YES(O(1), O(n^2)) 51.09/19.80 YES(O(1), O(n^2)) 51.30/19.83 51.30/19.83 51.30/19.83
51.30/19.83 51.30/19.830 CpxTRS51.30/19.83
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))51.30/19.83
↳2 CdtProblem51.30/19.83
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))51.30/19.83
↳4 CdtProblem51.30/19.83
↳5 CdtNarrowingProof (BOTH BOUNDS(ID, ID))51.30/19.83
↳6 CdtProblem51.30/19.83
↳7 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))51.30/19.83
↳8 CdtProblem51.30/19.83
↳9 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))51.30/19.83
↳10 CdtProblem51.30/19.83
↳11 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))51.30/19.83
↳12 CdtProblem51.30/19.83
↳13 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))51.30/19.83
↳14 CdtProblem51.30/19.83
↳15 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))51.30/19.83
↳16 CdtProblem51.30/19.83
↳17 CdtNarrowingProof (BOTH BOUNDS(ID, ID))51.30/19.83
↳18 CdtProblem51.30/19.83
↳19 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))51.30/19.83
↳20 CdtProblem51.30/19.83
↳21 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))51.30/19.83
↳22 CdtProblem51.30/19.83
↳23 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))51.30/19.83
↳24 CdtProblem51.30/19.83
↳25 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))51.30/19.83
↳26 CdtProblem51.30/19.83
↳27 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))51.30/19.83
↳28 CdtProblem51.30/19.83
↳29 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))51.30/19.83
↳30 CdtProblem51.30/19.83
↳31 SIsEmptyProof (BOTH BOUNDS(ID, ID))51.30/19.83
↳32 BOUNDS(O(1), O(1))51.30/19.83
-(x, 0) → x 51.30/19.83
-(s(x), s(y)) → -(x, y) 51.30/19.83
p(s(x)) → x 51.30/19.83
f(s(x), y) → f(p(-(s(x), y)), p(-(y, s(x)))) 51.30/19.83
f(x, s(y)) → f(p(-(x, s(y))), p(-(s(y), x)))
Tuples:
-(z0, 0) → z0 51.30/19.83
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.83
p(s(z0)) → z0 51.30/19.83
f(s(z0), z1) → f(p(-(s(z0), z1)), p(-(z1, s(z0)))) 51.30/19.83
f(z0, s(z1)) → f(p(-(z0, s(z1))), p(-(s(z1), z0)))
S tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.84
F(s(z0), z1) → c3(F(p(-(s(z0), z1)), p(-(z1, s(z0)))), P(-(s(z0), z1)), -'(s(z0), z1), P(-(z1, s(z0))), -'(z1, s(z0))) 51.30/19.84
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), P(-(z0, s(z1))), -'(z0, s(z1)), P(-(s(z1), z0)), -'(s(z1), z0))
K tuples:none
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.84
F(s(z0), z1) → c3(F(p(-(s(z0), z1)), p(-(z1, s(z0)))), P(-(s(z0), z1)), -'(s(z0), z1), P(-(z1, s(z0))), -'(z1, s(z0))) 51.30/19.84
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), P(-(z0, s(z1))), -'(z0, s(z1)), P(-(s(z1), z0)), -'(s(z1), z0))
-, p, f
-', F
c1, c3, c4
Tuples:
-(z0, 0) → z0 51.30/19.84
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.84
p(s(z0)) → z0 51.30/19.84
f(s(z0), z1) → f(p(-(s(z0), z1)), p(-(z1, s(z0)))) 51.30/19.84
f(z0, s(z1)) → f(p(-(z0, s(z1))), p(-(s(z1), z0)))
S tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.84
F(s(z0), z1) → c3(F(p(-(s(z0), z1)), p(-(z1, s(z0)))), -'(s(z0), z1), -'(z1, s(z0))) 51.30/19.84
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0))
K tuples:none
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.84
F(s(z0), z1) → c3(F(p(-(s(z0), z1)), p(-(z1, s(z0)))), -'(s(z0), z1), -'(z1, s(z0))) 51.30/19.84
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0))
-, p, f
-', F
c1, c3, c4
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.84
F(s(x0), 0) → c3(F(p(s(x0)), p(-(0, s(x0)))), -'(s(x0), 0), -'(0, s(x0))) 51.30/19.84
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0)))
Tuples:
-(z0, 0) → z0 51.30/19.84
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.84
p(s(z0)) → z0 51.30/19.84
