YES(O(1), O(n^1)) 6.24/2.05 YES(O(1), O(n^1)) 6.62/2.13 6.62/2.13 6.62/2.13
6.62/2.13 6.62/2.130 CpxTRS6.62/2.13
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))6.62/2.13
↳2 CdtProblem6.62/2.13
↳3 CdtUnreachableProof (⇔)6.62/2.13
↳4 CdtProblem6.62/2.13
↳5 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))6.62/2.13
↳6 CdtProblem6.62/2.13
↳7 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))6.62/2.13
↳8 CdtProblem6.62/2.13
↳9 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))6.62/2.13
↳10 CdtProblem6.62/2.13
↳11 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))6.62/2.13
↳12 CdtProblem6.62/2.13
↳13 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))6.62/2.13
↳14 CdtProblem6.62/2.13
↳15 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))6.62/2.14
↳16 CdtProblem6.62/2.14
↳17 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))6.62/2.14
↳18 CdtProblem6.62/2.14
↳19 SIsEmptyProof (BOTH BOUNDS(ID, ID))6.62/2.14
↳20 BOUNDS(O(1), O(1))6.62/2.14
terms(N) → cons(recip(sqr(N)), n__terms(n__s(N))) 6.62/2.14
sqr(0) → 0 6.62/2.14
sqr(s(X)) → s(n__add(n__sqr(activate(X)), n__dbl(activate(X)))) 6.62/2.14
dbl(0) → 0 6.62/2.14
dbl(s(X)) → s(n__s(n__dbl(activate(X)))) 6.62/2.14
add(0, X) → X 6.62/2.14
add(s(X), Y) → s(n__add(activate(X), Y)) 6.62/2.14
first(0, X) → nil 6.62/2.14
first(s(X), cons(Y, Z)) → cons(Y, n__first(activate(X), activate(Z))) 6.62/2.14
terms(X) → n__terms(X) 6.62/2.14
s(X) → n__s(X) 6.62/2.14
add(X1, X2) → n__add(X1, X2) 6.62/2.14
sqr(X) → n__sqr(X) 6.62/2.14
dbl(X) → n__dbl(X) 6.62/2.14
first(X1, X2) → n__first(X1, X2) 6.62/2.14
activate(n__terms(X)) → terms(activate(X)) 6.62/2.14
activate(n__s(X)) → s(X) 6.62/2.14
activate(n__add(X1, X2)) → add(activate(X1), activate(X2)) 6.62/2.14
activate(n__sqr(X)) → sqr(activate(X)) 6.62/2.14
activate(n__dbl(X)) → dbl(activate(X)) 6.62/2.14
activate(n__first(X1, X2)) → first(activate(X1), activate(X2)) 6.62/2.14
activate(X) → X
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 6.62/2.14
terms(z0) → n__terms(z0) 6.62/2.14
sqr(0) → 0 6.62/2.14
sqr(s(z0)) → s(n__add(n__sqr(activate(z0)), n__dbl(activate(z0)))) 6.62/2.14
sqr(z0) → n__sqr(z0) 6.62/2.14
dbl(0) → 0 6.62/2.14
dbl(s(z0)) → s(n__s(n__dbl(activate(z0)))) 6.62/2.14
dbl(z0) → n__dbl(z0) 6.62/2.14
add(0, z0) → z0 6.62/2.14
add(s(z0), z1) → s(n__add(activate(z0), z1)) 6.62/2.14
add(z0, z1) → n__add(z0, z1) 6.62/2.14
first(0, z0) → nil 6.62/2.14
first(s(z0), cons(z1, z2)) → cons(z1, n__first(activate(z0), activate(z2))) 6.62/2.14
first(z0, z1) → n__first(z0, z1) 6.62/2.14
s(z0) → n__s(z0) 6.62/2.14
activate(n__terms(z0)) → terms(activate(z0)) 6.62/2.14
activate(n__s(z0)) → s(z0) 6.62/2.14
activate(n__add(z0, z1)) → add(activate(z0), activate(z1)) 6.62/2.14
activate(n__sqr(z0)) → sqr(activate(z0)) 6.62/2.14
activate(n__dbl(z0)) → dbl(activate(z0)) 6.62/2.14
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 6.62/2.14
activate(z0) → z0
S tuples:
TERMS(z0) → c(SQR(z0)) 6.62/2.14
SQR(s(z0)) → c3(S(n__add(n__sqr(activate(z0)), n__dbl(activate(z0)))), ACTIVATE(z0), ACTIVATE(z0)) 6.62/2.14
DBL(s(z0)) → c6(S(n__s(n__dbl(activate(z0)))), ACTIVATE(z0)) 6.62/2.14
ADD(s(z0), z1) → c9(S(n__add(activate(z0), z1)), ACTIVATE(z0)) 6.62/2.14
FIRST(s(z0), cons(z1, z2)) → c12(ACTIVATE(z0), ACTIVATE(z2)) 6.62/2.14
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__s(z0)) → c16(S(z0)) 6.62/2.14
ACTIVATE(n__add(z0, z1)) → c17(ADD(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.14
