YES(O(1), O(n^1)) 3.04/1.30 YES(O(1), O(n^1)) 3.41/1.35 3.41/1.35 3.41/1.35
3.41/1.35 3.41/1.350 CpxTRS3.41/1.35
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))3.41/1.35
↳2 CdtProblem3.41/1.35
↳3 CdtUnreachableProof (⇔)3.41/1.35
↳4 CdtProblem3.41/1.35
↳5 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))3.41/1.35
↳6 CdtProblem3.41/1.35
↳7 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))3.41/1.35
↳8 CdtProblem3.41/1.35
↳9 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))3.41/1.35
↳10 CdtProblem3.41/1.35
↳11 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))3.41/1.35
↳12 CdtProblem3.41/1.35
↳13 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))3.41/1.35
↳14 CdtProblem3.41/1.35
↳15 SIsEmptyProof (BOTH BOUNDS(ID, ID))3.41/1.35
↳16 BOUNDS(O(1), O(1))3.41/1.35
terms(N) → cons(recip(sqr(N)), n__terms(n__s(N))) 3.41/1.35
sqr(0) → 0 3.41/1.35
sqr(s(X)) → s(add(sqr(X), dbl(X))) 3.41/1.35
dbl(0) → 0 3.41/1.35
dbl(s(X)) → s(s(dbl(X))) 3.41/1.35
add(0, X) → X 3.41/1.35
add(s(X), Y) → s(add(X, Y)) 3.41/1.35
first(0, X) → nil 3.41/1.35
first(s(X), cons(Y, Z)) → cons(Y, n__first(X, activate(Z))) 3.41/1.35
half(0) → 0 3.41/1.35
half(s(0)) → 0 3.41/1.35
half(s(s(X))) → s(half(X)) 3.41/1.35
half(dbl(X)) → X 3.41/1.35
terms(X) → n__terms(X) 3.41/1.35
s(X) → n__s(X) 3.41/1.35
first(X1, X2) → n__first(X1, X2) 3.41/1.35
activate(n__terms(X)) → terms(activate(X)) 3.41/1.35
activate(n__s(X)) → s(activate(X)) 3.41/1.35
activate(n__first(X1, X2)) → first(activate(X1), activate(X2)) 3.41/1.35
activate(X) → X
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 3.41/1.35
terms(z0) → n__terms(z0) 3.41/1.35
sqr(0) → 0 3.41/1.35
sqr(s(z0)) → s(add(sqr(z0), dbl(z0))) 3.41/1.35
dbl(0) → 0 3.41/1.35
dbl(s(z0)) → s(s(dbl(z0))) 3.41/1.35
add(0, z0) → z0 3.41/1.35
add(s(z0), z1) → s(add(z0, z1)) 3.41/1.35
first(0, z0) → nil 3.41/1.35
first(s(z0), cons(z1, z2)) → cons(z1, n__first(z0, activate(z2))) 3.41/1.35
first(z0, z1) → n__first(z0, z1) 3.41/1.35
half(0) → 0 3.41/1.35
half(s(0)) → 0 3.41/1.35
half(s(s(z0))) → s(half(z0)) 3.41/1.35
half(dbl(z0)) → z0 3.41/1.35
s(z0) → n__s(z0) 3.41/1.35
activate(n__terms(z0)) → terms(activate(z0)) 3.41/1.35
activate(n__s(z0)) → s(activate(z0)) 3.41/1.35
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 3.41/1.35
activate(z0) → z0
S tuples:
TERMS(z0) → c(SQR(z0)) 3.41/1.35
SQR(s(z0)) → c3(S(add(sqr(z0), dbl(z0))), ADD(sqr(z0), dbl(z0)), SQR(z0), DBL(z0)) 3.41/1.35
DBL(s(z0)) → c5(S(s(dbl(z0))), S(dbl(z0)), DBL(z0)) 3.41/1.35
ADD(s(z0), z1) → c7(S(add(z0, z1)), ADD(z0, z1)) 3.41/1.35
FIRST(s(z0), cons(z1, z2)) → c9(ACTIVATE(z2)) 3.41/1.35
HALF(s(s(z0))) → c13(S(half(z0)), HALF(z0)) 3.41/1.35
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__s(z0)) → c17(S(activate(z0)), ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(FIRST(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1))
K tuples:none
TERMS(z0) → c(SQR(z0)) 3.41/1.35
SQR(s(z0)) → c3(S(add(sqr(z0), dbl(z0))), ADD(sqr(z0), dbl(z0)), SQR(z0), DBL(z0)) 3.41/1.35
DBL(s(z0)) → c5(S(s(dbl(z0))), S(dbl(z0)), DBL(z0)) 3.41/1.35
