54(HALF(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
PROPER(half(half(z0))) → c54(HALF(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
PROPER(half(0)) → c54(HALF(ok(0)))
382.08/118.42
PROPER(half(nil)) → c54(HALF(ok(nil)))
382.08/118.42
TOP(mark(terms(z0))) → c55(TOP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.42
TOP(mark(cons(z0, z1))) → c55(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.42
TOP(mark(recip(z0))) → c55(TOP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.42
TOP(mark(sqr(z0))) → c55(TOP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.42
TOP(mark(s(z0))) → c55(TOP(s(proper(z0))), PROPER(s(z0)))
382.08/118.42
TOP(mark(add(z0, z1))) → c55(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.42
TOP(mark(dbl(z0))) → c55(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.42
TOP(mark(first(z0, z1))) → c55(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.42
TOP(mark(half(z0))) → c55(TOP(half(proper(z0))), PROPER(half(z0)))
382.08/118.42
TOP(mark(0)) → c55(TOP(ok(0)))
382.08/118.42
TOP(mark(nil)) → c55(TOP(ok(nil)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, TOP, PROPER
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c56, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c54, c54, c55, c55
382.08/118.42
382.08/118.42
(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
TOP(
ok(
z0)) →
c56(
TOP(
active(
z0)),
ACTIVE(
z0)) by
TOP(ok(terms(z0))) → c56(TOP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
TOP(ok(sqr(0))) → c56(TOP(mark(0)), ACTIVE(sqr(0)))
382.08/118.42
TOP(ok(sqr(s(z0)))) → c56(TOP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
TOP(ok(dbl(0))) → c56(TOP(mark(0)), ACTIVE(dbl(0)))
382.08/118.42
TOP(ok(dbl(s(z0)))) → c56(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
TOP(ok(add(0, z0))) → c56(TOP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
TOP(ok(add(s(z0), z1))) → c56(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
TOP(ok(first(0, z0))) → c56(TOP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
TOP(ok(first(s(z0), cons(z1, z2)))) → c56(TOP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
TOP(ok(half(0))) → c56(TOP(mark(0)), ACTIVE(half(0)))
382.08/118.42
TOP(ok(half(s(0)))) → c56(TOP(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
TOP(ok(half(s(s(z0))))) → c56(TOP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
TOP(ok(half(dbl(z0)))) → c56(TOP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
TOP(ok(terms(z0))) → c56(TOP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
TOP(ok(cons(z0, z1))) → c56(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
TOP(ok(recip(z0))) → c56(TOP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
TOP(ok(sqr(z0))) → c56(TOP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
TOP(ok(s(z0))) → c56(TOP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
TOP(ok(add(z0, z1))) → c56(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
TOP(ok(add(z0, z1))) → c56(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
TOP(ok(dbl(z0))) → c56(TOP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
TOP(ok(first(z0, z1))) → c56(TOP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
TOP(ok(first(z0, z1))) → c56(TOP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
TOP(ok(half(z0))) → c56(TOP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
382.08/118.42
(70) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.42
active(sqr(0)) → mark(0)
382.08/118.42
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.42
active(dbl(0)) → mark(0)
382.08/118.42
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.42
active(add(0, z0)) → mark(z0)
382.08/118.42
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.42
active(first(0, z0)) → mark(nil)
382.08/118.42
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.42
active(half(0)) → mark(0)
382.08/118.42
active(half(s(0))) → mark(0)
382.08/118.42
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.42
active(half(dbl(z0))) → mark(z0)
382.08/118.42
active(terms(z0)) → terms(active(z0))
382.08/118.42
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.42
active(recip(z0)) → recip(active(z0))
382.08/118.42
active(sqr(z0)) → sqr(active(z0))
382.08/118.42
active(s(z0)) → s(active(z0))
382.08/118.42
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.42
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.42
active(dbl(z0)) → dbl(active(z0))
382.08/118.42
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.42
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.42
active(half(z0)) → half(active(z0))
382.08/118.42
terms(mark(z0)) → mark(terms(z0))
382.08/118.42
terms(ok(z0)) → ok(terms(z0))
382.08/118.42
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.42
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.42
recip(mark(z0)) → mark(recip(z0))
382.08/118.42
recip(ok(z0)) → ok(recip(z0))
382.08/118.42
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.42
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.42
s(mark(z0)) → mark(s(z0))
382.08/118.42
s(ok(z0)) → ok(s(z0))
382.08/118.42
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.42
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.42
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.42
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.42
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.42
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.42
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.42
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.42
half(mark(z0)) → mark(half(z0))
382.08/118.42
half(ok(z0)) → ok(half(z0))
382.08/118.42
proper(terms(z0)) → terms(proper(z0))
382.08/118.42
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.42
proper(recip(z0)) → recip(proper(z0))
382.08/118.42
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.42
proper(s(z0)) → s(proper(z0))
382.08/118.42
proper(0) → ok(0)
382.08/118.42
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.42
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.42
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.42
proper(nil) → ok(nil)
382.08/118.42
proper(half(z0)) → half(proper(z0))
382.08/118.42
top(mark(z0)) → top(proper(z0))
382.08/118.42
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
382.08/118.42
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
382.08/118.42
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
382.08/118.42
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
382.08/118.42
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.42
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.42
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.42
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.42
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.42
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.42
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.42
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.42
S(mark(z0)) → c32(S(z0))
382.08/118.42
S(ok(z0)) → c33(S(z0))
382.08/118.42
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.42
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.42
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.42
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.42
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.42
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.42
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.42
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.42
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.42
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.42
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
382.08/118.42
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
382.08/118.42
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
382.08/118.42
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
382.08/118.42
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
382.08/118.42
ACTIVE(terms(z0)) → c1(SQR(z0))
382.08/118.42
ACTIVE(terms(z0)) → c1(S(z0))
382.08/118.42
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
382.08/118.42
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
382.08/118.42
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.42
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.42
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.42
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
382.08/118.42
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
382.08/118.42
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
382.08/118.42
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
382.08/118.42
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
382.08/118.42
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
382.08/118.42
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.42
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
382.08/118.42
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
382.08/118.42
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
382.08/118.42
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
382.08/118.42
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
382.08/118.42
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
382.08/118.42
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
382.08/118.42
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
382.08/118.42
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
382.08/118.43
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.43
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
382.08/118.43
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
382.08/118.43
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
382.08/118.43
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
382.08/118.43
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.43
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
382.08/118.43
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
382.08/118.43
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
382.08/118.43
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
382.08/118.43
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
382.08/118.43
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
382.08/118.43
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.43
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
382.08/118.43
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
382.08/118.43
ACTIVE(s(half(0))) → c17(S(mark(0)))
382.08/118.43
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
382.08/118.43
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
382.08/118.43
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
382.08/118.43
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
382.08/118.43
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(terms(0)) → c44(TERMS(ok(0)))
382.08/118.43
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
382.08/118.43
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.43
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.43
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.43
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.43
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.43
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.43
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.43
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.43
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
382.08/118.43
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
382.08/118.43
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(recip(0)) → c46(RECIP(ok(0)))
382.08/118.43
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
382.08/118.43
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(sqr(0)) → c47(SQR(ok(0)))
382.08/118.43
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
382.08/118.43
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(s(0)) → c48(S(ok(0)))
382.08/118.43
PROPER(s(nil)) → c48(S(ok(nil)))
382.08/118.43
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.43
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.43
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.43
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.43
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.43
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.43
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.43
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.43
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.43
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.43
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.43
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.43
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.43
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.43
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
382.08/118.43
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
382.08/118.43
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(dbl(0)) → c51(DBL(ok(0)))
382.08/118.43
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
382.08/118.43
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.43
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.43
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.43
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.43
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.43
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.43
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.43
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.43
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.43
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.43
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.43
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.43
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.43
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.43
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0))
382.08/118.43
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0))
382.08/118.43
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(half(terms(z0))) → c54(HALF(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(half(cons(z0, z1))) → c54(HALF(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(half(recip(z0))) → c54(HALF(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(half(sqr(z0))) → c54(HALF(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(half(s(z0))) → c54(HALF(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(half(add(z0, z1))) → c54(HALF(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(half(dbl(z0))) → c54(HALF(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(half(first(z0, z1))) → c54(HALF(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(half(half(z0))) → c54(HALF(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(half(0)) → c54(HALF(ok(0)))
382.08/118.43
PROPER(half(nil)) → c54(HALF(ok(nil)))
382.08/118.43
TOP(mark(terms(z0))) → c55(TOP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
TOP(mark(cons(z0, z1))) → c55(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
TOP(mark(recip(z0))) → c55(TOP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
TOP(mark(sqr(z0))) → c55(TOP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
TOP(mark(s(z0))) → c55(TOP(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
TOP(mark(add(z0, z1))) → c55(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
TOP(mark(dbl(z0))) → c55(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
TOP(mark(first(z0, z1))) → c55(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