ACTIVATE(n__sqr(z0)) → c18(SQR(activate(z0)), ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__dbl(z0)) → c19(DBL(activate(z0)), ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__first(z0, z1)) → c20(FIRST(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1))
K tuples:none
TERMS(z0) → c(SQR(z0)) 6.62/2.14
SQR(s(z0)) → c3(S(n__add(n__sqr(activate(z0)), n__dbl(activate(z0)))), ACTIVATE(z0), ACTIVATE(z0)) 6.62/2.14
DBL(s(z0)) → c6(S(n__s(n__dbl(activate(z0)))), ACTIVATE(z0)) 6.62/2.14
ADD(s(z0), z1) → c9(S(n__add(activate(z0), z1)), ACTIVATE(z0)) 6.62/2.14
FIRST(s(z0), cons(z1, z2)) → c12(ACTIVATE(z0), ACTIVATE(z2)) 6.62/2.14
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__s(z0)) → c16(S(z0)) 6.62/2.14
ACTIVATE(n__add(z0, z1)) → c17(ADD(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.14
ACTIVATE(n__sqr(z0)) → c18(SQR(activate(z0)), ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__dbl(z0)) → c19(DBL(activate(z0)), ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__first(z0, z1)) → c20(FIRST(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1))
terms, sqr, dbl, add, first, s, activate
TERMS, SQR, DBL, ADD, FIRST, ACTIVATE
c, c3, c6, c9, c12, c15, c16, c17, c18, c19, c20
SQR(s(z0)) → c3(S(n__add(n__sqr(activate(z0)), n__dbl(activate(z0)))), ACTIVATE(z0), ACTIVATE(z0)) 6.62/2.14
DBL(s(z0)) → c6(S(n__s(n__dbl(activate(z0)))), ACTIVATE(z0)) 6.62/2.14
ADD(s(z0), z1) → c9(S(n__add(activate(z0), z1)), ACTIVATE(z0)) 6.62/2.14
FIRST(s(z0), cons(z1, z2)) → c12(ACTIVATE(z0), ACTIVATE(z2))
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 6.62/2.14
terms(z0) → n__terms(z0) 6.62/2.14
sqr(0) → 0 6.62/2.14
sqr(s(z0)) → s(n__add(n__sqr(activate(z0)), n__dbl(activate(z0)))) 6.62/2.14
sqr(z0) → n__sqr(z0) 6.62/2.14
dbl(0) → 0 6.62/2.14
dbl(s(z0)) → s(n__s(n__dbl(activate(z0)))) 6.62/2.14
dbl(z0) → n__dbl(z0) 6.62/2.14
add(0, z0) → z0 6.62/2.14
add(s(z0), z1) → s(n__add(activate(z0), z1)) 6.62/2.14
add(z0, z1) → n__add(z0, z1) 6.62/2.14
first(0, z0) → nil 6.62/2.14
first(s(z0), cons(z1, z2)) → cons(z1, n__first(activate(z0), activate(z2))) 6.62/2.14
first(z0, z1) → n__first(z0, z1) 6.62/2.14
s(z0) → n__s(z0) 6.62/2.14
activate(n__terms(z0)) → terms(activate(z0)) 6.62/2.14
activate(n__s(z0)) → s(z0) 6.62/2.14
activate(n__add(z0, z1)) → add(activate(z0), activate(z1)) 6.62/2.14
activate(n__sqr(z0)) → sqr(activate(z0)) 6.62/2.14
activate(n__dbl(z0)) → dbl(activate(z0)) 6.62/2.14
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 6.62/2.14
activate(z0) → z0
S tuples:
TERMS(z0) → c(SQR(z0)) 6.62/2.14
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__s(z0)) → c16(S(z0)) 6.62/2.14
ACTIVATE(n__add(z0, z1)) → c17(ADD(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.14
ACTIVATE(n__sqr(z0)) → c18(SQR(activate(z0)), ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__dbl(z0)) → c19(DBL(activate(z0)), ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__first(z0, z1)) → c20(FIRST(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1))
K tuples:none
TERMS(z0) → c(SQR(z0)) 6.62/2.14
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__s(z0)) → c16(S(z0)) 6.62/2.14
ACTIVATE(n__add(z0, z1)) → c17(ADD(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.14
ACTIVATE(n__sqr(z0)) → c18(SQR(activate(z0)), ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__dbl(z0)) → c19(DBL(activate(z0)), ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__first(z0, z1)) → c20(FIRST(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1))