ADD(s(z0), z1) → c7(S(add(z0, z1)), ADD(z0, z1)) 3.41/1.35
FIRST(s(z0), cons(z1, z2)) → c9(ACTIVATE(z2)) 3.41/1.35
HALF(s(s(z0))) → c13(S(half(z0)), HALF(z0)) 3.41/1.35
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__s(z0)) → c17(S(activate(z0)), ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(FIRST(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1))
terms, sqr, dbl, add, first, half, s, activate
TERMS, SQR, DBL, ADD, FIRST, HALF, ACTIVATE
c, c3, c5, c7, c9, c13, c16, c17, c18
SQR(s(z0)) → c3(S(add(sqr(z0), dbl(z0))), ADD(sqr(z0), dbl(z0)), SQR(z0), DBL(z0)) 3.41/1.35
DBL(s(z0)) → c5(S(s(dbl(z0))), S(dbl(z0)), DBL(z0)) 3.41/1.35
ADD(s(z0), z1) → c7(S(add(z0, z1)), ADD(z0, z1)) 3.41/1.35
FIRST(s(z0), cons(z1, z2)) → c9(ACTIVATE(z2)) 3.41/1.35
HALF(s(s(z0))) → c13(S(half(z0)), HALF(z0))
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 3.41/1.35
terms(z0) → n__terms(z0) 3.41/1.35
sqr(0) → 0 3.41/1.35
sqr(s(z0)) → s(add(sqr(z0), dbl(z0))) 3.41/1.35
dbl(0) → 0 3.41/1.35
dbl(s(z0)) → s(s(dbl(z0))) 3.41/1.35
add(0, z0) → z0 3.41/1.35
add(s(z0), z1) → s(add(z0, z1)) 3.41/1.35
first(0, z0) → nil 3.41/1.35
first(s(z0), cons(z1, z2)) → cons(z1, n__first(z0, activate(z2))) 3.41/1.35
first(z0, z1) → n__first(z0, z1) 3.41/1.35
half(0) → 0 3.41/1.35
half(s(0)) → 0 3.41/1.35
half(s(s(z0))) → s(half(z0)) 3.41/1.35
half(dbl(z0)) → z0 3.41/1.35
s(z0) → n__s(z0) 3.41/1.35
activate(n__terms(z0)) → terms(activate(z0)) 3.41/1.35
activate(n__s(z0)) → s(activate(z0)) 3.41/1.35
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 3.41/1.35
activate(z0) → z0
S tuples:
TERMS(z0) → c(SQR(z0)) 3.41/1.35
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__s(z0)) → c17(S(activate(z0)), ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(FIRST(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1))
K tuples:none
TERMS(z0) → c(SQR(z0)) 3.41/1.35
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__s(z0)) → c17(S(activate(z0)), ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(FIRST(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1))
terms, sqr, dbl, add, first, half, s, activate
TERMS, ACTIVATE
c, c16, c17, c18
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 3.41/1.35
terms(z0) → n__terms(z0) 3.41/1.35
sqr(0) → 0 3.41/1.35
sqr(s(z0)) → s(add(sqr(z0), dbl(z0))) 3.41/1.35
dbl(0) → 0 3.41/1.35
dbl(s(z0)) → s(s(dbl(z0))) 3.41/1.35
add(0, z0) → z0 3.41/1.35
add(s(z0), z1) → s(add(z0, z1)) 3.41/1.35
first(0, z0) → nil 3.41/1.35
first(s(z0), cons(z1, z2)) → cons(z1, n__first(z0, activate(z2))) 3.41/1.35
first(z0, z1) → n__first(z0, z1) 3.41/1.35
half(0) → 0 3.41/1.35
half(s(0)) → 0 3.41/1.35
half(s(s(z0))) → s(half(z0)) 3.41/1.35
half(dbl(z0)) → z0 3.41/1.35
s(z0) → n__s(z0) 3.41/1.35
activate(n__terms(z0)) → terms(activate(z0)) 3.41/1.35
activate(n__s(z0)) → s(activate(z0)) 3.41/1.35
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 3.41/1.35
activate(z0) → z0
S tuples:
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
TERMS(z0) → c 3.41/1.35
ACTIVATE(n__s(z0)) → c17(ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(ACTIVATE(z0), ACTIVATE(z1))