TOP(mark(half(z0))) → c55(TOP(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
TOP(mark(0)) → c55(TOP(ok(0)))
382.08/118.43
TOP(mark(nil)) → c55(TOP(ok(nil)))
382.08/118.43
TOP(ok(terms(z0))) → c56(TOP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
TOP(ok(sqr(0))) → c56(TOP(mark(0)), ACTIVE(sqr(0)))
382.08/118.43
TOP(ok(sqr(s(z0)))) → c56(TOP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
TOP(ok(dbl(0))) → c56(TOP(mark(0)), ACTIVE(dbl(0)))
382.08/118.43
TOP(ok(dbl(s(z0)))) → c56(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
TOP(ok(add(0, z0))) → c56(TOP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
TOP(ok(add(s(z0), z1))) → c56(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
TOP(ok(first(0, z0))) → c56(TOP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
TOP(ok(first(s(z0), cons(z1, z2)))) → c56(TOP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
TOP(ok(half(0))) → c56(TOP(mark(0)), ACTIVE(half(0)))
382.08/118.43
TOP(ok(half(s(0)))) → c56(TOP(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
TOP(ok(half(s(s(z0))))) → c56(TOP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
TOP(ok(half(dbl(z0)))) → c56(TOP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
TOP(ok(terms(z0))) → c56(TOP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
TOP(ok(cons(z0, z1))) → c56(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
TOP(ok(recip(z0))) → c56(TOP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
TOP(ok(sqr(z0))) → c56(TOP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
TOP(ok(s(z0))) → c56(TOP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
TOP(ok(add(z0, z1))) → c56(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
TOP(ok(add(z0, z1))) → c56(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
TOP(ok(dbl(z0))) → c56(TOP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
TOP(ok(first(z0, z1))) → c56(TOP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
TOP(ok(first(z0, z1))) → c56(TOP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
TOP(ok(half(z0))) → c56(TOP(half(active(z0))), ACTIVE(half(z0)))
S tuples:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
382.08/118.43
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
382.08/118.43
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
382.08/118.43
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
382.08/118.43
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.43
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.43
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.43
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.43
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.43
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.43
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.43
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.43
S(mark(z0)) → c32(S(z0))
382.08/118.43
S(ok(z0)) → c33(S(z0))
382.08/118.43
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.43
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.43
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.43
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.43
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.43
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.43
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.43
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.43
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.43
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.43
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
382.08/118.43
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
382.08/118.43
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
382.08/118.43
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
382.08/118.43
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
382.08/118.43
ACTIVE(terms(z0)) → c1(SQR(z0))
382.08/118.43
ACTIVE(terms(z0)) → c1(S(z0))
382.08/118.43
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
382.08/118.43
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
382.08/118.43
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
382.08/118.43
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.43
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
382.08/118.43
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
382.08/118.43
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
382.08/118.43
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
382.08/118.43
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.43
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
382.08/118.43
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
382.08/118.43
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
382.08/118.43
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
382.08/118.43
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
382.08/118.43
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
382.08/118.43
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.43
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
382.08/118.43
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
382.08/118.43
ACTIVE(s(half(0))) → c17(S(mark(0)))
382.08/118.43
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
382.08/118.43
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
382.08/118.43
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
382.08/118.43
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
382.08/118.43
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(terms(0)) → c44(TERMS(ok(0)))
382.08/118.43
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
382.08/118.43
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.43
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.43
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.43
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.43
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.43
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.43
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.43
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.43
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
382.08/118.43
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
382.08/118.43
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(recip(0)) → c46(RECIP(ok(0)))
382.08/118.43
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
382.08/118.43
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(sqr(0)) → c47(SQR(ok(0)))
382.08/118.43
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
382.08/118.43
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(s(0)) → c48(S(ok(0)))
382.08/118.43
PROPER(s(nil)) → c48(S(ok(nil)))
382.08/118.43
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.43
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.43
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.43
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.43
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.43
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.43
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.43
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.43
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.43
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.43
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.43
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.43
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.43
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.43
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
382.08/118.43
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
382.08/118.43
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(dbl(0)) → c51(DBL(ok(0)))
382.08/118.43
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
382.08/118.43
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.43
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.43
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.43
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.43
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.43
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.43
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.43
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.43
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.43
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.43
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.43
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.43
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.43
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.43
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0))
382.08/118.43
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0))
382.08/118.43
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(half(terms(z0))) → c54(HALF(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(half(cons(z0, z1))) → c54(HALF(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(half(recip(z0))) → c54(HALF(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(half(sqr(z0))) → c54(HALF(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(half(s(z0))) → c54(HALF(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(half(add(z0, z1))) → c54(HALF(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(half(dbl(z0))) → c54(HALF(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(half(first(z0, z1))) → c54(HALF(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(half(half(z0))) → c54(HALF(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(half(0)) → c54(HALF(ok(0)))
382.08/118.43
PROPER(half(nil)) → c54(HALF(ok(nil)))
382.08/118.43
TOP(mark(terms(z0))) → c55(TOP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
TOP(mark(cons(z0, z1))) → c55(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
TOP(mark(recip(z0))) → c55(TOP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
TOP(mark(sqr(z0))) → c55(TOP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
TOP(mark(s(z0))) → c55(TOP(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
TOP(mark(add(z0, z1))) → c55(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
TOP(mark(dbl(z0))) → c55(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
TOP(mark(first(z0, z1))) → c55(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
TOP(mark(half(z0))) → c55(TOP(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
TOP(mark(0)) → c55(TOP(ok(0)))
382.08/118.43
TOP(mark(nil)) → c55(TOP(ok(nil)))
382.08/118.43
TOP(ok(terms(z0))) → c56(TOP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
TOP(ok(sqr(0))) → c56(TOP(mark(0)), ACTIVE(sqr(0)))
382.08/118.43
TOP(ok(sqr(s(z0)))) → c56(TOP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
TOP(ok(dbl(0))) → c56(TOP(mark(0)), ACTIVE(dbl(0)))
382.08/118.43
TOP(ok(dbl(s(z0)))) → c56(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
TOP(ok(add(0, z0))) → c56(TOP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
TOP(ok(add(s(z0), z1))) → c56(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
TOP(ok(first(0, z0))) → c56(TOP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
TOP(ok(first(s(z0), cons(z1, z2)))) → c56(TOP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
TOP(ok(half(0))) → c56(TOP(mark(0)), ACTIVE(half(0)))
382.08/118.43
TOP(ok(half(s(0)))) → c56(TOP(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
TOP(ok(half(s(s(z0))))) → c56(TOP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
TOP(ok(half(dbl(z0)))) → c56(TOP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
TOP(ok(terms(z0))) → c56(TOP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
TOP(ok(cons(z0, z1))) → c56(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
TOP(ok(recip(z0))) → c56(TOP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
TOP(ok(sqr(z0))) → c56(TOP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
TOP(ok(s(z0))) → c56(TOP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
TOP(ok(add(z0, z1))) → c56(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
TOP(ok(add(z0, z1))) → c56(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
TOP(ok(dbl(z0))) → c56(TOP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
TOP(ok(first(z0, z1))) → c56(TOP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
TOP(ok(first(z0, z1))) → c56(TOP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
TOP(ok(half(z0))) → c56(TOP(half(active(z0))), ACTIVE(half(z0)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, PROPER, TOP
Compound Symbols:
c18, c19, c21, c22, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c4, c6, c11, c1, c13, c14, c15, c16, c13, c14, c15, c16, c17, c17, c20, c20, c23, c23, c44, c44, c45, c45, c46, c46, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c54, c54, c55, c55, c56
382.08/118.43
382.08/118.43
(71) CdtUnreachableProof (EQUIVALENT transformation)
The following tuples could be removed as they are not reachable from basic start terms:
ACTIVE(add(z0, z1)) → c18(ADD(active(z0), z1), ACTIVE(z0))
382.08/118.43
ACTIVE(add(z0, z1)) → c19(ADD(z0, active(z1)), ACTIVE(z1))
382.08/118.43
ACTIVE(first(z0, z1)) → c21(FIRST(active(z0), z1), ACTIVE(z0))
382.08/118.43
ACTIVE(first(z0, z1)) → c22(FIRST(z0, active(z1)), ACTIVE(z1))
382.08/118.43
ACTIVE(dbl(s(z0))) → c4(DBL(z0))
382.08/118.43
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))
382.08/118.43
ACTIVE(half(s(s(z0)))) → c11(HALF(z0))
382.08/118.43
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
382.08/118.43
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
382.08/118.43
ACTIVE(terms(z0)) → c1(SQR(z0))
382.08/118.43
ACTIVE(terms(z0)) → c1(S(z0))
382.08/118.43
ACTIVE(sqr(s(z0))) → c1(SQR(z0))
382.08/118.43
ACTIVE(sqr(s(z0))) → c1(DBL(z0))
382.08/118.43