terms, sqr, dbl, add, first, s, activate
TERMS, ACTIVATE
c, c15, c16, c17, c18, c19, c20
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 6.62/2.14
terms(z0) → n__terms(z0) 6.62/2.14
sqr(0) → 0 6.62/2.14
sqr(s(z0)) → s(n__add(n__sqr(activate(z0)), n__dbl(activate(z0)))) 6.62/2.14
sqr(z0) → n__sqr(z0) 6.62/2.14
dbl(0) → 0 6.62/2.14
dbl(s(z0)) → s(n__s(n__dbl(activate(z0)))) 6.62/2.14
dbl(z0) → n__dbl(z0) 6.62/2.14
add(0, z0) → z0 6.62/2.14
add(s(z0), z1) → s(n__add(activate(z0), z1)) 6.62/2.14
add(z0, z1) → n__add(z0, z1) 6.62/2.14
first(0, z0) → nil 6.62/2.14
first(s(z0), cons(z1, z2)) → cons(z1, n__first(activate(z0), activate(z2))) 6.62/2.14
first(z0, z1) → n__first(z0, z1) 6.62/2.14
s(z0) → n__s(z0) 6.62/2.14
activate(n__terms(z0)) → terms(activate(z0)) 6.62/2.14
activate(n__s(z0)) → s(z0) 6.62/2.14
activate(n__add(z0, z1)) → add(activate(z0), activate(z1)) 6.62/2.14
activate(n__sqr(z0)) → sqr(activate(z0)) 6.62/2.14
activate(n__dbl(z0)) → dbl(activate(z0)) 6.62/2.14
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 6.62/2.14
activate(z0) → z0
S tuples:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.14
TERMS(z0) → c 6.62/2.14
ACTIVATE(n__s(z0)) → c16 6.62/2.14
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.14
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
K tuples:none
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.14
TERMS(z0) → c 6.62/2.14
ACTIVATE(n__s(z0)) → c16 6.62/2.14
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.14
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.14
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
terms, sqr, dbl, add, first, s, activate
ACTIVATE, TERMS
c15, c, c16, c17, c18, c19, c20
TERMS(z0) → c 6.62/2.14
ACTIVATE(n__s(z0)) → c16
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 6.62/2.14
terms(z0) → n__terms(z0) 6.62/2.14
sqr(0) → 0 6.62/2.14
sqr(s(z0)) → s(n__add(n__sqr(activate(z0)), n__dbl(activate(z0)))) 6.62/2.14
sqr(z0) → n__sqr(z0) 6.62/2.14
dbl(0) → 0 6.62/2.14
dbl(s(z0)) → s(n__s(n__dbl(activate(z0)))) 6.62/2.14
dbl(z0) → n__dbl(z0) 6.62/2.14
add(0, z0) → z0 6.62/2.14
add(s(z0), z1) → s(n__add(activate(z0), z1)) 6.62/2.14
add(z0, z1) → n__add(z0, z1) 6.62/2.14
first(0, z0) → nil 6.62/2.14
first(s(z0), cons(z1, z2)) → cons(z1, n__first(activate(z0), activate(z2))) 6.62/2.14
first(z0, z1) → n__first(z0, z1) 6.62/2.15
s(z0) → n__s(z0) 6.62/2.15
activate(n__terms(z0)) → terms(activate(z0)) 6.62/2.15
activate(n__s(z0)) → s(z0) 6.62/2.15
activate(n__add(z0, z1)) → add(activate(z0), activate(z1)) 6.62/2.15
activate(n__sqr(z0)) → sqr(activate(z0)) 6.62/2.15
activate(n__dbl(z0)) → dbl(activate(z0)) 6.62/2.15
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 6.62/2.15
activate(z0) → z0
S tuples:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.15
TERMS(z0) → c 6.62/2.15
ACTIVATE(n__s(z0)) → c16 6.62/2.15
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.15
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.15
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.15
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
K tuples:none
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.15
TERMS(z0) → c 6.62/2.15
ACTIVATE(n__s(z0)) → c16 6.62/2.15
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.15
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.15
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.15
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