K tuples:none
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
TERMS(z0) → c 3.41/1.35
ACTIVATE(n__s(z0)) → c17(ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(ACTIVATE(z0), ACTIVATE(z1))
terms, sqr, dbl, add, first, half, s, activate
ACTIVATE, TERMS
c16, c, c17, c18
TERMS(z0) → c
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 3.41/1.35
terms(z0) → n__terms(z0) 3.41/1.35
sqr(0) → 0 3.41/1.35
sqr(s(z0)) → s(add(sqr(z0), dbl(z0))) 3.41/1.35
dbl(0) → 0 3.41/1.35
dbl(s(z0)) → s(s(dbl(z0))) 3.41/1.35
add(0, z0) → z0 3.41/1.35
add(s(z0), z1) → s(add(z0, z1)) 3.41/1.35
first(0, z0) → nil 3.41/1.35
first(s(z0), cons(z1, z2)) → cons(z1, n__first(z0, activate(z2))) 3.41/1.35
first(z0, z1) → n__first(z0, z1) 3.41/1.35
half(0) → 0 3.41/1.35
half(s(0)) → 0 3.41/1.35
half(s(s(z0))) → s(half(z0)) 3.41/1.35
half(dbl(z0)) → z0 3.41/1.35
s(z0) → n__s(z0) 3.41/1.35
activate(n__terms(z0)) → terms(activate(z0)) 3.41/1.35
activate(n__s(z0)) → s(activate(z0)) 3.41/1.35
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 3.41/1.35
activate(z0) → z0
S tuples:
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
TERMS(z0) → c 3.41/1.35
ACTIVATE(n__s(z0)) → c17(ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(ACTIVATE(z0), ACTIVATE(z1))
K tuples:none
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
TERMS(z0) → c 3.41/1.35
ACTIVATE(n__s(z0)) → c17(ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(ACTIVATE(z0), ACTIVATE(z1))
terms, sqr, dbl, add, first, half, s, activate
ACTIVATE, TERMS
c16, c, c17, c18
We considered the (Usable) Rules:
ACTIVATE(n__s(z0)) → c17(ACTIVATE(z0))
And the Tuples:
activate(n__terms(z0)) → terms(activate(z0)) 3.41/1.35
activate(n__s(z0)) → s(activate(z0)) 3.41/1.35
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 3.41/1.35
activate(z0) → z0 3.41/1.35
first(0, z0) → nil 3.41/1.35
first(z0, z1) → n__first(z0, z1) 3.41/1.35
s(z0) → n__s(z0) 3.41/1.35
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 3.41/1.35
terms(z0) → n__terms(z0) 3.41/1.35
sqr(0) → 0
The order we found is given by the following interpretation:
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
TERMS(z0) → c 3.41/1.35
ACTIVATE(n__s(z0)) → c17(ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(ACTIVATE(z0), ACTIVATE(z1))
POL(0) = 0 3.41/1.35
POL(ACTIVATE(x1)) = x1 3.41/1.35
POL(TERMS(x1)) = 0 3.41/1.35
POL(activate(x1)) = 0 3.41/1.35
POL(c) = 0 3.41/1.35
POL(c16(x1, x2)) = x1 + x2 3.41/1.35
POL(c17(x1)) = x1 3.41/1.35
POL(c18(x1, x2)) = x1 + x2 3.41/1.35
POL(cons(x1, x2)) = [3] + x1 3.41/1.35
POL(first(x1, x2)) = [3] 3.41/1.35
POL(n__first(x1, x2)) = x1 + x2 3.41/1.35
POL(n__s(x1)) = [1] + x1 3.41/1.35
POL(n__terms(x1)) = x1 3.41/1.35
POL(nil) = [3] 3.41/1.35
POL(recip(x1)) = [3] + x1 3.41/1.35
POL(s(x1)) = [3] 3.41/1.35
POL(sqr(x1)) = [1] 3.41/1.35
POL(terms(x1)) = [3]
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 3.41/1.35
terms(z0) → n__terms(z0) 3.41/1.35
sqr(0) → 0 3.41/1.35
sqr(s(z0)) → s(add(sqr(z0), dbl(z0))) 3.41/1.35
dbl(0) → 0 3.41/1.35
dbl(s(z0)) → s(s(dbl(z0))) 3.41/1.35
add(0, z0) → z0 3.41/1.35