ACTIVE(terms(terms(z0))) → c13(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(terms(sqr(s(z0)))) → c13(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(terms(dbl(s(z0)))) → c13(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(terms(add(0, z0))) → c13(TERMS(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(terms(add(s(z0), z1))) → c13(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(terms(first(0, z0))) → c13(TERMS(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c13(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(terms(half(s(0)))) → c13(TERMS(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(terms(half(s(s(z0))))) → c13(TERMS(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(terms(half(dbl(z0)))) → c13(TERMS(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(terms(terms(z0))) → c13(TERMS(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(terms(cons(z0, z1))) → c13(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(terms(recip(z0))) → c13(TERMS(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(terms(sqr(z0))) → c13(TERMS(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(terms(s(z0))) → c13(TERMS(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(terms(add(z0, z1))) → c13(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(terms(dbl(z0))) → c13(TERMS(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(terms(first(z0, z1))) → c13(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(terms(half(z0))) → c13(TERMS(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(cons(terms(z0), x1)) → c14(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(cons(sqr(s(z0)), x1)) → c14(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(cons(dbl(s(z0)), x1)) → c14(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(cons(add(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(cons(add(s(z0), z1), x1)) → c14(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(cons(first(0, z0), x1)) → c14(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c14(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(cons(half(s(0)), x1)) → c14(CONS(mark(0), x1), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(cons(half(s(s(z0))), x1)) → c14(CONS(mark(s(half(z0))), x1), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(cons(half(dbl(z0)), x1)) → c14(CONS(mark(z0), x1), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(cons(terms(z0), x1)) → c14(CONS(terms(active(z0)), x1), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(cons(recip(z0), x1)) → c14(CONS(recip(active(z0)), x1), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(cons(sqr(z0), x1)) → c14(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(cons(add(z0, z1), x1)) → c14(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(cons(dbl(z0), x1)) → c14(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(cons(first(z0, z1), x1)) → c14(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(cons(half(z0), x1)) → c14(CONS(half(active(z0)), x1), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(recip(terms(z0))) → c15(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(recip(sqr(s(z0)))) → c15(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(recip(dbl(s(z0)))) → c15(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(recip(add(0, z0))) → c15(RECIP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(recip(add(s(z0), z1))) → c15(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(recip(first(0, z0))) → c15(RECIP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c15(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(recip(half(s(0)))) → c15(RECIP(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(recip(half(s(s(z0))))) → c15(RECIP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(recip(half(dbl(z0)))) → c15(RECIP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(recip(terms(z0))) → c15(RECIP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(recip(cons(z0, z1))) → c15(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(recip(recip(z0))) → c15(RECIP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(recip(sqr(z0))) → c15(RECIP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(recip(s(z0))) → c15(RECIP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(recip(add(z0, z1))) → c15(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(recip(dbl(z0))) → c15(RECIP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(recip(first(z0, z1))) → c15(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(recip(half(z0))) → c15(RECIP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(sqr(terms(z0))) → c16(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(sqr(sqr(s(z0)))) → c16(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(sqr(dbl(s(z0)))) → c16(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(sqr(add(0, z0))) → c16(SQR(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(sqr(add(s(z0), z1))) → c16(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(sqr(first(0, z0))) → c16(SQR(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c16(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(sqr(half(s(0)))) → c16(SQR(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(sqr(half(s(s(z0))))) → c16(SQR(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(sqr(half(dbl(z0)))) → c16(SQR(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(sqr(terms(z0))) → c16(SQR(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(sqr(cons(z0, z1))) → c16(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(sqr(recip(z0))) → c16(SQR(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(sqr(sqr(z0))) → c16(SQR(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(sqr(s(z0))) → c16(SQR(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(sqr(add(z0, z1))) → c16(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(sqr(dbl(z0))) → c16(SQR(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(sqr(first(z0, z1))) → c16(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(sqr(half(z0))) → c16(SQR(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(terms(sqr(0))) → c13(TERMS(mark(0)))
382.08/118.43
ACTIVE(cons(sqr(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.43
ACTIVE(recip(sqr(0))) → c15(RECIP(mark(0)))
382.08/118.43
ACTIVE(sqr(sqr(0))) → c16(SQR(mark(0)))
382.08/118.43
ACTIVE(s(terms(z0))) → c17(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(s(sqr(s(z0)))) → c17(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(s(dbl(s(z0)))) → c17(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(s(add(0, z0))) → c17(S(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(s(add(s(z0), z1))) → c17(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(s(first(0, z0))) → c17(S(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c17(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(s(half(s(0)))) → c17(S(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(s(half(s(s(z0))))) → c17(S(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(s(half(dbl(z0)))) → c17(S(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(s(terms(z0))) → c17(S(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(s(cons(z0, z1))) → c17(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(s(recip(z0))) → c17(S(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(s(sqr(z0))) → c17(S(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(s(add(z0, z1))) → c17(S(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(s(add(z0, z1))) → c17(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(s(dbl(z0))) → c17(S(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(s(first(z0, z1))) → c17(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(s(first(z0, z1))) → c17(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(s(half(z0))) → c17(S(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(s(sqr(0))) → c17(S(mark(0)))
382.08/118.43
ACTIVE(dbl(terms(z0))) → c20(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(dbl(sqr(s(z0)))) → c20(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(dbl(dbl(s(z0)))) → c20(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(dbl(add(0, z0))) → c20(DBL(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(dbl(add(s(z0), z1))) → c20(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(dbl(first(0, z0))) → c20(DBL(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c20(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(dbl(half(s(0)))) → c20(DBL(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(dbl(half(s(s(z0))))) → c20(DBL(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(dbl(half(dbl(z0)))) → c20(DBL(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(dbl(terms(z0))) → c20(DBL(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(dbl(cons(z0, z1))) → c20(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(dbl(recip(z0))) → c20(DBL(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(dbl(sqr(z0))) → c20(DBL(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(dbl(s(z0))) → c20(DBL(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(dbl(add(z0, z1))) → c20(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(dbl(dbl(z0))) → c20(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(dbl(first(z0, z1))) → c20(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(dbl(half(z0))) → c20(DBL(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(terms(dbl(0))) → c13(TERMS(mark(0)))
382.08/118.43
ACTIVE(cons(dbl(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.43
ACTIVE(recip(dbl(0))) → c15(RECIP(mark(0)))
382.08/118.43
ACTIVE(sqr(dbl(0))) → c16(SQR(mark(0)))
382.08/118.43
ACTIVE(s(dbl(0))) → c17(S(mark(0)))
382.08/118.43
ACTIVE(dbl(sqr(0))) → c20(DBL(mark(0)))
382.08/118.43
ACTIVE(dbl(dbl(0))) → c20(DBL(mark(0)))
382.08/118.43
ACTIVE(half(terms(z0))) → c23(HALF(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(half(sqr(s(z0)))) → c23(HALF(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
ACTIVE(half(dbl(s(z0)))) → c23(HALF(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
ACTIVE(half(add(0, z0))) → c23(HALF(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
ACTIVE(half(add(s(z0), z1))) → c23(HALF(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
ACTIVE(half(first(0, z0))) → c23(HALF(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
ACTIVE(half(first(s(z0), cons(z1, z2)))) → c23(HALF(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
ACTIVE(half(half(s(0)))) → c23(HALF(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
ACTIVE(half(half(s(s(z0))))) → c23(HALF(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
ACTIVE(half(half(dbl(z0)))) → c23(HALF(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
ACTIVE(half(terms(z0))) → c23(HALF(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
ACTIVE(half(cons(z0, z1))) → c23(HALF(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
ACTIVE(half(recip(z0))) → c23(HALF(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
ACTIVE(half(sqr(z0))) → c23(HALF(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
ACTIVE(half(s(z0))) → c23(HALF(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
ACTIVE(half(add(z0, z1))) → c23(HALF(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(half(add(z0, z1))) → c23(HALF(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
ACTIVE(half(dbl(z0))) → c23(HALF(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
ACTIVE(half(first(z0, z1))) → c23(HALF(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(half(first(z0, z1))) → c23(HALF(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
ACTIVE(half(half(z0))) → c23(HALF(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
ACTIVE(terms(half(0))) → c13(TERMS(mark(0)))
382.08/118.43
ACTIVE(cons(half(0), x1)) → c14(CONS(mark(0), x1))
382.08/118.43
ACTIVE(recip(half(0))) → c15(RECIP(mark(0)))
382.08/118.43
ACTIVE(sqr(half(0))) → c16(SQR(mark(0)))
382.08/118.43
ACTIVE(s(half(0))) → c17(S(mark(0)))
382.08/118.43
ACTIVE(dbl(half(0))) → c20(DBL(mark(0)))
382.08/118.43
ACTIVE(half(sqr(0))) → c23(HALF(mark(0)))
382.08/118.43
ACTIVE(half(dbl(0))) → c23(HALF(mark(0)))
382.08/118.43
ACTIVE(half(half(0))) → c23(HALF(mark(0)))
382.08/118.43
PROPER(terms(terms(z0))) → c44(TERMS(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(terms(cons(z0, z1))) → c44(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(terms(recip(z0))) → c44(TERMS(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(terms(sqr(z0))) → c44(TERMS(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(terms(s(z0))) → c44(TERMS(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(terms(add(z0, z1))) → c44(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(terms(dbl(z0))) → c44(TERMS(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(terms(first(z0, z1))) → c44(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(terms(half(z0))) → c44(TERMS(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(terms(0)) → c44(TERMS(ok(0)))
382.08/118.43
PROPER(terms(nil)) → c44(TERMS(ok(nil)))
382.08/118.43
PROPER(cons(x0, terms(z0))) → c45(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.43
PROPER(cons(x0, cons(z0, z1))) → c45(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(cons(x0, recip(z0))) → c45(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.43
PROPER(cons(x0, sqr(z0))) → c45(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.43
PROPER(cons(x0, s(z0))) → c45(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.43
PROPER(cons(x0, add(z0, z1))) → c45(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.43
PROPER(cons(x0, dbl(z0))) → c45(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.43
PROPER(cons(x0, first(z0, z1))) → c45(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.43
PROPER(cons(x0, half(z0))) → c45(CONS(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.43
PROPER(cons(terms(z0), x1)) → c45(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(cons(z0, z1), x1)) → c45(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(cons(recip(z0), x1)) → c45(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(sqr(z0), x1)) → c45(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(s(z0), x1)) → c45(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(add(z0, z1), x1)) → c45(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(cons(dbl(z0), x1)) → c45(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(first(z0, z1), x1)) → c45(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(cons(half(z0), x1)) → c45(CONS(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.43
PROPER(cons(x0, 0)) → c45(CONS(proper(x0), ok(0)), PROPER(x0))
382.08/118.43
PROPER(cons(x0, nil)) → c45(CONS(proper(x0), ok(nil)), PROPER(x0))
382.08/118.43
PROPER(cons(0, x1)) → c45(CONS(ok(0), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(cons(nil, x1)) → c45(CONS(ok(nil), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(recip(terms(z0))) → c46(RECIP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(recip(cons(z0, z1))) → c46(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(recip(recip(z0))) → c46(RECIP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(recip(sqr(z0))) → c46(RECIP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(recip(s(z0))) → c46(RECIP(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(recip(add(z0, z1))) → c46(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(recip(dbl(z0))) → c46(RECIP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(recip(first(z0, z1))) → c46(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(recip(half(z0))) → c46(RECIP(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(recip(0)) → c46(RECIP(ok(0)))
382.08/118.43
PROPER(recip(nil)) → c46(RECIP(ok(nil)))
382.08/118.43
PROPER(sqr(terms(z0))) → c47(SQR(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(sqr(cons(z0, z1))) → c47(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(sqr(recip(z0))) → c47(SQR(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(sqr(sqr(z0))) → c47(SQR(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(sqr(s(z0))) → c47(SQR(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(sqr(add(z0, z1))) → c47(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(sqr(dbl(z0))) → c47(SQR(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(sqr(first(z0, z1))) → c47(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(sqr(half(z0))) → c47(SQR(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(sqr(0)) → c47(SQR(ok(0)))
382.08/118.43
PROPER(sqr(nil)) → c47(SQR(ok(nil)))
382.08/118.43
PROPER(s(terms(z0))) → c48(S(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(s(cons(z0, z1))) → c48(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(s(recip(z0))) → c48(S(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(s(sqr(z0))) → c48(S(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(s(s(z0))) → c48(S(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(s(add(z0, z1))) → c48(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(s(dbl(z0))) → c48(S(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(s(first(z0, z1))) → c48(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(s(half(z0))) → c48(S(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(s(0)) → c48(S(ok(0)))
382.08/118.43
PROPER(s(nil)) → c48(S(ok(nil)))
382.08/118.43
PROPER(add(x0, terms(z0))) → c50(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.43