terms, sqr, dbl, add, first, s, activate
ACTIVATE, TERMS
c15, c, c16, c17, c18, c19, c20
We considered the (Usable) Rules:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.15
TERMS(z0) → c
And the Tuples:
activate(n__terms(z0)) → terms(activate(z0)) 6.62/2.15
activate(n__s(z0)) → s(z0) 6.62/2.15
activate(n__add(z0, z1)) → add(activate(z0), activate(z1)) 6.62/2.15
activate(n__sqr(z0)) → sqr(activate(z0)) 6.62/2.15
activate(n__dbl(z0)) → dbl(activate(z0)) 6.62/2.15
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 6.62/2.15
activate(z0) → z0 6.62/2.15
first(0, z0) → nil 6.62/2.15
first(z0, z1) → n__first(z0, z1) 6.62/2.15
dbl(0) → 0 6.62/2.15
dbl(z0) → n__dbl(z0) 6.62/2.15
sqr(0) → 0 6.62/2.15
sqr(z0) → n__sqr(z0) 6.62/2.15
add(0, z0) → z0 6.62/2.15
add(z0, z1) → n__add(z0, z1) 6.62/2.15
s(z0) → n__s(z0) 6.62/2.15
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 6.62/2.15
terms(z0) → n__terms(z0)
The order we found is given by the following interpretation:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.15
TERMS(z0) → c 6.62/2.15
ACTIVATE(n__s(z0)) → c16 6.62/2.15
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.15
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.15
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.15
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
POL(0) = [3] 6.62/2.15
POL(ACTIVATE(x1)) = [4]x1 6.62/2.15
POL(TERMS(x1)) = [3] 6.62/2.15
POL(activate(x1)) = 0 6.62/2.15
POL(add(x1, x2)) = [3] 6.62/2.15
POL(c) = 0 6.62/2.15
POL(c15(x1, x2)) = x1 + x2 6.62/2.15
POL(c16) = 0 6.62/2.15
POL(c17(x1, x2)) = x1 + x2 6.62/2.15
POL(c18(x1)) = x1 6.62/2.15
POL(c19(x1)) = x1 6.62/2.15
POL(c20(x1, x2)) = x1 + x2 6.62/2.15
POL(cons(x1, x2)) = [3] 6.62/2.15
POL(dbl(x1)) = [3] 6.62/2.15
POL(first(x1, x2)) = [3] + [3]x1 + [3]x2 6.62/2.15
POL(n__add(x1, x2)) = x1 + x2 6.62/2.15
POL(n__dbl(x1)) = x1 6.62/2.15
POL(n__first(x1, x2)) = x1 + x2 6.62/2.15
POL(n__s(x1)) = x1 6.62/2.15
POL(n__sqr(x1)) = x1 6.62/2.15
POL(n__terms(x1)) = [1] + x1 6.62/2.15
POL(nil) = [3] 6.62/2.15
POL(recip(x1)) = [3] 6.62/2.15
POL(s(x1)) = [3] + [3]x1 6.62/2.15
POL(sqr(x1)) = [3] 6.62/2.15
POL(terms(x1)) = [3]
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 6.62/2.15
terms(z0) → n__terms(z0) 6.62/2.15
sqr(0) → 0 6.62/2.15
sqr(s(z0)) → s(n__add(n__sqr(activate(z0)), n__dbl(activate(z0)))) 6.62/2.15
sqr(z0) → n__sqr(z0) 6.62/2.15
dbl(0) → 0 6.62/2.15
dbl(s(z0)) → s(n__s(n__dbl(activate(z0)))) 6.62/2.15
dbl(z0) → n__dbl(z0) 6.62/2.15
add(0, z0) → z0 6.62/2.15
add(s(z0), z1) → s(n__add(activate(z0), z1)) 6.62/2.15
add(z0, z1) → n__add(z0, z1) 6.62/2.15
first(0, z0) → nil 6.62/2.15
first(s(z0), cons(z1, z2)) → cons(z1, n__first(activate(z0), activate(z2))) 6.62/2.15
first(z0, z1) → n__first(z0, z1) 6.62/2.15
s(z0) → n__s(z0) 6.62/2.15
activate(n__terms(z0)) → terms(activate(z0)) 6.62/2.15
activate(n__s(z0)) → s(z0) 6.62/2.15
activate(n__add(z0, z1)) → add(activate(z0), activate(z1)) 6.62/2.15
activate(n__sqr(z0)) → sqr(activate(z0)) 6.62/2.15
activate(n__dbl(z0)) → dbl(activate(z0)) 6.62/2.15
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 6.62/2.15
activate(z0) → z0
S tuples:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.15
TERMS(z0) → c 6.62/2.15
ACTIVATE(n__s(z0)) → c16 6.62/2.15
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.15
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
K tuples:
ACTIVATE(n__s(z0)) → c16 6.62/2.16
