g(0, f(x, x)) → x
g(x, s(y)) → g(f(x, y), 0)
g(s(x), y) → g(f(x, y), 0)
g(f(x, y), 0) → f(g(x, 0), g(y, 0))
↳ QTRS
↳ DependencyPairsProof
g(0, f(x, x)) → x
g(x, s(y)) → g(f(x, y), 0)
g(s(x), y) → g(f(x, y), 0)
g(f(x, y), 0) → f(g(x, 0), g(y, 0))
G(s(x), y) → G(f(x, y), 0)
G(x, s(y)) → G(f(x, y), 0)
G(f(x, y), 0) → G(y, 0)
G(f(x, y), 0) → G(x, 0)
g(0, f(x, x)) → x
g(x, s(y)) → g(f(x, y), 0)
g(s(x), y) → g(f(x, y), 0)
g(f(x, y), 0) → f(g(x, 0), g(y, 0))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
G(s(x), y) → G(f(x, y), 0)
G(x, s(y)) → G(f(x, y), 0)
G(f(x, y), 0) → G(y, 0)
G(f(x, y), 0) → G(x, 0)
g(0, f(x, x)) → x
g(x, s(y)) → g(f(x, y), 0)
g(s(x), y) → g(f(x, y), 0)
g(f(x, y), 0) → f(g(x, 0), g(y, 0))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
G(s(x), y) → G(f(x, y), 0)
G(f(x, y), 0) → G(y, 0)
G(f(x, y), 0) → G(x, 0)
g(0, f(x, x)) → x
g(x, s(y)) → g(f(x, y), 0)
g(s(x), y) → g(f(x, y), 0)
g(f(x, y), 0) → f(g(x, 0), g(y, 0))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
G(s(x), y) → G(f(x, y), 0)
Used ordering: Polynomial interpretation [25,35]:
G(f(x, y), 0) → G(y, 0)
G(f(x, y), 0) → G(x, 0)
The value of delta used in the strict ordering is 2.
POL(f(x1, x2)) = (2)x_1 + x_2
POL(s(x1)) = 4 + (4)x_1
POL(G(x1, x2)) = (2)x_1 + (3)x_2
POL(0) = 2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
G(f(x, y), 0) → G(y, 0)
G(f(x, y), 0) → G(x, 0)
g(0, f(x, x)) → x
g(x, s(y)) → g(f(x, y), 0)
g(s(x), y) → g(f(x, y), 0)
g(f(x, y), 0) → f(g(x, 0), g(y, 0))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
G(f(x, y), 0) → G(y, 0)
G(f(x, y), 0) → G(x, 0)
The value of delta used in the strict ordering is 4.
POL(f(x1, x2)) = 1 + (4)x_1 + (4)x_2
POL(G(x1, x2)) = (4)x_1
POL(0) = 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
g(0, f(x, x)) → x
g(x, s(y)) → g(f(x, y), 0)
g(s(x), y) → g(f(x, y), 0)
g(f(x, y), 0) → f(g(x, 0), g(y, 0))