PROPER(add(x0, cons(z0, z1))) → c50(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(add(x0, recip(z0))) → c50(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.43
PROPER(add(x0, sqr(z0))) → c50(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.43
PROPER(add(x0, s(z0))) → c50(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.43
PROPER(add(x0, add(z0, z1))) → c50(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.43
PROPER(add(x0, dbl(z0))) → c50(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.43
PROPER(add(x0, first(z0, z1))) → c50(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.43
PROPER(add(x0, half(z0))) → c50(ADD(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.43
PROPER(add(terms(z0), x1)) → c50(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.43
PROPER(add(cons(z0, z1), x1)) → c50(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(add(recip(z0), x1)) → c50(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.43
PROPER(add(sqr(z0), x1)) → c50(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.43
PROPER(add(s(z0), x1)) → c50(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.43
PROPER(add(add(z0, z1), x1)) → c50(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(add(dbl(z0), x1)) → c50(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.43
PROPER(add(first(z0, z1), x1)) → c50(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(add(half(z0), x1)) → c50(ADD(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.43
PROPER(add(x0, 0)) → c50(ADD(proper(x0), ok(0)), PROPER(x0))
382.08/118.43
PROPER(add(x0, nil)) → c50(ADD(proper(x0), ok(nil)), PROPER(x0))
382.08/118.43
PROPER(add(0, x1)) → c50(ADD(ok(0), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(add(nil, x1)) → c50(ADD(ok(nil), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(dbl(terms(z0))) → c51(DBL(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(dbl(cons(z0, z1))) → c51(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(dbl(recip(z0))) → c51(DBL(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(dbl(sqr(z0))) → c51(DBL(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(dbl(s(z0))) → c51(DBL(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(dbl(add(z0, z1))) → c51(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(dbl(dbl(z0))) → c51(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(dbl(first(z0, z1))) → c51(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(dbl(half(z0))) → c51(DBL(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(dbl(0)) → c51(DBL(ok(0)))
382.08/118.43
PROPER(dbl(nil)) → c51(DBL(ok(nil)))
382.08/118.43
PROPER(first(x0, terms(z0))) → c52(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0)))
382.08/118.43
PROPER(first(x0, cons(z0, z1))) → c52(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(first(x0, recip(z0))) → c52(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0)))
382.08/118.43
PROPER(first(x0, sqr(z0))) → c52(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0)))
382.08/118.43
PROPER(first(x0, s(z0))) → c52(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
382.08/118.43
PROPER(first(x0, add(z0, z1))) → c52(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1)))
382.08/118.43
PROPER(first(x0, dbl(z0))) → c52(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
382.08/118.43
PROPER(first(x0, first(z0, z1))) → c52(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1)))
382.08/118.43
PROPER(first(x0, half(z0))) → c52(FIRST(proper(x0), half(proper(z0))), PROPER(x0), PROPER(half(z0)))
382.08/118.43
PROPER(first(terms(z0), x1)) → c52(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1))
382.08/118.43
PROPER(first(cons(z0, z1), x1)) → c52(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(first(recip(z0), x1)) → c52(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1))
382.08/118.43
PROPER(first(sqr(z0), x1)) → c52(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1))
382.08/118.43
PROPER(first(s(z0), x1)) → c52(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
382.08/118.43
PROPER(first(add(z0, z1), x1)) → c52(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(first(dbl(z0), x1)) → c52(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
382.08/118.43
PROPER(first(first(z0, z1), x1)) → c52(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1))
382.08/118.43
PROPER(first(half(z0), x1)) → c52(FIRST(half(proper(z0)), proper(x1)), PROPER(half(z0)), PROPER(x1))
382.08/118.43
PROPER(first(x0, 0)) → c52(FIRST(proper(x0), ok(0)), PROPER(x0))
382.08/118.43
PROPER(first(x0, nil)) → c52(FIRST(proper(x0), ok(nil)), PROPER(x0))
382.08/118.43
PROPER(first(0, x1)) → c52(FIRST(ok(0), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(first(nil, x1)) → c52(FIRST(ok(nil), proper(x1)), PROPER(x1))
382.08/118.43
PROPER(half(terms(z0))) → c54(HALF(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
PROPER(half(cons(z0, z1))) → c54(HALF(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
PROPER(half(recip(z0))) → c54(HALF(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
PROPER(half(sqr(z0))) → c54(HALF(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
PROPER(half(s(z0))) → c54(HALF(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
PROPER(half(add(z0, z1))) → c54(HALF(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
PROPER(half(dbl(z0))) → c54(HALF(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
PROPER(half(first(z0, z1))) → c54(HALF(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
PROPER(half(half(z0))) → c54(HALF(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
PROPER(half(0)) → c54(HALF(ok(0)))
382.08/118.43
PROPER(half(nil)) → c54(HALF(ok(nil)))
382.08/118.43
TOP(mark(terms(z0))) → c55(TOP(terms(proper(z0))), PROPER(terms(z0)))
382.08/118.43
TOP(mark(cons(z0, z1))) → c55(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
382.08/118.43
TOP(mark(recip(z0))) → c55(TOP(recip(proper(z0))), PROPER(recip(z0)))
382.08/118.43
TOP(mark(sqr(z0))) → c55(TOP(sqr(proper(z0))), PROPER(sqr(z0)))
382.08/118.43
TOP(mark(s(z0))) → c55(TOP(s(proper(z0))), PROPER(s(z0)))
382.08/118.43
TOP(mark(add(z0, z1))) → c55(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))
382.08/118.43
TOP(mark(dbl(z0))) → c55(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
382.08/118.43
TOP(mark(first(z0, z1))) → c55(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1)))
382.08/118.43
TOP(mark(half(z0))) → c55(TOP(half(proper(z0))), PROPER(half(z0)))
382.08/118.43
TOP(ok(terms(z0))) → c56(TOP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0)))
382.08/118.43
TOP(ok(sqr(0))) → c56(TOP(mark(0)), ACTIVE(sqr(0)))
382.08/118.43
TOP(ok(sqr(s(z0)))) → c56(TOP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0))))
382.08/118.43
TOP(ok(dbl(0))) → c56(TOP(mark(0)), ACTIVE(dbl(0)))
382.08/118.43
TOP(ok(dbl(s(z0)))) → c56(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
382.08/118.43
TOP(ok(add(0, z0))) → c56(TOP(mark(z0)), ACTIVE(add(0, z0)))
382.08/118.43
TOP(ok(add(s(z0), z1))) → c56(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1)))
382.08/118.43
TOP(ok(first(0, z0))) → c56(TOP(mark(nil)), ACTIVE(first(0, z0)))
382.08/118.43
TOP(ok(first(s(z0), cons(z1, z2)))) → c56(TOP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
382.08/118.43
TOP(ok(half(0))) → c56(TOP(mark(0)), ACTIVE(half(0)))
382.08/118.43
TOP(ok(half(s(0)))) → c56(TOP(mark(0)), ACTIVE(half(s(0))))
382.08/118.43
TOP(ok(half(s(s(z0))))) → c56(TOP(mark(s(half(z0)))), ACTIVE(half(s(s(z0)))))
382.08/118.43
TOP(ok(half(dbl(z0)))) → c56(TOP(mark(z0)), ACTIVE(half(dbl(z0))))
382.08/118.43
TOP(ok(terms(z0))) → c56(TOP(terms(active(z0))), ACTIVE(terms(z0)))
382.08/118.43
TOP(ok(cons(z0, z1))) → c56(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
382.08/118.43
TOP(ok(recip(z0))) → c56(TOP(recip(active(z0))), ACTIVE(recip(z0)))
382.08/118.43
TOP(ok(sqr(z0))) → c56(TOP(sqr(active(z0))), ACTIVE(sqr(z0)))
382.08/118.43
TOP(ok(s(z0))) → c56(TOP(s(active(z0))), ACTIVE(s(z0)))
382.08/118.43
TOP(ok(add(z0, z1))) → c56(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1)))
382.08/118.43
TOP(ok(add(z0, z1))) → c56(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1)))
382.08/118.43
TOP(ok(dbl(z0))) → c56(TOP(dbl(active(z0))), ACTIVE(dbl(z0)))
382.08/118.43
TOP(ok(first(z0, z1))) → c56(TOP(first(active(z0), z1)), ACTIVE(first(z0, z1)))
382.08/118.43
TOP(ok(first(z0, z1))) → c56(TOP(first(z0, active(z1))), ACTIVE(first(z0, z1)))
382.08/118.43
TOP(ok(half(z0))) → c56(TOP(half(active(z0))), ACTIVE(half(z0)))
382.08/118.43
382.08/118.43
(72) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.43
active(sqr(0)) → mark(0)
382.08/118.43
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.43
active(dbl(0)) → mark(0)
382.08/118.43
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.43
active(add(0, z0)) → mark(z0)
382.08/118.43
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.43
active(first(0, z0)) → mark(nil)
382.08/118.43
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.43
active(half(0)) → mark(0)
382.08/118.43
active(half(s(0))) → mark(0)
382.08/118.43
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.43
active(half(dbl(z0))) → mark(z0)
382.08/118.43
active(terms(z0)) → terms(active(z0))
382.08/118.43
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.43
active(recip(z0)) → recip(active(z0))
382.08/118.43
active(sqr(z0)) → sqr(active(z0))
382.08/118.43
active(s(z0)) → s(active(z0))
382.08/118.43
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.43
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.43
active(dbl(z0)) → dbl(active(z0))
382.08/118.43
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.43
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.43
active(half(z0)) → half(active(z0))
382.08/118.43
terms(mark(z0)) → mark(terms(z0))
382.08/118.43
terms(ok(z0)) → ok(terms(z0))
382.08/118.43
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.43
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.43
recip(mark(z0)) → mark(recip(z0))
382.08/118.43
recip(ok(z0)) → ok(recip(z0))
382.08/118.43
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.43
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.43
s(mark(z0)) → mark(s(z0))
382.08/118.43
s(ok(z0)) → ok(s(z0))
382.08/118.43
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.43
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.43
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.43
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.43
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.43
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.43
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.43
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.43
half(mark(z0)) → mark(half(z0))
382.08/118.43
half(ok(z0)) → ok(half(z0))
382.08/118.43
proper(terms(z0)) → terms(proper(z0))
382.08/118.43
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.43
proper(recip(z0)) → recip(proper(z0))
382.08/118.43
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.43
proper(s(z0)) → s(proper(z0))
382.08/118.43
proper(0) → ok(0)
382.08/118.43
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.43
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.43
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.43
proper(nil) → ok(nil)
382.08/118.43
proper(half(z0)) → half(proper(z0))
382.08/118.43
top(mark(z0)) → top(proper(z0))
382.08/118.43
top(ok(z0)) → top(active(z0))
Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.43
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.43
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.43
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.43
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.43
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.43
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.43
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.43
S(mark(z0)) → c32(S(z0))
382.08/118.43
S(ok(z0)) → c33(S(z0))
382.08/118.43
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.43
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.43
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.43
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.43
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.43
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.43
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.43
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.43
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.43
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.43
TOP(mark(0)) → c55(TOP(ok(0)))
382.08/118.43
TOP(mark(nil)) → c55(TOP(ok(nil)))
S tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.43
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.43
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.43
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.43
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.43
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.43
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.43
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.43
S(mark(z0)) → c32(S(z0))
382.08/118.43
S(ok(z0)) → c33(S(z0))
382.08/118.43
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.43
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.43
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.43
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.43
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.43
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.43
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.43
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.43
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.43
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.43
TOP(mark(0)) → c55(TOP(ok(0)))
382.08/118.43
TOP(mark(nil)) → c55(TOP(ok(nil)))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, TOP
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c55
382.08/118.43
382.08/118.43
(73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
382.08/118.43
382.08/118.43
(74) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.43
active(sqr(0)) → mark(0)
382.08/118.43
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.43
active(dbl(0)) → mark(0)
382.08/118.43
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.43
active(add(0, z0)) → mark(z0)
382.08/118.43
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.43
active(first(0, z0)) → mark(nil)
382.08/118.43
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.43
active(half(0)) → mark(0)
382.08/118.43
active(half(s(0))) → mark(0)
382.08/118.43
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.43
active(half(dbl(z0))) → mark(z0)
382.08/118.43
active(terms(z0)) → terms(active(z0))
382.08/118.43
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.43
active(recip(z0)) → recip(active(z0))
382.08/118.43
active(sqr(z0)) → sqr(active(z0))
382.08/118.43
active(s(z0)) → s(active(z0))
382.08/118.43
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.43
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.43
active(dbl(z0)) → dbl(active(z0))
382.08/118.43
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.43
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.43
active(half(z0)) → half(active(z0))
382.08/118.43
terms(mark(z0)) → mark(terms(z0))
382.08/118.43
terms(ok(z0)) → ok(terms(z0))
382.08/118.43
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.43
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.43
recip(mark(z0)) → mark(recip(z0))
382.08/118.43