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
Defined Rule Symbols:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.16
TERMS(z0) → c
terms, sqr, dbl, add, first, s, activate
ACTIVATE, TERMS
c15, c, c16, c17, c18, c19, c20
We considered the (Usable) Rules:
ACTIVATE(n__s(z0)) → c16
And the Tuples:
activate(n__terms(z0)) → terms(activate(z0)) 6.62/2.16
activate(n__s(z0)) → s(z0) 6.62/2.16
activate(n__add(z0, z1)) → add(activate(z0), activate(z1)) 6.62/2.16
activate(n__sqr(z0)) → sqr(activate(z0)) 6.62/2.16
activate(n__dbl(z0)) → dbl(activate(z0)) 6.62/2.16
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 6.62/2.16
activate(z0) → z0 6.62/2.16
first(0, z0) → nil 6.62/2.16
first(z0, z1) → n__first(z0, z1) 6.62/2.16
dbl(0) → 0 6.62/2.16
dbl(z0) → n__dbl(z0) 6.62/2.16
sqr(0) → 0 6.62/2.16
sqr(z0) → n__sqr(z0) 6.62/2.16
add(0, z0) → z0 6.62/2.16
add(z0, z1) → n__add(z0, z1) 6.62/2.16
s(z0) → n__s(z0) 6.62/2.16
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 6.62/2.16
terms(z0) → n__terms(z0)
The order we found is given by the following interpretation:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.16
TERMS(z0) → c 6.62/2.16
ACTIVATE(n__s(z0)) → c16 6.62/2.16
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
POL(0) = [5] 6.62/2.16
POL(ACTIVATE(x1)) = [2]x1 6.62/2.16
POL(TERMS(x1)) = 0 6.62/2.16
POL(activate(x1)) = 0 6.62/2.16
POL(add(x1, x2)) = [3] 6.62/2.16
POL(c) = 0 6.62/2.16
POL(c15(x1, x2)) = x1 + x2 6.62/2.16
POL(c16) = 0 6.62/2.16
POL(c17(x1, x2)) = x1 + x2 6.62/2.16
POL(c18(x1)) = x1 6.62/2.16
POL(c19(x1)) = x1 6.62/2.16
POL(c20(x1, x2)) = x1 + x2 6.62/2.16
POL(cons(x1, x2)) = [3] 6.62/2.16
POL(dbl(x1)) = [3] 6.62/2.16
POL(first(x1, x2)) = [3] + [3]x1 + [3]x2 6.62/2.16
POL(n__add(x1, x2)) = x1 + x2 6.62/2.16
POL(n__dbl(x1)) = x1 6.62/2.16
POL(n__first(x1, x2)) = x1 + x2 6.62/2.16
POL(n__s(x1)) = [1] + x1 6.62/2.16
POL(n__sqr(x1)) = x1 6.62/2.16
POL(n__terms(x1)) = x1 6.62/2.16
POL(nil) = [3] 6.62/2.16
POL(recip(x1)) = [3] 6.62/2.16
POL(s(x1)) = [3] + [3]x1 6.62/2.16
POL(sqr(x1)) = [3] 6.62/2.16
POL(terms(x1)) = [3]
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 6.62/2.16
terms(z0) → n__terms(z0) 6.62/2.16
sqr(0) → 0 6.62/2.16
sqr(s(z0)) → s(n__add(n__sqr(activate(z0)), n__dbl(activate(z0)))) 6.62/2.16
sqr(z0) → n__sqr(z0) 6.62/2.16
dbl(0) → 0 6.62/2.16
dbl(s(z0)) → s(n__s(n__dbl(activate(z0)))) 6.62/2.16
dbl(z0) → n__dbl(z0) 6.62/2.16
add(0, z0) → z0 6.62/2.16
add(s(z0), z1) → s(n__add(activate(z0), z1)) 6.62/2.16
add(z0, z1) → n__add(z0, z1) 6.62/2.16
first(0, z0) → nil 6.62/2.16
first(s(z0), cons(z1, z2)) → cons(z1, n__first(activate(z0), activate(z2))) 6.62/2.16
first(z0, z1) → n__first(z0, z1) 6.62/2.16
s(z0) → n__s(z0) 6.62/2.16
activate(n__terms(z0)) → terms(activate(z0)) 6.62/2.16
activate(n__s(z0)) → s(z0) 6.62/2.16
activate(n__add(z0, z1)) → add(activate(z0), activate(z1)) 6.62/2.16
activate(n__sqr(z0)) → sqr(activate(z0)) 6.62/2.16
activate(n__dbl(z0)) → dbl(activate(z0)) 6.62/2.16
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 6.62/2.16
activate(z0) → z0
S tuples:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.16
TERMS(z0) → c 6.62/2.16
ACTIVATE(n__s(z0)) → c16 6.62/2.16
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
K tuples:
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
Defined Rule Symbols:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.16
TERMS(z0) → c 6.62/2.16
ACTIVATE(n__s(z0)) → c16
terms, sqr, dbl, add, first, s, activate