add(s(z0), z1) → s(add(z0, z1)) 3.41/1.35
first(0, z0) → nil 3.41/1.35
first(s(z0), cons(z1, z2)) → cons(z1, n__first(z0, activate(z2))) 3.41/1.35
first(z0, z1) → n__first(z0, z1) 3.41/1.35
half(0) → 0 3.41/1.35
half(s(0)) → 0 3.41/1.35
half(s(s(z0))) → s(half(z0)) 3.41/1.35
half(dbl(z0)) → z0 3.41/1.35
s(z0) → n__s(z0) 3.41/1.35
activate(n__terms(z0)) → terms(activate(z0)) 3.41/1.35
activate(n__s(z0)) → s(activate(z0)) 3.41/1.35
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 3.41/1.35
activate(z0) → z0
S tuples:
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
TERMS(z0) → c 3.41/1.35
ACTIVATE(n__s(z0)) → c17(ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(ACTIVATE(z0), ACTIVATE(z1))
K tuples:
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
TERMS(z0) → c 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(ACTIVATE(z0), ACTIVATE(z1))
Defined Rule Symbols:
ACTIVATE(n__s(z0)) → c17(ACTIVATE(z0))
terms, sqr, dbl, add, first, half, s, activate
ACTIVATE, TERMS
c16, c, c17, c18
We considered the (Usable) Rules:
ACTIVATE(n__first(z0, z1)) → c18(ACTIVATE(z0), ACTIVATE(z1))
And the Tuples:
activate(n__terms(z0)) → terms(activate(z0)) 3.41/1.35
activate(n__s(z0)) → s(activate(z0)) 3.41/1.35
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 3.41/1.35
activate(z0) → z0 3.41/1.35
first(0, z0) → nil 3.41/1.35
first(z0, z1) → n__first(z0, z1) 3.41/1.35
s(z0) → n__s(z0) 3.41/1.35
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 3.41/1.35
terms(z0) → n__terms(z0) 3.41/1.35
sqr(0) → 0
The order we found is given by the following interpretation:
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
TERMS(z0) → c 3.41/1.35
ACTIVATE(n__s(z0)) → c17(ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(ACTIVATE(z0), ACTIVATE(z1))
POL(0) = [2] 3.41/1.35
POL(ACTIVATE(x1)) = [5] + [4]x1 3.41/1.35
POL(TERMS(x1)) = 0 3.41/1.35
POL(activate(x1)) = 0 3.41/1.35
POL(c) = 0 3.41/1.35
POL(c16(x1, x2)) = x1 + x2 3.41/1.35
POL(c17(x1)) = x1 3.41/1.35
POL(c18(x1, x2)) = x1 + x2 3.41/1.35
POL(cons(x1, x2)) = [3] + x1 3.41/1.35
POL(first(x1, x2)) = [3] 3.41/1.35
POL(n__first(x1, x2)) = [4] + x1 + x2 3.41/1.35
POL(n__s(x1)) = x1 3.41/1.35
POL(n__terms(x1)) = x1 3.41/1.35
POL(nil) = [3] 3.41/1.35
POL(recip(x1)) = [3] + x1 3.41/1.35
POL(s(x1)) = [3] 3.41/1.35
POL(sqr(x1)) = [4] 3.41/1.35
POL(terms(x1)) = [3]
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 3.41/1.35
terms(z0) → n__terms(z0) 3.41/1.35
sqr(0) → 0 3.41/1.35
sqr(s(z0)) → s(add(sqr(z0), dbl(z0))) 3.41/1.35
dbl(0) → 0 3.41/1.35
dbl(s(z0)) → s(s(dbl(z0))) 3.41/1.35
add(0, z0) → z0 3.41/1.35
add(s(z0), z1) → s(add(z0, z1)) 3.41/1.35
first(0, z0) → nil 3.41/1.35
first(s(z0), cons(z1, z2)) → cons(z1, n__first(z0, activate(z2))) 3.41/1.35
first(z0, z1) → n__first(z0, z1) 3.41/1.35
half(0) → 0 3.41/1.35
half(s(0)) → 0 3.41/1.35
half(s(s(z0))) → s(half(z0)) 3.41/1.35
half(dbl(z0)) → z0 3.41/1.35
s(z0) → n__s(z0) 3.41/1.35
activate(n__terms(z0)) → terms(activate(z0)) 3.41/1.35
activate(n__s(z0)) → s(activate(z0)) 3.41/1.35
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 3.41/1.35
activate(z0) → z0