recip(ok(z0)) → ok(recip(z0))
382.08/118.43
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.43
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.43
s(mark(z0)) → mark(s(z0))
382.08/118.43
s(ok(z0)) → ok(s(z0))
382.08/118.43
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.43
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.43
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.43
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.43
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.43
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.43
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.43
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.43
half(mark(z0)) → mark(half(z0))
382.08/118.43
half(ok(z0)) → ok(half(z0))
382.08/118.43
proper(terms(z0)) → terms(proper(z0))
382.08/118.43
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.43
proper(recip(z0)) → recip(proper(z0))
382.08/118.43
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.43
proper(s(z0)) → s(proper(z0))
382.08/118.43
proper(0) → ok(0)
382.08/118.43
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.43
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.43
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.43
proper(nil) → ok(nil)
382.08/118.43
proper(half(z0)) → half(proper(z0))
382.08/118.43
top(mark(z0)) → top(proper(z0))
382.08/118.43
top(ok(z0)) → top(active(z0))
Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.43
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.43
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.43
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.43
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.43
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.43
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.43
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.43
S(mark(z0)) → c32(S(z0))
382.08/118.43
S(ok(z0)) → c33(S(z0))
382.08/118.43
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.43
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.43
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.43
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.43
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.43
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.43
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.43
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.43
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.43
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.43
TOP(mark(0)) → c55
382.08/118.43
TOP(mark(nil)) → c55
S tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.43
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.43
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.43
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.43
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.43
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.43
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.43
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.43
S(mark(z0)) → c32(S(z0))
382.08/118.43
S(ok(z0)) → c33(S(z0))
382.08/118.43
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.43
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.43
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.43
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.43
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.43
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.43
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.43
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.43
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.43
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.43
TOP(mark(0)) → c55
382.08/118.43
TOP(mark(nil)) → c55
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF, TOP
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c55
382.08/118.43
382.08/118.43
(75) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing nodes:
TOP(mark(0)) → c55
382.08/118.43
TOP(mark(nil)) → c55
382.08/118.43
382.08/118.43
(76) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.43
active(sqr(0)) → mark(0)
382.08/118.43
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.43
active(dbl(0)) → mark(0)
382.08/118.43
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.43
active(add(0, z0)) → mark(z0)
382.08/118.43
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.43
active(first(0, z0)) → mark(nil)
382.08/118.43
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.43
active(half(0)) → mark(0)
382.08/118.43
active(half(s(0))) → mark(0)
382.08/118.43
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.43
active(half(dbl(z0))) → mark(z0)
382.08/118.43
active(terms(z0)) → terms(active(z0))
382.08/118.43
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.43
active(recip(z0)) → recip(active(z0))
382.08/118.43
active(sqr(z0)) → sqr(active(z0))
382.08/118.43
active(s(z0)) → s(active(z0))
382.08/118.43
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.43
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.43
active(dbl(z0)) → dbl(active(z0))
382.08/118.43
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.43
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.43
active(half(z0)) → half(active(z0))
382.08/118.43
terms(mark(z0)) → mark(terms(z0))
382.08/118.43
terms(ok(z0)) → ok(terms(z0))
382.08/118.43
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.43
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.43
recip(mark(z0)) → mark(recip(z0))
382.08/118.43
recip(ok(z0)) → ok(recip(z0))
382.08/118.43
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.43
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.43
s(mark(z0)) → mark(s(z0))
382.08/118.43
s(ok(z0)) → ok(s(z0))
382.08/118.43
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.43
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.43
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.43
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.43
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.43
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.43
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.43
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.43
half(mark(z0)) → mark(half(z0))
382.08/118.43
half(ok(z0)) → ok(half(z0))
382.08/118.43
proper(terms(z0)) → terms(proper(z0))
382.08/118.43
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.43
proper(recip(z0)) → recip(proper(z0))
382.08/118.43
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.43
proper(s(z0)) → s(proper(z0))
382.08/118.43
proper(0) → ok(0)
382.08/118.43
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.43
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.43
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.43
proper(nil) → ok(nil)
382.08/118.43
proper(half(z0)) → half(proper(z0))
382.08/118.43
top(mark(z0)) → top(proper(z0))
382.08/118.43
top(ok(z0)) → top(active(z0))
Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.43
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.43
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.43
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.43
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.43
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.43
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.43
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.43
S(mark(z0)) → c32(S(z0))
382.08/118.43
S(ok(z0)) → c33(S(z0))
382.08/118.43
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.43
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.43
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.43
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.43
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.43
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.43
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.43
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.43
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.43
HALF(ok(z0)) → c43(HALF(z0))
S tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.43
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.43
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.43
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.43
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.43
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.43
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.43
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.43
S(mark(z0)) → c32(S(z0))
382.08/118.43
S(ok(z0)) → c33(S(z0))
382.08/118.43
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.43
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.43
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.43
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.43
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.43
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.43
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.43
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.43
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.43
HALF(ok(z0)) → c43(HALF(z0))
K tuples:none
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43
382.08/118.43
382.08/118.43
(77) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
S(mark(z0)) → c32(S(z0))
382.08/118.43
S(ok(z0)) → c33(S(z0))
We considered the (Usable) Rules:none
And the Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.43
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.43
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.43
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.43
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.43
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.43
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.43
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.43
S(mark(z0)) → c32(S(z0))
382.08/118.43
S(ok(z0)) → c33(S(z0))
382.08/118.43
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.43
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.43
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.43
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.43
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.43
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.43
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.43
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.43
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.43
HALF(ok(z0)) → c43(HALF(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
382.08/118.43
POL(ADD(x1, x2)) = 0
382.08/118.43
POL(CONS(x1, x2)) = 0
382.08/118.43
POL(DBL(x1)) = 0
382.08/118.43
POL(FIRST(x1, x2)) = 0
382.08/118.43
POL(HALF(x1)) = 0
382.08/118.43
POL(RECIP(x1)) = 0
382.08/118.43
POL(S(x1)) = x1
382.08/118.43
POL(SQR(x1)) = 0
382.08/118.43
POL(TERMS(x1)) = 0
382.08/118.43
POL(c24(x1)) = x1
382.08/118.43
POL(c25(x1)) = x1
382.08/118.43
POL(c26(x1)) = x1
382.08/118.43
POL(c27(x1)) = x1
382.08/118.43
POL(c28(x1)) = x1
382.08/118.43
POL(c29(x1)) = x1
382.08/118.43
POL(c30(x1)) = x1
382.08/118.43
POL(c31(x1)) = x1
382.08/118.43
POL(c32(x1)) = x1
382.08/118.43
POL(c33(x1)) = x1
382.08/118.43
POL(c34(x1)) = x1
382.08/118.43
POL(c35(x1)) = x1
382.08/118.43
POL(c36(x1)) = x1
382.08/118.43
POL(c37(x1)) = x1
382.08/118.43
POL(c38(x1)) = x1
382.08/118.43
POL(c39(x1)) = x1
382.08/118.43
POL(c40(x1)) = x1
382.08/118.43
POL(c41(x1)) = x1
382.08/118.43
POL(c42(x1)) = x1
382.08/118.43
POL(c43(x1)) = x1
382.08/118.43
POL(mark(x1)) = [2] + x1
382.08/118.43
POL(ok(x1)) = [1] + x1
382.08/118.43
382.08/118.43
(78) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.43
active(sqr(0)) → mark(0)
382.08/118.43
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.43
active(dbl(0)) → mark(0)
382.08/118.43
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.43
active(add(0, z0)) → mark(z0)
382.08/118.43
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.43
active(first(0, z0)) → mark(nil)
382.08/118.43
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.43
active(half(0)) → mark(0)
382.08/118.43
active(half(s(0))) → mark(0)
382.08/118.43
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.43
active(half(dbl(z0))) → mark(z0)
382.08/118.43
active(terms(z0)) → terms(active(z0))
382.08/118.43
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.43
active(recip(z0)) → recip(active(z0))
382.08/118.43
active(sqr(z0)) → sqr(active(z0))
382.08/118.43
active(s(z0)) → s(active(z0))
382.08/118.43
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.43
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.43
active(dbl(z0)) → dbl(active(z0))
382.08/118.43
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.43
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.43
active(half(z0)) → half(active(z0))
382.08/118.43
terms(mark(z0)) → mark(terms(z0))
382.08/118.43
terms(ok(z0)) → ok(terms(z0))
382.08/118.43
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.43
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.43
recip(mark(z0)) → mark(recip(z0))
382.08/118.43
recip(ok(z0)) → ok(recip(z0))
382.08/118.43
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.43
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.43
s(mark(z0)) → mark(s(z0))
382.08/118.43
s(ok(z0)) → ok(s(z0))
382.08/118.43
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.43
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.43
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.43
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.43
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.43
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.43
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.43
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.43
half(mark(z0)) → mark(half(z0))
382.08/118.43
half(ok(z0)) → ok(half(z0))
382.08/118.43
proper(terms(z0)) → terms(proper(z0))
382.08/118.43
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.43
proper(recip(z0)) → recip(proper(z0))
382.08/118.43
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.43
proper(s(z0)) → s(proper(z0))
382.08/118.43
proper(0) → ok(0)
382.08/118.43
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.43
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.43
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.43
proper(nil) → ok(nil)
382.08/118.43
proper(half(z0)) → half(proper(z0))
382.08/118.43
top(mark(z0)) → top(proper(z0))
382.08/118.43
top(ok(z0)) → top(active(z0))
Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.43
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.43
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.43
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.43
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.43
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.43
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.43
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.43
S(mark(z0)) → c32(S(z0))
382.08/118.43
S(ok(z0)) → c33(S(z0))
382.08/118.43
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.43
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.43
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.43
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.43
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.43
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.43
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.43
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.43
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.43
HALF(ok(z0)) → c43(HALF(z0))
S tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.43
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.43
