YES(O(1), O(n^1)) 0.00/0.82 YES(O(1), O(n^1)) 0.00/0.84 0.00/0.84 0.00/0.84
0.00/0.84 0.00/0.840 CpxTRS0.00/0.84
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.84
↳2 CdtProblem0.00/0.84
↳3 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.84
↳4 CdtProblem0.00/0.84
↳5 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.84
↳6 CdtProblem0.00/0.84
↳7 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.84
↳8 BOUNDS(O(1), O(1))0.00/0.84
g(f(x, y), z) → f(x, g(y, z)) 0.00/0.84
g(h(x, y), z) → g(x, f(y, z)) 0.00/0.84
g(x, h(y, z)) → h(g(x, y), z)
Tuples:
g(f(z0, z1), z2) → f(z0, g(z1, z2)) 0.00/0.84
g(h(z0, z1), z2) → g(z0, f(z1, z2)) 0.00/0.84
g(z0, h(z1, z2)) → h(g(z0, z1), z2)
S tuples:
G(f(z0, z1), z2) → c(G(z1, z2)) 0.00/0.84
G(h(z0, z1), z2) → c1(G(z0, f(z1, z2))) 0.00/0.84
G(z0, h(z1, z2)) → c2(G(z0, z1))
K tuples:none
G(f(z0, z1), z2) → c(G(z1, z2)) 0.00/0.84
G(h(z0, z1), z2) → c1(G(z0, f(z1, z2))) 0.00/0.84
G(z0, h(z1, z2)) → c2(G(z0, z1))
g
G
c, c1, c2
We considered the (Usable) Rules:none
G(f(z0, z1), z2) → c(G(z1, z2)) 0.00/0.84
G(h(z0, z1), z2) → c1(G(z0, f(z1, z2)))
The order we found is given by the following interpretation:
G(f(z0, z1), z2) → c(G(z1, z2)) 0.00/0.84
G(h(z0, z1), z2) → c1(G(z0, f(z1, z2))) 0.00/0.84
G(z0, h(z1, z2)) → c2(G(z0, z1))
POL(G(x1, x2)) = [4]x1 0.00/0.84
POL(c(x1)) = x1 0.00/0.84
POL(c1(x1)) = x1 0.00/0.84
POL(c2(x1)) = x1 0.00/0.84
POL(f(x1, x2)) = [1] + x1 + x2 0.00/0.84
POL(h(x1, x2)) = [4] + x1
Tuples:
g(f(z0, z1), z2) → f(z0, g(z1, z2)) 0.00/0.84
g(h(z0, z1), z2) → g(z0, f(z1, z2)) 0.00/0.84
g(z0, h(z1, z2)) → h(g(z0, z1), z2)
S tuples:
G(f(z0, z1), z2) → c(G(z1, z2)) 0.00/0.84
G(h(z0, z1), z2) → c1(G(z0, f(z1, z2))) 0.00/0.84
G(z0, h(z1, z2)) → c2(G(z0, z1))
K tuples:
G(z0, h(z1, z2)) → c2(G(z0, z1))
Defined Rule Symbols:
G(f(z0, z1), z2) → c(G(z1, z2)) 0.00/0.84
G(h(z0, z1), z2) → c1(G(z0, f(z1, z2)))
g
G
c, c1, c2
We considered the (Usable) Rules:none
G(z0, h(z1, z2)) → c2(G(z0, z1))
The order we found is given by the following interpretation:
G(f(z0, z1), z2) → c(G(z1, z2)) 0.00/0.84
G(h(z0, z1), z2) → c1(G(z0, f(z1, z2))) 0.00/0.84
G(z0, h(z1, z2)) → c2(G(z0, z1))
POL(G(x1, x2)) = [4]x1 + x2 0.00/0.84
POL(c(x1)) = x1 0.00/0.84
POL(c1(x1)) = x1 0.00/0.84
POL(c2(x1)) = x1 0.00/0.84
POL(f(x1, x2)) = [2] + x1 + x2 0.00/0.84
POL(h(x1, x2)) = [3] + x1 + x2
Tuples:
g(f(z0, z1), z2) → f(z0, g(z1, z2)) 0.00/0.84
g(h(z0, z1), z2) → g(z0, f(z1, z2)) 0.00/0.84
g(z0, h(z1, z2)) → h(g(z0, z1), z2)
S tuples:none
G(f(z0, z1), z2) → c(G(z1, z2)) 0.00/0.84
G(h(z0, z1), z2) → c1(G(z0, f(z1, z2))) 0.00/0.84
G(z0, h(z1, z2)) → c2(G(z0, z1))
Defined Rule Symbols:
G(f(z0, z1), z2) → c(G(z1, z2)) 0.00/0.84
G(h(z0, z1), z2) → c1(G(z0, f(z1, z2))) 0.00/0.84
G(z0, h(z1, z2)) → c2(G(z0, z1))
g
G
c, c1, c2