YES(O(1), O(n^1)) 0.00/0.75 YES(O(1), O(n^1)) 0.00/0.76 0.00/0.76 0.00/0.76
0.00/0.76 0.00/0.760 CpxRelTRS0.00/0.76
↳1 CpxRelTrsToCDT (UPPER BOUND (ID))0.00/0.76
↳2 CdtProblem0.00/0.76
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))0.00/0.76
↳4 CdtProblem0.00/0.76
↳5 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.76
↳6 CdtProblem0.00/0.76
↳7 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.76
↳8 BOUNDS(O(1), O(1))0.00/0.76
f(C(x1, x2)) → C(f(x1), f(x2)) 0.00/0.76
f(Z) → Z 0.00/0.76
eqZList(C(x1, x2), C(y1, y2)) → and(eqZList(x1, y1), eqZList(x2, y2)) 0.00/0.76
eqZList(C(x1, x2), Z) → False 0.00/0.76
eqZList(Z, C(y1, y2)) → False 0.00/0.76
eqZList(Z, Z) → True 0.00/0.76
second(C(x1, x2)) → x2 0.00/0.76
first(C(x1, x2)) → x1 0.00/0.76
g(x) → x
and(False, False) → False 0.00/0.76
and(True, False) → False 0.00/0.76
and(False, True) → False 0.00/0.76
and(True, True) → True
Tuples:
and(False, False) → False 0.00/0.76
and(True, False) → False 0.00/0.76
and(False, True) → False 0.00/0.76
and(True, True) → True 0.00/0.76
f(C(z0, z1)) → C(f(z0), f(z1)) 0.00/0.76
f(Z) → Z 0.00/0.76
eqZList(C(z0, z1), C(z2, z3)) → and(eqZList(z0, z2), eqZList(z1, z3)) 0.00/0.76
eqZList(C(z0, z1), Z) → False 0.00/0.76
eqZList(Z, C(z0, z1)) → False 0.00/0.76
eqZList(Z, Z) → True 0.00/0.76
second(C(z0, z1)) → z1 0.00/0.76
first(C(z0, z1)) → z0 0.00/0.76
g(z0) → z0
S tuples:
F(C(z0, z1)) → c4(F(z0), F(z1)) 0.00/0.76
EQZLIST(C(z0, z1), C(z2, z3)) → c6(AND(eqZList(z0, z2), eqZList(z1, z3)), EQZLIST(z0, z2), EQZLIST(z1, z3))
K tuples:none
F(C(z0, z1)) → c4(F(z0), F(z1)) 0.00/0.76
EQZLIST(C(z0, z1), C(z2, z3)) → c6(AND(eqZList(z0, z2), eqZList(z1, z3)), EQZLIST(z0, z2), EQZLIST(z1, z3))
f, eqZList, second, first, g, and
F, EQZLIST
c4, c6
Tuples:
and(False, False) → False 0.00/0.76
and(True, False) → False 0.00/0.76
and(False, True) → False 0.00/0.76
and(True, True) → True 0.00/0.76
f(C(z0, z1)) → C(f(z0), f(z1)) 0.00/0.76
f(Z) → Z 0.00/0.76
eqZList(C(z0, z1), C(z2, z3)) → and(eqZList(z0, z2), eqZList(z1, z3)) 0.00/0.76
eqZList(C(z0, z1), Z) → False 0.00/0.76
eqZList(Z, C(z0, z1)) → False 0.00/0.76
eqZList(Z, Z) → True 0.00/0.76
second(C(z0, z1)) → z1 0.00/0.76
first(C(z0, z1)) → z0 0.00/0.76
g(z0) → z0
S tuples:
F(C(z0, z1)) → c4(F(z0), F(z1)) 0.00/0.76
EQZLIST(C(z0, z1), C(z2, z3)) → c6(EQZLIST(z0, z2), EQZLIST(z1, z3))
K tuples:none
F(C(z0, z1)) → c4(F(z0), F(z1)) 0.00/0.76
EQZLIST(C(z0, z1), C(z2, z3)) → c6(EQZLIST(z0, z2), EQZLIST(z1, z3))
f, eqZList, second, first, g, and
F, EQZLIST
c4, c6
We considered the (Usable) Rules:none
F(C(z0, z1)) → c4(F(z0), F(z1)) 0.00/0.76
EQZLIST(C(z0, z1), C(z2, z3)) → c6(EQZLIST(z0, z2), EQZLIST(z1, z3))
The order we found is given by the following interpretation:
F(C(z0, z1)) → c4(F(z0), F(z1)) 0.00/0.76
EQZLIST(C(z0, z1), C(z2, z3)) → c6(EQZLIST(z0, z2), EQZLIST(z1, z3))
POL(C(x1, x2)) = [2] + x1 + x2 0.00/0.76
POL(EQZLIST(x1, x2)) = [3]x1 0.00/0.76
POL(F(x1)) = [3] + [2]x1 0.00/0.76
POL(c4(x1, x2)) = x1 + x2 0.00/0.76
POL(c6(x1, x2)) = x1 + x2
Tuples:
and(False, False) → False 0.00/0.76
and(True, False) → False 0.00/0.76
and(False, True) → False 0.00/0.76
and(True, True) → True 0.00/0.76
f(C(z0, z1)) → C(f(z0), f(z1)) 0.00/0.76
f(Z) → Z 0.00/0.76
eqZList(C(z0, z1), C(z2, z3)) → and(eqZList(z0, z2), eqZList(z1, z3)) 0.00/0.76
eqZList(C(z0, z1), Z) → False 0.00/0.76
eqZList(Z, C(z0, z1)) → False 0.00/0.76
eqZList(Z, Z) → True 0.00/0.76
second(C(z0, z1)) → z1 0.00/0.76
first(C(z0, z1)) → z0 0.00/0.76
g(z0) → z0
S tuples:none
F(C(z0, z1)) → c4(F(z0), F(z1)) 0.00/0.76
EQZLIST(C(z0, z1), C(z2, z3)) → c6(EQZLIST(z0, z2), EQZLIST(z1, z3))
Defined Rule Symbols:
F(C(z0, z1)) → c4(F(z0), F(z1)) 0.00/0.76
EQZLIST(C(z0, z1), C(z2, z3)) → c6(EQZLIST(z0, z2), EQZLIST(z1, z3))
f, eqZList, second, first, g, and
F, EQZLIST
c4, c6