ACTIVATE, TERMS
c15, c, c16, c17, c18, c19, c20
We considered the (Usable) Rules:
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
And the Tuples:
activate(n__terms(z0)) → terms(activate(z0)) 6.62/2.16
activate(n__s(z0)) → s(z0) 6.62/2.16
activate(n__add(z0, z1)) → add(activate(z0), activate(z1)) 6.62/2.16
activate(n__sqr(z0)) → sqr(activate(z0)) 6.62/2.16
activate(n__dbl(z0)) → dbl(activate(z0)) 6.62/2.16
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 6.62/2.16
activate(z0) → z0 6.62/2.16
first(0, z0) → nil 6.62/2.16
first(z0, z1) → n__first(z0, z1) 6.62/2.16
dbl(0) → 0 6.62/2.16
dbl(z0) → n__dbl(z0) 6.62/2.16
sqr(0) → 0 6.62/2.16
sqr(z0) → n__sqr(z0) 6.62/2.16
add(0, z0) → z0 6.62/2.16
add(z0, z1) → n__add(z0, z1) 6.62/2.16
s(z0) → n__s(z0) 6.62/2.16
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 6.62/2.16
terms(z0) → n__terms(z0)
The order we found is given by the following interpretation:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.16
TERMS(z0) → c 6.62/2.16
ACTIVATE(n__s(z0)) → c16 6.62/2.16
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
POL(0) = 0 6.62/2.16
POL(ACTIVATE(x1)) = [2] + [4]x1 6.62/2.16
POL(TERMS(x1)) = [5] 6.62/2.16
POL(activate(x1)) = 0 6.62/2.16
POL(add(x1, x2)) = [3] 6.62/2.16
POL(c) = 0 6.62/2.16
POL(c15(x1, x2)) = x1 + x2 6.62/2.16
POL(c16) = 0 6.62/2.16
POL(c17(x1, x2)) = x1 + x2 6.62/2.16
POL(c18(x1)) = x1 6.62/2.16
POL(c19(x1)) = x1 6.62/2.16
POL(c20(x1, x2)) = x1 + x2 6.62/2.16
POL(cons(x1, x2)) = [3] 6.62/2.16
POL(dbl(x1)) = [3] 6.62/2.16
POL(first(x1, x2)) = [3] + [3]x1 + [3]x2 6.62/2.16
POL(n__add(x1, x2)) = [1] + x1 + x2 6.62/2.16
POL(n__dbl(x1)) = x1 6.62/2.16
POL(n__first(x1, x2)) = [2] + x1 + x2 6.62/2.16
POL(n__s(x1)) = x1 6.62/2.16
POL(n__sqr(x1)) = x1 6.62/2.16
POL(n__terms(x1)) = [4] + x1 6.62/2.16
POL(nil) = [3] 6.62/2.16
POL(recip(x1)) = [3] 6.62/2.16
POL(s(x1)) = [3] + [3]x1 6.62/2.16
POL(sqr(x1)) = [3] 6.62/2.16
POL(terms(x1)) = [3]
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 6.62/2.16
terms(z0) → n__terms(z0) 6.62/2.16
sqr(0) → 0 6.62/2.16
sqr(s(z0)) → s(n__add(n__sqr(activate(z0)), n__dbl(activate(z0)))) 6.62/2.16
sqr(z0) → n__sqr(z0) 6.62/2.16
dbl(0) → 0 6.62/2.16
dbl(s(z0)) → s(n__s(n__dbl(activate(z0)))) 6.62/2.16
dbl(z0) → n__dbl(z0) 6.62/2.16
add(0, z0) → z0 6.62/2.16
add(s(z0), z1) → s(n__add(activate(z0), z1)) 6.62/2.16
add(z0, z1) → n__add(z0, z1) 6.62/2.16
first(0, z0) → nil 6.62/2.16
first(s(z0), cons(z1, z2)) → cons(z1, n__first(activate(z0), activate(z2))) 6.62/2.16
first(z0, z1) → n__first(z0, z1) 6.62/2.16
s(z0) → n__s(z0) 6.62/2.16
activate(n__terms(z0)) → terms(activate(z0)) 6.62/2.16
activate(n__s(z0)) → s(z0) 6.62/2.16
activate(n__add(z0, z1)) → add(activate(z0), activate(z1)) 6.62/2.16
activate(n__sqr(z0)) → sqr(activate(z0)) 6.62/2.16
activate(n__dbl(z0)) → dbl(activate(z0)) 6.62/2.16
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 6.62/2.16
activate(z0) → z0
S tuples:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.16
TERMS(z0) → c 6.62/2.16
ACTIVATE(n__s(z0)) → c16 6.62/2.16
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
K tuples:
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0))
Defined Rule Symbols:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.16
TERMS(z0) → c 6.62/2.16
ACTIVATE(n__s(z0)) → c16 6.62/2.16
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
terms, sqr, dbl, add, first, s, activate
ACTIVATE, TERMS
c15, c, c16, c17, c18, c19, c20
We considered the (Usable) Rules:
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0))
And the Tuples:
activate(n__terms(z0)) → terms(activate(z0)) 6.62/2.16
activate(n__s(z0)) → s(z0) 6.62/2.16
activate(n__add(z0, z1)) → add(activate(z0), activate(z1)) 6.62/2.16
activate(n__sqr(z0)) → sqr(activate(z0)) 6.62/2.16
activate(n__dbl(z0)) → dbl(activate(z0)) 6.62/2.16
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 6.62/2.16
activate(z0) → z0 6.62/2.16
first(0, z0) → nil 6.62/2.16
first(z0, z1) → n__first(z0, z1) 6.62/2.16
dbl(0) → 0 6.62/2.16
dbl(z0) → n__dbl(z0) 6.62/2.16
sqr(0) → 0 6.62/2.16
sqr(z0) → n__sqr(z0) 6.62/2.16
add(0, z0) → z0 6.62/2.16
add(z0, z1) → n__add(z0, z1) 6.62/2.16
s(z0) → n__s(z0) 6.62/2.16
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 6.62/2.16
terms(z0) → n__terms(z0)
The order we found is given by the following interpretation:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.16
TERMS(z0) → c 6.62/2.16
ACTIVATE(n__s(z0)) → c16 6.62/2.16
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
POL(0) = [3] 6.62/2.16
POL(ACTIVATE(x1)) = [2]x1 6.62/2.16
POL(TERMS(x1)) = 0 6.62/2.16
POL(activate(x1)) = 0 6.62/2.16
POL(add(x1, x2)) = [3] 6.62/2.16
POL(c) = 0 6.62/2.16
POL(c15(x1, x2)) = x1 + x2 6.62/2.16
POL(c16) = 0 6.62/2.16
POL(c17(x1, x2)) = x1 + x2 6.62/2.16
POL(c18(x1)) = x1 6.62/2.16
POL(c19(x1)) = x1 6.62/2.16
POL(c20(x1, x2)) = x1 + x2 6.62/2.16
POL(cons(x1, x2)) = [3] 6.62/2.16
POL(dbl(x1)) = [3] 6.62/2.16
POL(first(x1, x2)) = [3] + [3]x1 + [3]x2 6.62/2.16
POL(n__add(x1, x2)) = x1 + x2 6.62/2.16
POL(n__dbl(x1)) = x1 6.62/2.16
POL(n__first(x1, x2)) = x1 + x2 6.62/2.16
POL(n__s(x1)) = x1 6.62/2.16
POL(n__sqr(x1)) = [1] + x1 6.62/2.16
POL(n__terms(x1)) = x1 6.62/2.16
POL(nil) = [3] 6.62/2.16
POL(recip(x1)) = [3] 6.62/2.16
POL(s(x1)) = [3] + [3]x1 6.62/2.16
POL(sqr(x1)) = [3] 6.62/2.16
POL(terms(x1)) = [3]
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 6.62/2.16
terms(z0) → n__terms(z0) 6.62/2.16
sqr(0) → 0 6.62/2.16
sqr(s(z0)) → s(n__add(n__sqr(activate(z0)), n__dbl(activate(z0)))) 6.62/2.16
sqr(z0) → n__sqr(z0) 6.62/2.16
dbl(0) → 0 6.62/2.16
dbl(s(z0)) → s(n__s(n__dbl(activate(z0)))) 6.62/2.16
dbl(z0) → n__dbl(z0) 6.62/2.16
add(0, z0) → z0 6.62/2.16
add(s(z0), z1) → s(n__add(activate(z0), z1)) 6.62/2.16
add(z0, z1) → n__add(z0, z1) 6.62/2.16
first(0, z0) → nil 6.62/2.16
first(s(z0), cons(z1, z2)) → cons(z1, n__first(activate(z0), activate(z2))) 6.62/2.16
first(z0, z1) → n__first(z0, z1) 6.62/2.16
s(z0) → n__s(z0) 6.62/2.16
activate(n__terms(z0)) → terms(activate(z0)) 6.62/2.16
activate(n__s(z0)) → s(z0) 6.62/2.16
activate(n__add(z0, z1)) → add(activate(z0), activate(z1)) 6.62/2.16
activate(n__sqr(z0)) → sqr(activate(z0)) 6.62/2.16
activate(n__dbl(z0)) → dbl(activate(z0)) 6.62/2.16
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 6.62/2.16
activate(z0) → z0
S tuples:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.16
TERMS(z0) → c 6.62/2.16
ACTIVATE(n__s(z0)) → c16 6.62/2.16
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
K tuples:
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0))
Defined Rule Symbols:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.16
TERMS(z0) → c 6.62/2.16
ACTIVATE(n__s(z0)) → c16 6.62/2.16
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0))
terms, sqr, dbl, add, first, s, activate
ACTIVATE, TERMS
c15, c, c16, c17, c18, c19, c20
We considered the (Usable) Rules:
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0))