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.43
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.43
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.43
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.43
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.43
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.43
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.43
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.43
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.43
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.43
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.43
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.43
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.43
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.43
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.43
HALF(ok(z0)) → c43(HALF(z0))
K tuples:
S(mark(z0)) → c32(S(z0))
382.08/118.43
S(ok(z0)) → c33(S(z0))
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43
382.08/118.43
382.08/118.43
(79) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
SQR(mark(z0)) → c30(SQR(z0))
We considered the (Usable) Rules:none
And the Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.43
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.43
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.43
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.43
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.43
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.43
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.43
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.43
S(mark(z0)) → c32(S(z0))
382.08/118.43
S(ok(z0)) → c33(S(z0))
382.08/118.43
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.43
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.43
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.43
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.43
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.43
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.43
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.43
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.43
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.43
HALF(ok(z0)) → c43(HALF(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
382.08/118.43
POL(ADD(x1, x2)) = 0
382.08/118.43
POL(CONS(x1, x2)) = 0
382.08/118.43
POL(DBL(x1)) = 0
382.08/118.43
POL(FIRST(x1, x2)) = 0
382.08/118.43
POL(HALF(x1)) = 0
382.08/118.43
POL(RECIP(x1)) = 0
382.08/118.43
POL(S(x1)) = [5]x1
382.08/118.43
POL(SQR(x1)) = x1
382.08/118.43
POL(TERMS(x1)) = 0
382.08/118.43
POL(c24(x1)) = x1
382.08/118.43
POL(c25(x1)) = x1
382.08/118.43
POL(c26(x1)) = x1
382.08/118.43
POL(c27(x1)) = x1
382.08/118.43
POL(c28(x1)) = x1
382.08/118.43
POL(c29(x1)) = x1
382.08/118.43
POL(c30(x1)) = x1
382.08/118.43
POL(c31(x1)) = x1
382.08/118.43
POL(c32(x1)) = x1
382.08/118.43
POL(c33(x1)) = x1
382.08/118.43
POL(c34(x1)) = x1
382.08/118.43
POL(c35(x1)) = x1
382.08/118.43
POL(c36(x1)) = x1
382.08/118.43
POL(c37(x1)) = x1
382.08/118.43
POL(c38(x1)) = x1
382.08/118.43
POL(c39(x1)) = x1
382.08/118.43
POL(c40(x1)) = x1
382.08/118.43
POL(c41(x1)) = x1
382.08/118.43
POL(c42(x1)) = x1
382.08/118.43
POL(c43(x1)) = x1
382.08/118.43
POL(mark(x1)) = [1] + x1
382.08/118.43
POL(ok(x1)) = x1
382.08/118.43
382.08/118.43
(80) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.43
active(sqr(0)) → mark(0)
382.08/118.43
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.43
active(dbl(0)) → mark(0)
382.08/118.43
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.43
active(add(0, z0)) → mark(z0)
382.08/118.43
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.43
active(first(0, z0)) → mark(nil)
382.08/118.43
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.43
active(half(0)) → mark(0)
382.08/118.43
active(half(s(0))) → mark(0)
382.08/118.43
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.43
active(half(dbl(z0))) → mark(z0)
382.08/118.43
active(terms(z0)) → terms(active(z0))
382.08/118.43
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.43
active(recip(z0)) → recip(active(z0))
382.08/118.43
active(sqr(z0)) → sqr(active(z0))
382.08/118.43
active(s(z0)) → s(active(z0))
382.08/118.43
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.43
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.43
active(dbl(z0)) → dbl(active(z0))
382.08/118.43
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.43
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.43
active(half(z0)) → half(active(z0))
382.08/118.43
terms(mark(z0)) → mark(terms(z0))
382.08/118.43
terms(ok(z0)) → ok(terms(z0))
382.08/118.43
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.43
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.43
recip(mark(z0)) → mark(recip(z0))
382.08/118.43
recip(ok(z0)) → ok(recip(z0))
382.08/118.43
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.43
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.43
s(mark(z0)) → mark(s(z0))
382.08/118.43
s(ok(z0)) → ok(s(z0))
382.08/118.43
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.43
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.43
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.43
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.43
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.43
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.43
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.43
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.43
half(mark(z0)) → mark(half(z0))
382.08/118.43
half(ok(z0)) → ok(half(z0))
382.08/118.43
proper(terms(z0)) → terms(proper(z0))
382.08/118.43
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.43
proper(recip(z0)) → recip(proper(z0))
382.08/118.43
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.43
proper(s(z0)) → s(proper(z0))
382.08/118.43
proper(0) → ok(0)
382.08/118.43
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.43
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.43
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.43
proper(nil) → ok(nil)
382.08/118.43
proper(half(z0)) → half(proper(z0))
382.08/118.43
top(mark(z0)) → top(proper(z0))
382.08/118.43
top(ok(z0)) → top(active(z0))
Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.43
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.43
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.43
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.43
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.43
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.43
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.43
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.43
S(mark(z0)) → c32(S(z0))
382.08/118.43
S(ok(z0)) → c33(S(z0))
382.08/118.43
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.43
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.43
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.43
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.43
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.43
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.43
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.43
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.43
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.43
HALF(ok(z0)) → c43(HALF(z0))
S tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.43
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.43
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.43
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.43
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.43
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.43
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.43
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.43
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.43
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.43
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.43
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.43
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.43
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.43
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.43
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.43
HALF(ok(z0)) → c43(HALF(z0))
K tuples:
S(mark(z0)) → c32(S(z0))
382.08/118.43
S(ok(z0)) → c33(S(z0))
382.08/118.43
SQR(mark(z0)) → c30(SQR(z0))
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43
382.08/118.43
382.08/118.43
(81) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^3))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.43
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.43
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.43
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.43
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.43
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.43
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.43
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.43
HALF(mark(z0)) → c42(HALF(z0))
We considered the (Usable) Rules:none
And the Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.43
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.43
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.43
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.43
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.43
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.43
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.43
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.43
S(mark(z0)) → c32(S(z0))
382.08/118.43
S(ok(z0)) → c33(S(z0))
382.08/118.43
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.43
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.43
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.43
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.43
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.43
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.43
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.43
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.43
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.43
HALF(ok(z0)) → c43(HALF(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
382.08/118.43
POL(ADD(x1, x2)) = x2 + x22 + x1·x2 + x12 + x13 + x12·x2 + x1·x22 + x23
382.08/118.43
POL(CONS(x1, x2)) = x22 + x1·x2 + x12 + x13 + x12·x2 + x1·x22 + x23
382.08/118.43
POL(DBL(x1)) = x1 + x12 + x13
382.08/118.43
POL(FIRST(x1, x2)) = x2 + x22 + x1·x2 + x12 + x13 + x12·x2 + x1·x22 + x23
382.08/118.43
POL(HALF(x1)) = x1 + x12 + x13
382.08/118.43
POL(RECIP(x1)) = x1 + x12 + x13
382.08/118.43
POL(S(x1)) = x1 + x12 + x13
382.08/118.43
POL(SQR(x1)) = x1 + x12 + x13
382.08/118.43
POL(TERMS(x1)) = x1 + x12 + x13
382.08/118.43
POL(c24(x1)) = x1
382.08/118.43
POL(c25(x1)) = x1
382.08/118.43
POL(c26(x1)) = x1
382.08/118.43
POL(c27(x1)) = x1
382.08/118.43
POL(c28(x1)) = x1
382.08/118.43
POL(c29(x1)) = x1
382.08/118.43
POL(c30(x1)) = x1
382.08/118.43
POL(c31(x1)) = x1
382.08/118.43
POL(c32(x1)) = x1
382.08/118.43
POL(c33(x1)) = x1
382.08/118.44
POL(c34(x1)) = x1
382.08/118.44
POL(c35(x1)) = x1
382.08/118.44
POL(c36(x1)) = x1
382.08/118.44
POL(c37(x1)) = x1
382.08/118.44
POL(c38(x1)) = x1
382.08/118.44
POL(c39(x1)) = x1
382.08/118.44
POL(c40(x1)) = x1
382.08/118.44
POL(c41(x1)) = x1
382.08/118.44
POL(c42(x1)) = x1
382.08/118.44
POL(c43(x1)) = x1
382.08/118.44
POL(mark(x1)) = [1] + x1
382.08/118.44
POL(ok(x1)) = x1
382.08/118.44
382.08/118.44
(82) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.44
active(sqr(0)) → mark(0)
382.08/118.44
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.44
active(dbl(0)) → mark(0)
382.08/118.44
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.44
active(add(0, z0)) → mark(z0)
382.08/118.44
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.44
active(first(0, z0)) → mark(nil)
382.08/118.44
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.44
active(half(0)) → mark(0)
382.08/118.44
active(half(s(0))) → mark(0)
382.08/118.44
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.44
active(half(dbl(z0))) → mark(z0)
382.08/118.44
active(terms(z0)) → terms(active(z0))
382.08/118.44
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.44
active(recip(z0)) → recip(active(z0))
382.08/118.44
active(sqr(z0)) → sqr(active(z0))
382.08/118.44
active(s(z0)) → s(active(z0))
382.08/118.44
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.44
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.44
active(dbl(z0)) → dbl(active(z0))
382.08/118.44
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.44
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.44
active(half(z0)) → half(active(z0))
382.08/118.44
terms(mark(z0)) → mark(terms(z0))
382.08/118.44
terms(ok(z0)) → ok(terms(z0))
382.08/118.44
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.44
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.44
recip(mark(z0)) → mark(recip(z0))
382.08/118.44
recip(ok(z0)) → ok(recip(z0))
382.08/118.44
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.44
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.44
s(mark(z0)) → mark(s(z0))
382.08/118.44
s(ok(z0)) → ok(s(z0))
382.08/118.44
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.44
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.44
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.44
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.44
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.44
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.44
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.44
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.44
half(mark(z0)) → mark(half(z0))
382.08/118.44
half(ok(z0)) → ok(half(z0))
382.08/118.44
proper(terms(z0)) → terms(proper(z0))
382.08/118.44
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.44
proper(recip(z0)) → recip(proper(z0))
382.08/118.44
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.44
proper(s(z0)) → s(proper(z0))
382.08/118.44
proper(0) → ok(0)
382.08/118.44
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.44
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.44
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.44
proper(nil) → ok(nil)
382.08/118.44
proper(half(z0)) → half(proper(z0))
382.08/118.44
top(mark(z0)) → top(proper(z0))
382.08/118.44
top(ok(z0)) → top(active(z0))
Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.44
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.44
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.44
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.44
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.44
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.44
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.44
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.44
S(mark(z0)) → c32(S(z0))
382.08/118.44
S(ok(z0)) → c33(S(z0))
382.08/118.44
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.44
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.44
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.44
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.44
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.44
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.44
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.44
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.44
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.44
HALF(ok(z0)) → c43(HALF(z0))
S tuples:
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.44
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.44
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.44