f(s(z0), z1) → f(p(-(s(z0), z1)), p(-(z1, s(z0)))) 51.30/19.84
f(z0, s(z1)) → f(p(-(z0, s(z1))), p(-(s(z1), z0)))
S tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.84
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0)) 51.30/19.84
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.84
F(s(x0), 0) → c3(F(p(s(x0)), p(-(0, s(x0)))), -'(s(x0), 0), -'(0, s(x0))) 51.30/19.84
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0)))
K tuples:none
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.84
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0)) 51.30/19.84
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.84
F(s(x0), 0) → c3(F(p(s(x0)), p(-(0, s(x0)))), -'(s(x0), 0), -'(0, s(x0))) 51.30/19.84
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0)))
-, p, f
-', F
c1, c4, c3
Tuples:
-(z0, 0) → z0 51.30/19.84
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.84
p(s(z0)) → z0 51.30/19.84
f(s(z0), z1) → f(p(-(s(z0), z1)), p(-(z1, s(z0)))) 51.30/19.84
f(z0, s(z1)) → f(p(-(z0, s(z1))), p(-(s(z1), z0)))
S tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.84
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0)) 51.30/19.84
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.84
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.84
F(s(x0), 0) → c3
K tuples:none
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.84
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0)) 51.30/19.84
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.84
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.84
F(s(x0), 0) → c3
-, p, f
-', F
c1, c4, c3, c3
F(s(x0), 0) → c3
Tuples:
-(z0, 0) → z0 51.30/19.84
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.84
p(s(z0)) → z0 51.30/19.84
f(s(z0), z1) → f(p(-(s(z0), z1)), p(-(z1, s(z0)))) 51.30/19.84
f(z0, s(z1)) → f(p(-(z0, s(z1))), p(-(s(z1), z0)))
S tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.84
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0)) 51.30/19.84
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.84
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.84
F(s(x0), 0) → c3
K tuples:none
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.84
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0)) 51.30/19.84
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.84
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.84
F(s(x0), 0) → c3
-, p, f
-', F
c1, c4, c3, c3
We considered the (Usable) Rules:
F(s(x0), 0) → c3
And the Tuples:
-(z0, 0) → z0 51.30/19.84
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.84
p(s(z0)) → z0
The order we found is given by the following interpretation:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.84
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0)) 51.30/19.84
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.84
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.84
F(s(x0), 0) → c3
POL(-(x1, x2)) = 0 51.30/19.84
POL(-'(x1, x2)) = 0 51.30/19.84
POL(0) = [1] 51.30/19.84
POL(F(x1, x2)) = [1] 51.30/19.84
POL(c1(x1)) = x1 51.30/19.84
POL(c3) = 0 51.30/19.84
POL(c3(x1, x2, x3)) = x1 + x2 + x3 51.30/19.84
POL(c4(x1, x2, x3)) = x1 + x2 + x3 51.30/19.84
POL(p(x1)) = 0 51.30/19.84
POL(s(x1)) = 0
Tuples:
-(z0, 0) → z0 51.30/19.84
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.84
p(s(z0)) → z0 51.30/19.84
f(s(z0), z1) → f(p(-(s(z0), z1)), p(-(z1, s(z0)))) 51.30/19.84
f(z0, s(z1)) → f(p(-(z0, s(z1))), p(-(s(z1), z0)))
S tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.84
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0)) 51.30/19.84
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.84
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.84
F(s(x0), 0) → c3
K tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.84