S tuples:
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
TERMS(z0) → c 3.41/1.35
ACTIVATE(n__s(z0)) → c17(ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(ACTIVATE(z0), ACTIVATE(z1))
K tuples:
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
TERMS(z0) → c
Defined Rule Symbols:
ACTIVATE(n__s(z0)) → c17(ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(ACTIVATE(z0), ACTIVATE(z1))
terms, sqr, dbl, add, first, half, s, activate
ACTIVATE, TERMS
c16, c, c17, c18
We considered the (Usable) Rules:
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
TERMS(z0) → c
And the Tuples:
activate(n__terms(z0)) → terms(activate(z0)) 3.41/1.35
activate(n__s(z0)) → s(activate(z0)) 3.41/1.35
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 3.41/1.35
activate(z0) → z0 3.41/1.35
first(0, z0) → nil 3.41/1.35
first(z0, z1) → n__first(z0, z1) 3.41/1.35
s(z0) → n__s(z0) 3.41/1.35
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 3.41/1.35
terms(z0) → n__terms(z0) 3.41/1.35
sqr(0) → 0
The order we found is given by the following interpretation:
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
TERMS(z0) → c 3.41/1.35
ACTIVATE(n__s(z0)) → c17(ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(ACTIVATE(z0), ACTIVATE(z1))
POL(0) = [2] 3.41/1.35
POL(ACTIVATE(x1)) = [2]x1 3.41/1.35
POL(TERMS(x1)) = [3] 3.41/1.35
POL(activate(x1)) = [2]x1 3.41/1.35
POL(c) = 0 3.41/1.35
POL(c16(x1, x2)) = x1 + x2 3.41/1.35
POL(c17(x1)) = x1 3.41/1.35
POL(c18(x1, x2)) = x1 + x2 3.41/1.35
POL(cons(x1, x2)) = [3] + x1 3.41/1.35
POL(first(x1, x2)) = x1 + x2 3.41/1.35
POL(n__first(x1, x2)) = x1 + x2 3.41/1.35
POL(n__s(x1)) = x1 3.41/1.35
POL(n__terms(x1)) = [2] + x1 3.41/1.35
POL(nil) = [2] 3.41/1.35
POL(recip(x1)) = [1] 3.41/1.35
POL(s(x1)) = x1 3.41/1.35
POL(sqr(x1)) = [4] 3.41/1.35
POL(terms(x1)) = [4] + x1
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 3.41/1.35
terms(z0) → n__terms(z0) 3.41/1.35
sqr(0) → 0 3.41/1.35
sqr(s(z0)) → s(add(sqr(z0), dbl(z0))) 3.41/1.35
dbl(0) → 0 3.41/1.35
dbl(s(z0)) → s(s(dbl(z0))) 3.41/1.35
add(0, z0) → z0 3.41/1.35
add(s(z0), z1) → s(add(z0, z1)) 3.41/1.35
first(0, z0) → nil 3.41/1.35
first(s(z0), cons(z1, z2)) → cons(z1, n__first(z0, activate(z2))) 3.41/1.35
first(z0, z1) → n__first(z0, z1) 3.41/1.35
half(0) → 0 3.41/1.35
half(s(0)) → 0 3.41/1.35
half(s(s(z0))) → s(half(z0)) 3.41/1.35
half(dbl(z0)) → z0 3.41/1.35
s(z0) → n__s(z0) 3.41/1.35
activate(n__terms(z0)) → terms(activate(z0)) 3.41/1.35
activate(n__s(z0)) → s(activate(z0)) 3.41/1.35
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 3.41/1.35
activate(z0) → z0
S tuples:none
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
TERMS(z0) → c 3.41/1.35
ACTIVATE(n__s(z0)) → c17(ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(ACTIVATE(z0), ACTIVATE(z1))
Defined Rule Symbols:
ACTIVATE(n__s(z0)) → c17(ACTIVATE(z0)) 3.41/1.35
ACTIVATE(n__first(z0, z1)) → c18(ACTIVATE(z0), ACTIVATE(z1)) 3.41/1.35
ACTIVATE(n__terms(z0)) → c16(TERMS(activate(z0)), ACTIVATE(z0)) 3.41/1.35
TERMS(z0) → c
terms, sqr, dbl, add, first, half, s, activate
ACTIVATE, TERMS
c16, c, c17, c18