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.44
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.44
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.44
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.44
HALF(ok(z0)) → c43(HALF(z0))
K tuples:
S(mark(z0)) → c32(S(z0))
382.08/118.44
S(ok(z0)) → c33(S(z0))
382.08/118.44
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.44
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.44
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.44
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.44
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.44
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.44
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.44
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.44
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.44
HALF(mark(z0)) → c42(HALF(z0))
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43
382.08/118.44
382.08/118.44
(83) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.44
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.44
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.44
HALF(ok(z0)) → c43(HALF(z0))
We considered the (Usable) Rules:none
And the Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.44
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.44
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.44
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.44
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.44
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.44
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.44
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.44
S(mark(z0)) → c32(S(z0))
382.08/118.44
S(ok(z0)) → c33(S(z0))
382.08/118.44
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.44
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.44
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.44
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.44
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.44
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.44
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.44
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.44
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.44
HALF(ok(z0)) → c43(HALF(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
382.08/118.44
POL(ADD(x1, x2)) = 0
382.08/118.44
POL(CONS(x1, x2)) = x2
382.08/118.44
POL(DBL(x1)) = 0
382.08/118.44
POL(FIRST(x1, x2)) = x2
382.08/118.44
POL(HALF(x1)) = x1
382.08/118.44
POL(RECIP(x1)) = 0
382.08/118.44
POL(S(x1)) = [3]x1
382.08/118.44
POL(SQR(x1)) = 0
382.08/118.44
POL(TERMS(x1)) = [2]x1
382.08/118.44
POL(c24(x1)) = x1
382.08/118.44
POL(c25(x1)) = x1
382.08/118.44
POL(c26(x1)) = x1
382.08/118.44
POL(c27(x1)) = x1
382.08/118.44
POL(c28(x1)) = x1
382.08/118.44
POL(c29(x1)) = x1
382.08/118.44
POL(c30(x1)) = x1
382.08/118.44
POL(c31(x1)) = x1
382.08/118.44
POL(c32(x1)) = x1
382.08/118.44
POL(c33(x1)) = x1
382.08/118.44
POL(c34(x1)) = x1
382.08/118.44
POL(c35(x1)) = x1
382.08/118.44
POL(c36(x1)) = x1
382.08/118.44
POL(c37(x1)) = x1
382.08/118.44
POL(c38(x1)) = x1
382.08/118.44
POL(c39(x1)) = x1
382.08/118.44
POL(c40(x1)) = x1
382.08/118.44
POL(c41(x1)) = x1
382.08/118.44
POL(c42(x1)) = x1
382.08/118.44
POL(c43(x1)) = x1
382.08/118.44
POL(mark(x1)) = x1
382.08/118.44
POL(ok(x1)) = [1] + x1
382.08/118.44
382.08/118.44
(84) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.44
active(sqr(0)) → mark(0)
382.08/118.44
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.44
active(dbl(0)) → mark(0)
382.08/118.44
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.44
active(add(0, z0)) → mark(z0)
382.08/118.44
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.44
active(first(0, z0)) → mark(nil)
382.08/118.44
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.44
active(half(0)) → mark(0)
382.08/118.44
active(half(s(0))) → mark(0)
382.08/118.44
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.44
active(half(dbl(z0))) → mark(z0)
382.08/118.44
active(terms(z0)) → terms(active(z0))
382.08/118.44
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.44
active(recip(z0)) → recip(active(z0))
382.08/118.44
active(sqr(z0)) → sqr(active(z0))
382.08/118.44
active(s(z0)) → s(active(z0))
382.08/118.44
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.44
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.44
active(dbl(z0)) → dbl(active(z0))
382.08/118.44
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.44
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.44
active(half(z0)) → half(active(z0))
382.08/118.44
terms(mark(z0)) → mark(terms(z0))
382.08/118.44
terms(ok(z0)) → ok(terms(z0))
382.08/118.44
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.44
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.44
recip(mark(z0)) → mark(recip(z0))
382.08/118.44
recip(ok(z0)) → ok(recip(z0))
382.08/118.44
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.44
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.44
s(mark(z0)) → mark(s(z0))
382.08/118.44
s(ok(z0)) → ok(s(z0))
382.08/118.44
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.44
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.44
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.44
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.44
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.44
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.44
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.44
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.44
half(mark(z0)) → mark(half(z0))
382.08/118.44
half(ok(z0)) → ok(half(z0))
382.08/118.44
proper(terms(z0)) → terms(proper(z0))
382.08/118.44
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.44
proper(recip(z0)) → recip(proper(z0))
382.08/118.44
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.44
proper(s(z0)) → s(proper(z0))
382.08/118.44
proper(0) → ok(0)
382.08/118.44
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.44
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.44
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.44
proper(nil) → ok(nil)
382.08/118.44
proper(half(z0)) → half(proper(z0))
382.08/118.44
top(mark(z0)) → top(proper(z0))
382.08/118.44
top(ok(z0)) → top(active(z0))
Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.44
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.44
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.44
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.44
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.44
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.44
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.44
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.44
S(mark(z0)) → c32(S(z0))
382.08/118.44
S(ok(z0)) → c33(S(z0))
382.08/118.44
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.44
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.44
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.44
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.44
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.44
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.44
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.44
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.44
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.44
HALF(ok(z0)) → c43(HALF(z0))
S tuples:
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.44
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.44
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.44
DBL(ok(z0)) → c38(DBL(z0))
K tuples:
S(mark(z0)) → c32(S(z0))
382.08/118.44
S(ok(z0)) → c33(S(z0))
382.08/118.44
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.44
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.44
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.44
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.44
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.44
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.44
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.44
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.44
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.44
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.44
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.44
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.44
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.44
HALF(ok(z0)) → c43(HALF(z0))
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43
382.08/118.44
382.08/118.44
(85) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
DBL(ok(z0)) → c38(DBL(z0))
We considered the (Usable) Rules:none
And the Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.44
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.44
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.44
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.44
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.44
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.44
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.44
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.44
S(mark(z0)) → c32(S(z0))
382.08/118.44
S(ok(z0)) → c33(S(z0))
382.08/118.44
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.44
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.44
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.44
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.44
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.44
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.44
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.44
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.44
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.44
HALF(ok(z0)) → c43(HALF(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
382.08/118.44
POL(ADD(x1, x2)) = 0
382.08/118.44
POL(CONS(x1, x2)) = x1 + x2
382.08/118.44
POL(DBL(x1)) = x1
382.08/118.44
POL(FIRST(x1, x2)) = x1 + x2
382.08/118.44
POL(HALF(x1)) = [3]x1 + [3]x12
382.08/118.44
POL(RECIP(x1)) = 0
382.08/118.44
POL(S(x1)) = [3]x1 + [3]x12
382.08/118.44
POL(SQR(x1)) = 0
382.08/118.44
POL(TERMS(x1)) = [3]x1 + [3]x12
382.08/118.44
POL(c24(x1)) = x1
382.08/118.44
POL(c25(x1)) = x1
382.08/118.44
POL(c26(x1)) = x1
382.08/118.44
POL(c27(x1)) = x1
382.08/118.44
POL(c28(x1)) = x1
382.08/118.44
POL(c29(x1)) = x1
382.08/118.44
POL(c30(x1)) = x1
382.08/118.44
POL(c31(x1)) = x1
382.08/118.44
POL(c32(x1)) = x1
382.08/118.44
POL(c33(x1)) = x1
382.08/118.44
POL(c34(x1)) = x1
382.08/118.44
POL(c35(x1)) = x1
382.08/118.44
POL(c36(x1)) = x1
382.08/118.44
POL(c37(x1)) = x1
382.08/118.44
POL(c38(x1)) = x1
382.08/118.44
POL(c39(x1)) = x1
382.08/118.44
POL(c40(x1)) = x1
382.08/118.44
POL(c41(x1)) = x1
382.08/118.44
POL(c42(x1)) = x1
382.08/118.44
POL(c43(x1)) = x1
382.08/118.44
POL(mark(x1)) = [3] + x1
382.08/118.44
POL(ok(x1)) = [1] + x1
382.08/118.44
382.08/118.44
(86) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.44
active(sqr(0)) → mark(0)
382.08/118.44
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.44
active(dbl(0)) → mark(0)
382.08/118.44
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.44
active(add(0, z0)) → mark(z0)
382.08/118.44
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.44
active(first(0, z0)) → mark(nil)
382.08/118.44
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.44
active(half(0)) → mark(0)
382.08/118.44
active(half(s(0))) → mark(0)
382.08/118.44
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.44
active(half(dbl(z0))) → mark(z0)
382.08/118.44
active(terms(z0)) → terms(active(z0))
382.08/118.44
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.44
active(recip(z0)) → recip(active(z0))
382.08/118.44
active(sqr(z0)) → sqr(active(z0))
382.08/118.44
active(s(z0)) → s(active(z0))
382.08/118.44
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.44
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.44
active(dbl(z0)) → dbl(active(z0))
382.08/118.44
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.44
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.44
active(half(z0)) → half(active(z0))
382.08/118.44
terms(mark(z0)) → mark(terms(z0))
382.08/118.44
terms(ok(z0)) → ok(terms(z0))
382.08/118.44
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.44
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.44
recip(mark(z0)) → mark(recip(z0))
382.08/118.44
recip(ok(z0)) → ok(recip(z0))
382.08/118.44
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.44
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.44
s(mark(z0)) → mark(s(z0))
382.08/118.44
s(ok(z0)) → ok(s(z0))
382.08/118.44
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.44
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.44
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.44
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.44
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.44
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.44
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.44
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.44
half(mark(z0)) → mark(half(z0))
382.08/118.44
half(ok(z0)) → ok(half(z0))
382.08/118.44
proper(terms(z0)) → terms(proper(z0))
382.08/118.44
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.44
proper(recip(z0)) → recip(proper(z0))
382.08/118.44
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.44
proper(s(z0)) → s(proper(z0))
382.08/118.44
proper(0) → ok(0)
382.08/118.44
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.44
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.44
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.44
proper(nil) → ok(nil)
382.08/118.44
proper(half(z0)) → half(proper(z0))
382.08/118.44
top(mark(z0)) → top(proper(z0))
382.08/118.44
top(ok(z0)) → top(active(z0))
Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.44
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.44
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.44
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.44
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.44
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.44
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.44
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.44
S(mark(z0)) → c32(S(z0))
382.08/118.44
S(ok(z0)) → c33(S(z0))
382.08/118.44
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.44
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.44
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.44
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.44
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.44
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.44
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.44
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.44
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.44
HALF(ok(z0)) → c43(HALF(z0))
S tuples:
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.44
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.44
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
K tuples:
S(mark(z0)) → c32(S(z0))
382.08/118.44
S(ok(z0)) → c33(S(z0))
382.08/118.44
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.44
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.44
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.44
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.44
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.44
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.44
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.44
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.44