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0)) 51.30/19.84
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.84
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0)))
Defined Rule Symbols:
F(s(x0), 0) → c3
-, p, f
-', F
c1, c4, c3, c3
We considered the (Usable) Rules:
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0)))
And the Tuples:
-(z0, 0) → z0 51.30/19.84
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.84
p(s(z0)) → z0
The order we found is given by the following interpretation:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.84
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0)) 51.30/19.84
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.84
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.84
F(s(x0), 0) → c3
POL(-(x1, x2)) = x1 51.30/19.84
POL(-'(x1, x2)) = 0 51.30/19.84
POL(0) = 0 51.30/19.84
POL(F(x1, x2)) = [4]x1 51.30/19.84
POL(c1(x1)) = x1 51.30/19.84
POL(c3) = 0 51.30/19.84
POL(c3(x1, x2, x3)) = x1 + x2 + x3 51.30/19.84
POL(c4(x1, x2, x3)) = x1 + x2 + x3 51.30/19.84
POL(p(x1)) = x1 51.30/19.84
POL(s(x1)) = [2] + x1
Tuples:
-(z0, 0) → z0 51.30/19.84
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.84
p(s(z0)) → z0 51.30/19.84
f(s(z0), z1) → f(p(-(s(z0), z1)), p(-(z1, s(z0)))) 51.30/19.84
f(z0, s(z1)) → f(p(-(z0, s(z1))), p(-(s(z1), z0)))
S tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.84
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0)) 51.30/19.84
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.84
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.85
F(s(x0), 0) → c3
K tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.85
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0)) 51.30/19.85
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1)))
Defined Rule Symbols:
F(s(x0), 0) → c3 51.30/19.85
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0)))
-, p, f
-', F
c1, c4, c3, c3
We considered the (Usable) Rules:
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1)))
And the Tuples:
-(z0, 0) → z0 51.30/19.85
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.85
p(s(z0)) → z0
The order we found is given by the following interpretation:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.85
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0)) 51.30/19.85
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(x0), 0) → c3
POL(-(x1, x2)) = x1 51.30/19.86
POL(-'(x1, x2)) = 0 51.30/19.86
POL(0) = 0 51.30/19.86
POL(F(x1, x2)) = [2]x2 51.30/19.86
POL(c1(x1)) = x1 51.30/19.86
POL(c3) = 0 51.30/19.86
POL(c3(x1, x2, x3)) = x1 + x2 + x3 51.30/19.86
POL(c4(x1, x2, x3)) = x1 + x2 + x3 51.30/19.86
POL(p(x1)) = x1 51.30/19.86
POL(s(x1)) = [4] + x1
Tuples:
-(z0, 0) → z0 51.30/19.86
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.86
p(s(z0)) → z0 51.30/19.86
f(s(z0), z1) → f(p(-(s(z0), z1)), p(-(z1, s(z0)))) 51.30/19.86
f(z0, s(z1)) → f(p(-(z0, s(z1))), p(-(s(z1), z0)))
S tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0)) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(x0), 0) → c3
K tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(z0, s(z1)) → c4(F(p(-(z0, s(z1))), p(-(s(z1), z0))), -'(z0, s(z1)), -'(s(z1), z0))
Defined Rule Symbols:
F(s(x0), 0) → c3 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1)))
-, p, f
-', F
c1, c4, c3, c3
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(0, s(x1)) → c4(F(p(-(0, s(x1))), p(s(x1))), -'(0, s(x1)), -'(s(x1), 0)) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0)))
Tuples:
-(z0, 0) → z0 51.30/19.86
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.86
p(s(z0)) → z0 51.30/19.86
f(s(z0), z1) → f(p(-(s(z0), z1)), p(-(z1, s(z0)))) 51.30/19.86