And the Tuples:
activate(n__terms(z0)) → terms(activate(z0)) 6.62/2.16
activate(n__s(z0)) → s(z0) 6.62/2.16
activate(n__add(z0, z1)) → add(activate(z0), activate(z1)) 6.62/2.16
activate(n__sqr(z0)) → sqr(activate(z0)) 6.62/2.16
activate(n__dbl(z0)) → dbl(activate(z0)) 6.62/2.16
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 6.62/2.16
activate(z0) → z0 6.62/2.16
first(0, z0) → nil 6.62/2.16
first(z0, z1) → n__first(z0, z1) 6.62/2.16
dbl(0) → 0 6.62/2.16
dbl(z0) → n__dbl(z0) 6.62/2.16
sqr(0) → 0 6.62/2.16
sqr(z0) → n__sqr(z0) 6.62/2.16
add(0, z0) → z0 6.62/2.16
add(z0, z1) → n__add(z0, z1) 6.62/2.16
s(z0) → n__s(z0) 6.62/2.16
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 6.62/2.16
terms(z0) → n__terms(z0)
The order we found is given by the following interpretation:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.16
TERMS(z0) → c 6.62/2.16
ACTIVATE(n__s(z0)) → c16 6.62/2.16
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
POL(0) = [3] 6.62/2.16
POL(ACTIVATE(x1)) = [2]x1 6.62/2.16
POL(TERMS(x1)) = 0 6.62/2.16
POL(activate(x1)) = 0 6.62/2.16
POL(add(x1, x2)) = [3] 6.62/2.16
POL(c) = 0 6.62/2.16
POL(c15(x1, x2)) = x1 + x2 6.62/2.16
POL(c16) = 0 6.62/2.16
POL(c17(x1, x2)) = x1 + x2 6.62/2.16
POL(c18(x1)) = x1 6.62/2.16
POL(c19(x1)) = x1 6.62/2.16
POL(c20(x1, x2)) = x1 + x2 6.62/2.16
POL(cons(x1, x2)) = [3] 6.62/2.16
POL(dbl(x1)) = [3] 6.62/2.16
POL(first(x1, x2)) = [3] + [3]x1 + [3]x2 6.62/2.16
POL(n__add(x1, x2)) = [3] + x1 + x2 6.62/2.16
POL(n__dbl(x1)) = [1] + x1 6.62/2.16
POL(n__first(x1, x2)) = x1 + x2 6.62/2.16
POL(n__s(x1)) = x1 6.62/2.16
POL(n__sqr(x1)) = x1 6.62/2.16
POL(n__terms(x1)) = x1 6.62/2.16
POL(nil) = [3] 6.62/2.16
POL(recip(x1)) = [3] 6.62/2.16
POL(s(x1)) = [3] + [3]x1 6.62/2.16
POL(sqr(x1)) = [3] 6.62/2.16
POL(terms(x1)) = [3]
Tuples:
terms(z0) → cons(recip(sqr(z0)), n__terms(n__s(z0))) 6.62/2.16
terms(z0) → n__terms(z0) 6.62/2.16
sqr(0) → 0 6.62/2.16
sqr(s(z0)) → s(n__add(n__sqr(activate(z0)), n__dbl(activate(z0)))) 6.62/2.16
sqr(z0) → n__sqr(z0) 6.62/2.16
dbl(0) → 0 6.62/2.16
dbl(s(z0)) → s(n__s(n__dbl(activate(z0)))) 6.62/2.16
dbl(z0) → n__dbl(z0) 6.62/2.16
add(0, z0) → z0 6.62/2.16
add(s(z0), z1) → s(n__add(activate(z0), z1)) 6.62/2.16
add(z0, z1) → n__add(z0, z1) 6.62/2.16
first(0, z0) → nil 6.62/2.16
first(s(z0), cons(z1, z2)) → cons(z1, n__first(activate(z0), activate(z2))) 6.62/2.16
first(z0, z1) → n__first(z0, z1) 6.62/2.16
s(z0) → n__s(z0) 6.62/2.16
activate(n__terms(z0)) → terms(activate(z0)) 6.62/2.16
activate(n__s(z0)) → s(z0) 6.62/2.16
activate(n__add(z0, z1)) → add(activate(z0), activate(z1)) 6.62/2.16
activate(n__sqr(z0)) → sqr(activate(z0)) 6.62/2.16
activate(n__dbl(z0)) → dbl(activate(z0)) 6.62/2.16
activate(n__first(z0, z1)) → first(activate(z0), activate(z1)) 6.62/2.16
activate(z0) → z0
S tuples:none
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.16
TERMS(z0) → c 6.62/2.16
ACTIVATE(n__s(z0)) → c16 6.62/2.16
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1))
Defined Rule Symbols:
ACTIVATE(n__terms(z0)) → c15(TERMS(activate(z0)), ACTIVATE(z0)) 6.62/2.16
TERMS(z0) → c 6.62/2.16
ACTIVATE(n__s(z0)) → c16 6.62/2.16
ACTIVATE(n__add(z0, z1)) → c17(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__first(z0, z1)) → c20(ACTIVATE(z0), ACTIVATE(z1)) 6.62/2.16
ACTIVATE(n__sqr(z0)) → c18(ACTIVATE(z0)) 6.62/2.16
ACTIVATE(n__dbl(z0)) → c19(ACTIVATE(z0))
terms, sqr, dbl, add, first, s, activate
ACTIVATE, TERMS
c15, c, c16, c17, c18, c19, c20