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.44
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.44
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.44
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.44
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.44
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.44
DBL(ok(z0)) → c38(DBL(z0))
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43
382.08/118.44
382.08/118.44
(87) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
RECIP(ok(z0)) → c29(RECIP(z0))
We considered the (Usable) Rules:none
And the Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.44
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.44
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.44
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.44
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.44
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.44
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.44
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.44
S(mark(z0)) → c32(S(z0))
382.08/118.44
S(ok(z0)) → c33(S(z0))
382.08/118.44
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.44
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.44
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.44
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.44
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.44
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.44
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.44
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.44
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.44
HALF(ok(z0)) → c43(HALF(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
382.08/118.44
POL(ADD(x1, x2)) = 0
382.08/118.44
POL(CONS(x1, x2)) = [3]x1 + [5]x2
382.08/118.44
POL(DBL(x1)) = [3]x1
382.08/118.44
POL(FIRST(x1, x2)) = [3]x1 + [3]x2
382.08/118.44
POL(HALF(x1)) = [3]x1
382.08/118.44
POL(RECIP(x1)) = [2]x1
382.08/118.44
POL(S(x1)) = [5]x1
382.08/118.44
POL(SQR(x1)) = 0
382.08/118.44
POL(TERMS(x1)) = [3]x1
382.08/118.44
POL(c24(x1)) = x1
382.08/118.44
POL(c25(x1)) = x1
382.08/118.44
POL(c26(x1)) = x1
382.08/118.44
POL(c27(x1)) = x1
382.08/118.44
POL(c28(x1)) = x1
382.08/118.44
POL(c29(x1)) = x1
382.08/118.44
POL(c30(x1)) = x1
382.08/118.44
POL(c31(x1)) = x1
382.08/118.44
POL(c32(x1)) = x1
382.08/118.44
POL(c33(x1)) = x1
382.08/118.44
POL(c34(x1)) = x1
382.08/118.44
POL(c35(x1)) = x1
382.08/118.44
POL(c36(x1)) = x1
382.08/118.44
POL(c37(x1)) = x1
382.08/118.44
POL(c38(x1)) = x1
382.08/118.44
POL(c39(x1)) = x1
382.08/118.44
POL(c40(x1)) = x1
382.08/118.44
POL(c41(x1)) = x1
382.08/118.44
POL(c42(x1)) = x1
382.08/118.44
POL(c43(x1)) = x1
382.08/118.44
POL(mark(x1)) = x1
382.08/118.44
POL(ok(x1)) = [1] + x1
382.08/118.44
382.08/118.44
(88) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.44
active(sqr(0)) → mark(0)
382.08/118.44
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.44
active(dbl(0)) → mark(0)
382.08/118.44
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.44
active(add(0, z0)) → mark(z0)
382.08/118.44
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.44
active(first(0, z0)) → mark(nil)
382.08/118.44
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.44
active(half(0)) → mark(0)
382.08/118.44
active(half(s(0))) → mark(0)
382.08/118.44
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.44
active(half(dbl(z0))) → mark(z0)
382.08/118.44
active(terms(z0)) → terms(active(z0))
382.08/118.44
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.44
active(recip(z0)) → recip(active(z0))
382.08/118.44
active(sqr(z0)) → sqr(active(z0))
382.08/118.44
active(s(z0)) → s(active(z0))
382.08/118.44
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.44
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.44
active(dbl(z0)) → dbl(active(z0))
382.08/118.44
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.44
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.44
active(half(z0)) → half(active(z0))
382.08/118.44
terms(mark(z0)) → mark(terms(z0))
382.08/118.44
terms(ok(z0)) → ok(terms(z0))
382.08/118.44
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.44
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.44
recip(mark(z0)) → mark(recip(z0))
382.08/118.44
recip(ok(z0)) → ok(recip(z0))
382.08/118.44
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.44
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.44
s(mark(z0)) → mark(s(z0))
382.08/118.44
s(ok(z0)) → ok(s(z0))
382.08/118.44
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.44
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.44
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.44
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.44
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.44
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.44
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.44
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.44
half(mark(z0)) → mark(half(z0))
382.08/118.44
half(ok(z0)) → ok(half(z0))
382.08/118.44
proper(terms(z0)) → terms(proper(z0))
382.08/118.44
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.44
proper(recip(z0)) → recip(proper(z0))
382.08/118.44
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.44
proper(s(z0)) → s(proper(z0))
382.08/118.44
proper(0) → ok(0)
382.08/118.44
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.44
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.44
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.44
proper(nil) → ok(nil)
382.08/118.44
proper(half(z0)) → half(proper(z0))
382.08/118.44
top(mark(z0)) → top(proper(z0))
382.08/118.44
top(ok(z0)) → top(active(z0))
Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.44
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.44
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.44
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.44
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.44
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.44
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.44
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.44
S(mark(z0)) → c32(S(z0))
382.08/118.44
S(ok(z0)) → c33(S(z0))
382.08/118.44
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.44
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.44
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.44
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.44
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.44
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.44
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.44
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.44
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.44
HALF(ok(z0)) → c43(HALF(z0))
S tuples:
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.44
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
K tuples:
S(mark(z0)) → c32(S(z0))
382.08/118.44
S(ok(z0)) → c33(S(z0))
382.08/118.44
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.44
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.44
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.44
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.44
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.44
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.44
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.44
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.44
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.44
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.44
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.44
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.44
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.44
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.44
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.44
RECIP(ok(z0)) → c29(RECIP(z0))
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43
382.08/118.44
382.08/118.44
(89) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.44
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.44
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.44
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.44
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.44
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.44
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.44
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.44
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.44
S(mark(z0)) → c32(S(z0))
382.08/118.44
S(ok(z0)) → c33(S(z0))
382.08/118.44
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.44
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.44
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.44
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.44
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.44
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.44
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.44
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.44
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.44
HALF(ok(z0)) → c43(HALF(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
382.08/118.44
POL(ADD(x1, x2)) = [2]x1 + [3]x2
382.08/118.44
POL(CONS(x1, x2)) = [3]x1 + [5]x2
382.08/118.44
POL(DBL(x1)) = [3]x1
382.08/118.44
POL(FIRST(x1, x2)) = [3]x1 + [3]x2
382.08/118.44
POL(HALF(x1)) = [5]x1
382.08/118.44
POL(RECIP(x1)) = [3]x1
382.08/118.44
POL(S(x1)) = [3]x1
382.08/118.44
POL(SQR(x1)) = [3]x1
382.08/118.44
POL(TERMS(x1)) = [5]x1
382.08/118.44
POL(c24(x1)) = x1
382.08/118.44
POL(c25(x1)) = x1
382.08/118.44
POL(c26(x1)) = x1
382.08/118.44
POL(c27(x1)) = x1
382.08/118.44
POL(c28(x1)) = x1
382.08/118.44
POL(c29(x1)) = x1
382.08/118.44
POL(c30(x1)) = x1
382.08/118.44
POL(c31(x1)) = x1
382.08/118.44
POL(c32(x1)) = x1
382.08/118.44
POL(c33(x1)) = x1
382.08/118.44
POL(c34(x1)) = x1
382.08/118.44
POL(c35(x1)) = x1
382.08/118.44
POL(c36(x1)) = x1
382.08/118.44
POL(c37(x1)) = x1
382.08/118.44
POL(c38(x1)) = x1
382.08/118.44
POL(c39(x1)) = x1
382.08/118.44
POL(c40(x1)) = x1
382.08/118.44
POL(c41(x1)) = x1
382.08/118.44
POL(c42(x1)) = x1
382.08/118.44
POL(c43(x1)) = x1
382.08/118.44
POL(mark(x1)) = x1
382.08/118.44
POL(ok(x1)) = [3] + x1
382.08/118.44
382.08/118.44
(90) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0))))
382.08/118.44
active(sqr(0)) → mark(0)
382.08/118.44
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0))))
382.08/118.44
active(dbl(0)) → mark(0)
382.08/118.44
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
382.08/118.44
active(add(0, z0)) → mark(z0)
382.08/118.44
active(add(s(z0), z1)) → mark(s(add(z0, z1)))
382.08/118.44
active(first(0, z0)) → mark(nil)
382.08/118.44
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
382.08/118.44
active(half(0)) → mark(0)
382.08/118.44
active(half(s(0))) → mark(0)
382.08/118.44
active(half(s(s(z0)))) → mark(s(half(z0)))
382.08/118.44
active(half(dbl(z0))) → mark(z0)
382.08/118.44
active(terms(z0)) → terms(active(z0))
382.08/118.44
active(cons(z0, z1)) → cons(active(z0), z1)
382.08/118.44
active(recip(z0)) → recip(active(z0))
382.08/118.44
active(sqr(z0)) → sqr(active(z0))
382.08/118.44
active(s(z0)) → s(active(z0))
382.08/118.44
active(add(z0, z1)) → add(active(z0), z1)
382.08/118.44
active(add(z0, z1)) → add(z0, active(z1))
382.08/118.44
active(dbl(z0)) → dbl(active(z0))
382.08/118.44
active(first(z0, z1)) → first(active(z0), z1)
382.08/118.44
active(first(z0, z1)) → first(z0, active(z1))
382.08/118.44
active(half(z0)) → half(active(z0))
382.08/118.44
terms(mark(z0)) → mark(terms(z0))
382.08/118.44
terms(ok(z0)) → ok(terms(z0))
382.08/118.44
cons(mark(z0), z1) → mark(cons(z0, z1))
382.08/118.44
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
382.08/118.44
recip(mark(z0)) → mark(recip(z0))
382.08/118.44
recip(ok(z0)) → ok(recip(z0))
382.08/118.44
sqr(mark(z0)) → mark(sqr(z0))
382.08/118.44
sqr(ok(z0)) → ok(sqr(z0))
382.08/118.44
s(mark(z0)) → mark(s(z0))
382.08/118.44
s(ok(z0)) → ok(s(z0))
382.08/118.44
add(mark(z0), z1) → mark(add(z0, z1))
382.08/118.44
add(z0, mark(z1)) → mark(add(z0, z1))
382.08/118.44
add(ok(z0), ok(z1)) → ok(add(z0, z1))
382.08/118.44
dbl(mark(z0)) → mark(dbl(z0))
382.08/118.44
dbl(ok(z0)) → ok(dbl(z0))
382.08/118.44
first(mark(z0), z1) → mark(first(z0, z1))
382.08/118.44
first(z0, mark(z1)) → mark(first(z0, z1))
382.08/118.44
first(ok(z0), ok(z1)) → ok(first(z0, z1))
382.08/118.44
half(mark(z0)) → mark(half(z0))
382.08/118.44
half(ok(z0)) → ok(half(z0))
382.08/118.44
proper(terms(z0)) → terms(proper(z0))
382.08/118.44
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
382.08/118.44
proper(recip(z0)) → recip(proper(z0))
382.08/118.44
proper(sqr(z0)) → sqr(proper(z0))
382.08/118.44
proper(s(z0)) → s(proper(z0))
382.08/118.44
proper(0) → ok(0)
382.08/118.44
proper(add(z0, z1)) → add(proper(z0), proper(z1))
382.08/118.44
proper(dbl(z0)) → dbl(proper(z0))
382.08/118.44
proper(first(z0, z1)) → first(proper(z0), proper(z1))
382.08/118.44
proper(nil) → ok(nil)
382.08/118.44
proper(half(z0)) → half(proper(z0))
382.08/118.44
top(mark(z0)) → top(proper(z0))
382.08/118.44
top(ok(z0)) → top(active(z0))
Tuples:
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.44
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.44
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.44
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.44
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.44
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.44
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.44
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.44
S(mark(z0)) → c32(S(z0))
382.08/118.44
S(ok(z0)) → c33(S(z0))
382.08/118.44
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.44
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.44
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
382.08/118.44
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.44
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.44
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.44
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.44
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.44
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.44
HALF(ok(z0)) → c43(HALF(z0))
S tuples:none
K tuples:
S(mark(z0)) → c32(S(z0))
382.08/118.44
S(ok(z0)) → c33(S(z0))
382.08/118.44
SQR(mark(z0)) → c30(SQR(z0))
382.08/118.44
TERMS(mark(z0)) → c24(TERMS(z0))
382.08/118.44
CONS(mark(z0), z1) → c26(CONS(z0, z1))
382.08/118.44
RECIP(mark(z0)) → c28(RECIP(z0))
382.08/118.44
ADD(mark(z0), z1) → c34(ADD(z0, z1))
382.08/118.44
ADD(z0, mark(z1)) → c35(ADD(z0, z1))
382.08/118.44
DBL(mark(z0)) → c37(DBL(z0))
382.08/118.44
FIRST(mark(z0), z1) → c39(FIRST(z0, z1))
382.08/118.44
FIRST(z0, mark(z1)) → c40(FIRST(z0, z1))
382.08/118.44
HALF(mark(z0)) → c42(HALF(z0))
382.08/118.44
TERMS(ok(z0)) → c25(TERMS(z0))
382.08/118.44
CONS(ok(z0), ok(z1)) → c27(CONS(z0, z1))
382.08/118.44
FIRST(ok(z0), ok(z1)) → c41(FIRST(z0, z1))
382.08/118.44
HALF(ok(z0)) → c43(HALF(z0))
382.08/118.44
DBL(ok(z0)) → c38(DBL(z0))
382.08/118.44
RECIP(ok(z0)) → c29(RECIP(z0))
382.08/118.44
SQR(ok(z0)) → c31(SQR(z0))
382.08/118.44
ADD(ok(z0), ok(z1)) → c36(ADD(z0, z1))
Defined Rule Symbols:
active, terms, cons, recip, sqr, s, add, dbl, first, half, proper, top
Defined Pair Symbols:
TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, HALF
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43
382.08/118.44
382.08/118.44
(91) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)
The set S is empty
382.08/118.44
382.08/118.44
(92) BOUNDS(O(1), O(1))
382.08/118.44