f(z0, s(z1)) → f(p(-(z0, s(z1))), p(-(s(z1), z0)))
S tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(x0), 0) → c3 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(0, s(x1)) → c4(F(p(-(0, s(x1))), p(s(x1))), -'(0, s(x1)), -'(s(x1), 0)) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0)))
K tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(0, s(x1)) → c4(F(p(-(0, s(x1))), p(s(x1))), -'(0, s(x1)), -'(s(x1), 0)) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0)))
Defined Rule Symbols:
F(s(x0), 0) → c3 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1)))
-, p, f
-', F
c1, c3, c3, c4
Tuples:
-(z0, 0) → z0 51.30/19.86
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.86
p(s(z0)) → z0 51.30/19.86
f(s(z0), z1) → f(p(-(s(z0), z1)), p(-(z1, s(z0)))) 51.30/19.86
f(z0, s(z1)) → f(p(-(z0, s(z1))), p(-(s(z1), z0)))
S tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(x0), 0) → c3 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(0, s(x1)) → c4
K tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(0, s(x1)) → c4
Defined Rule Symbols:
F(s(x0), 0) → c3 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1)))
-, p, f
-', F
c1, c3, c3, c4, c4
F(s(x0), 0) → c3 51.30/19.86
F(0, s(x1)) → c4
Tuples:
-(z0, 0) → z0 51.30/19.86
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.86
p(s(z0)) → z0 51.30/19.86
f(s(z0), z1) → f(p(-(s(z0), z1)), p(-(z1, s(z0)))) 51.30/19.86
f(z0, s(z1)) → f(p(-(z0, s(z1))), p(-(s(z1), z0)))
S tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(x0), 0) → c3 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(0, s(x1)) → c4
K tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(0, s(x1)) → c4
Defined Rule Symbols:
F(s(x0), 0) → c3 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1)))
-, p, f
-', F
c1, c3, c3, c4, c4
We considered the (Usable) Rules:
F(0, s(x1)) → c4
And the Tuples:
-(z0, 0) → z0 51.30/19.86
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.86
p(s(z0)) → z0
The order we found is given by the following interpretation:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(x0), 0) → c3 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(0, s(x1)) → c4
POL(-(x1, x2)) = 0 51.30/19.86
POL(-'(x1, x2)) = 0 51.30/19.86
POL(0) = [1] 51.30/19.86
POL(F(x1, x2)) = [1] 51.30/19.86
POL(c1(x1)) = x1 51.30/19.86
POL(c3) = 0 51.30/19.86
POL(c3(x1, x2, x3)) = x1 + x2 + x3 51.30/19.86
POL(c4) = 0 51.30/19.86
POL(c4(x1, x2, x3)) = x1 + x2 + x3 51.30/19.86
POL(p(x1)) = 0 51.30/19.86
POL(s(x1)) = 0
Tuples:
-(z0, 0) → z0 51.30/19.86
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.86
p(s(z0)) → z0 51.30/19.86
f(s(z0), z1) → f(p(-(s(z0), z1)), p(-(z1, s(z0)))) 51.30/19.86
f(z0, s(z1)) → f(p(-(z0, s(z1))), p(-(s(z1), z0)))
S tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(x0), 0) → c3 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(0, s(x1)) → c4
K tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0)))
Defined Rule Symbols:
F(s(x0), 0) → c3 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(0, s(x1)) → c4
-, p, f
-', F
c1, c3, c3, c4, c4
We considered the (Usable) Rules:
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1)))
And the Tuples:
-(z0, 0) → z0 51.30/19.86
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.86
p(s(z0)) → z0
The order we found is given by the following interpretation:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(x0), 0) → c3 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(0, s(x1)) → c4
POL(-(x1, x2)) = x1 51.30/19.86
POL(-'(x1, x2)) = 0 51.30/19.86
POL(0) = 0 51.30/19.86
POL(F(x1, x2)) = x2 51.30/19.86
POL(c1(x1)) = x1 51.30/19.86
POL(c3) = 0 51.30/19.86
POL(c3(x1, x2, x3)) = x1 + x2 + x3 51.30/19.86
POL(c4) = 0 51.30/19.86
