YES(O(1), O(n^2)) 0.00/0.81 YES(O(1), O(n^2)) 0.00/0.83 0.00/0.83 0.00/0.83
0.00/0.83 0.00/0.830 CpxTRS0.00/0.83
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.83
↳2 CdtProblem0.00/0.83
↳3 CdtUnreachableProof (⇔)0.00/0.83
↳4 CdtProblem0.00/0.83
↳5 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))0.00/0.83
↳6 CdtProblem0.00/0.83
↳7 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))0.00/0.83
↳8 CdtProblem0.00/0.83
↳9 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))0.00/0.83
↳10 CdtProblem0.00/0.83
↳11 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.83
↳12 CdtProblem0.00/0.83
↳13 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.83
↳14 BOUNDS(O(1), O(1))0.00/0.83
f(a) → g(h(a)) 0.00/0.83
h(g(x)) → g(h(f(x))) 0.00/0.83
k(x, h(x), a) → h(x) 0.00/0.83
k(f(x), y, x) → f(x)
Tuples:
f(a) → g(h(a)) 0.00/0.83
h(g(z0)) → g(h(f(z0))) 0.00/0.83
k(z0, h(z0), a) → h(z0) 0.00/0.83
k(f(z0), z1, z0) → f(z0)
S tuples:
F(a) → c(H(a)) 0.00/0.83
H(g(z0)) → c1(H(f(z0)), F(z0)) 0.00/0.83
K(z0, h(z0), a) → c2(H(z0)) 0.00/0.83
K(f(z0), z1, z0) → c3(F(z0))
K tuples:none
F(a) → c(H(a)) 0.00/0.83
H(g(z0)) → c1(H(f(z0)), F(z0)) 0.00/0.83
K(z0, h(z0), a) → c2(H(z0)) 0.00/0.83
K(f(z0), z1, z0) → c3(F(z0))
f, h, k
F, H, K
c, c1, c2, c3
K(z0, h(z0), a) → c2(H(z0)) 0.00/0.83
K(f(z0), z1, z0) → c3(F(z0))
Tuples:
f(a) → g(h(a)) 0.00/0.83
h(g(z0)) → g(h(f(z0))) 0.00/0.83
k(z0, h(z0), a) → h(z0) 0.00/0.83
k(f(z0), z1, z0) → f(z0)
S tuples:
F(a) → c(H(a)) 0.00/0.83
H(g(z0)) → c1(H(f(z0)), F(z0))
K tuples:none
F(a) → c(H(a)) 0.00/0.83
H(g(z0)) → c1(H(f(z0)), F(z0))
f, h, k
F, H
c, c1
Tuples:
f(a) → g(h(a)) 0.00/0.83
h(g(z0)) → g(h(f(z0))) 0.00/0.83
k(z0, h(z0), a) → h(z0) 0.00/0.83
k(f(z0), z1, z0) → f(z0)
S tuples:
H(g(z0)) → c1(H(f(z0)), F(z0)) 0.00/0.83
F(a) → c
K tuples:none
H(g(z0)) → c1(H(f(z0)), F(z0)) 0.00/0.83
F(a) → c
f, h, k
H, F
c1, c
F(a) → c
Tuples:
f(a) → g(h(a)) 0.00/0.83
h(g(z0)) → g(h(f(z0))) 0.00/0.83
k(z0, h(z0), a) → h(z0) 0.00/0.83
k(f(z0), z1, z0) → f(z0)
S tuples:
H(g(z0)) → c1(H(f(z0)), F(z0)) 0.00/0.83
F(a) → c
K tuples:none
H(g(z0)) → c1(H(f(z0)), F(z0)) 0.00/0.83
F(a) → c
f, h, k
H, F
c1, c
We considered the (Usable) Rules:
F(a) → c
And the Tuples:
f(a) → g(h(a))
The order we found is given by the following interpretation:
H(g(z0)) → c1(H(f(z0)), F(z0)) 0.00/0.83
F(a) → c
POL(F(x1)) = x12 0.00/0.83
POL(H(x1)) = x1 + x12 0.00/0.83
POL(a) = [1] 0.00/0.83
POL(c) = 0 0.00/0.83
POL(c1(x1, x2)) = x1 + x2 0.00/0.83
POL(f(x1)) = 0 0.00/0.83
POL(g(x1)) = x1 0.00/0.83
POL(h(x1)) = 0
Tuples:
f(a) → g(h(a)) 0.00/0.83
h(g(z0)) → g(h(f(z0))) 0.00/0.83
k(z0, h(z0), a) → h(z0) 0.00/0.83
k(f(z0), z1, z0) → f(z0)
S tuples:
H(g(z0)) → c1(H(f(z0)), F(z0)) 0.00/0.83
F(a) → c
K tuples:
H(g(z0)) → c1(H(f(z0)), F(z0))
Defined Rule Symbols:
F(a) → c
f, h, k
H, F
c1, c
We considered the (Usable) Rules:
H(g(z0)) → c1(H(f(z0)), F(z0))
And the Tuples:
f(a) → g(h(a))
The order we found is given by the following interpretation:
H(g(z0)) → c1(H(f(z0)), F(z0)) 0.00/0.83
F(a) → c
POL(F(x1)) = [1] 0.00/0.83
POL(H(x1)) = [4]x1 0.00/0.83
POL(a) = [4] 0.00/0.83
POL(c) = 0 0.00/0.83
POL(c1(x1, x2)) = x1 + x2 0.00/0.83
POL(f(x1)) = x1 0.00/0.83
POL(g(x1)) = [4] + x1 0.00/0.83
POL(h(x1)) = 0
Tuples:
f(a) → g(h(a)) 0.00/0.83
h(g(z0)) → g(h(f(z0))) 0.00/0.83
k(z0, h(z0), a) → h(z0) 0.00/0.83
k(f(z0), z1, z0) → f(z0)
S tuples:none
H(g(z0)) → c1(H(f(z0)), F(z0)) 0.00/0.83
F(a) → c
Defined Rule Symbols:
F(a) → c 0.00/0.83
H(g(z0)) → c1(H(f(z0)), F(z0))
f, h, k
H, F
c1, c