POL(c4(x1, x2, x3)) = x1 + x2 + x3 51.30/19.86
POL(p(x1)) = x1 51.30/19.86
POL(s(x1)) = [1] + x1
Tuples:
-(z0, 0) → z0 51.30/19.86
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.86
p(s(z0)) → z0 51.30/19.86
f(s(z0), z1) → f(p(-(s(z0), z1)), p(-(z1, s(z0)))) 51.30/19.86
f(z0, s(z1)) → f(p(-(z0, s(z1))), p(-(s(z1), z0)))
S tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(x0), 0) → c3 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(0, s(x1)) → c4
K tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0)))
Defined Rule Symbols:
F(s(x0), 0) → c3 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(0, s(x1)) → c4 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1)))
-, p, f
-', F
c1, c3, c3, c4, c4
We considered the (Usable) Rules:
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0)))
And the Tuples:
-(z0, 0) → z0 51.30/19.86
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.86
p(s(z0)) → z0
The order we found is given by the following interpretation:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(x0), 0) → c3 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(0, s(x1)) → c4
POL(-(x1, x2)) = x1 51.30/19.86
POL(-'(x1, x2)) = 0 51.30/19.86
POL(0) = 0 51.30/19.86
POL(F(x1, x2)) = x1 51.30/19.86
POL(c1(x1)) = x1 51.30/19.86
POL(c3) = 0 51.30/19.86
POL(c3(x1, x2, x3)) = x1 + x2 + x3 51.30/19.86
POL(c4) = 0 51.30/19.86
POL(c4(x1, x2, x3)) = x1 + x2 + x3 51.30/19.86
POL(p(x1)) = x1 51.30/19.86
POL(s(x1)) = [1] + x1
Tuples:
-(z0, 0) → z0 51.30/19.86
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.86
p(s(z0)) → z0 51.30/19.86
f(s(z0), z1) → f(p(-(s(z0), z1)), p(-(z1, s(z0)))) 51.30/19.86
f(z0, s(z1)) → f(p(-(z0, s(z1))), p(-(s(z1), z0)))
S tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(x0), 0) → c3 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(0, s(x1)) → c4
K tuples:
-'(s(z0), s(z1)) → c1(-'(z0, z1))
Defined Rule Symbols:
F(s(x0), 0) → c3 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(0, s(x1)) → c4 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0)))
-, p, f
-', F
c1, c3, c3, c4, c4
We considered the (Usable) Rules:
-'(s(z0), s(z1)) → c1(-'(z0, z1))
And the Tuples:
-(z0, 0) → z0 51.30/19.86
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.86
p(s(z0)) → z0
The order we found is given by the following interpretation:
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(x0), 0) → c3 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(0, s(x1)) → c4
POL(-(x1, x2)) = x1 51.30/19.86
POL(-'(x1, x2)) = x2 51.30/19.86
POL(0) = [3] 51.30/19.86
POL(F(x1, x2)) = [3]x2 + x22 + [2]x1·x2 + [2]x12 51.30/19.86
POL(c1(x1)) = x1 51.30/19.86
POL(c3) = 0 51.30/19.86
POL(c3(x1, x2, x3)) = x1 + x2 + x3 51.30/19.86
POL(c4) = 0 51.30/19.86
POL(c4(x1, x2, x3)) = x1 + x2 + x3 51.30/19.86
POL(p(x1)) = x1 51.30/19.86
POL(s(x1)) = [2] + x1
Tuples:
-(z0, 0) → z0 51.30/19.86
-(s(z0), s(z1)) → -(z0, z1) 51.30/19.86
p(s(z0)) → z0 51.30/19.86
f(s(z0), z1) → f(p(-(s(z0), z1)), p(-(z1, s(z0)))) 51.30/19.86
f(z0, s(z1)) → f(p(-(z0, s(z1))), p(-(s(z1), z0)))
S tuples:none
-'(s(z0), s(z1)) → c1(-'(z0, z1)) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(x0), 0) → c3 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(0, s(x1)) → c4
Defined Rule Symbols:
F(s(x0), 0) → c3 51.30/19.86
F(s(z0), s(z1)) → c3(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
F(s(z1), s(z0)) → c3(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(0, s(x1)) → c4 51.30/19.86
F(s(z1), s(z0)) → c4(F(p(-(s(z1), s(z0))), p(-(z0, z1))), -'(s(z1), s(z0)), -'(s(z0), s(z1))) 51.30/19.86
F(s(z0), s(z1)) → c4(F(p(-(z0, z1)), p(-(s(z1), s(z0)))), -'(s(z0), s(z1)), -'(s(z1), s(z0))) 51.30/19.86
-'(s(z0), s(z1)) → c1(-'(z0, z1))
-, p, f
-', F
c1, c3, c3, c4, c4