f(a) → b
f(c) → d
f(g(x, y)) → g(f(x), f(y))
f(h(x, y)) → g(h(y, f(x)), h(x, f(y)))
g(x, x) → h(e, x)
↳ QTRS
↳ DependencyPairsProof
f(a) → b
f(c) → d
f(g(x, y)) → g(f(x), f(y))
f(h(x, y)) → g(h(y, f(x)), h(x, f(y)))
g(x, x) → h(e, x)
F(g(x, y)) → F(y)
F(g(x, y)) → G(f(x), f(y))
F(h(x, y)) → F(x)
F(g(x, y)) → F(x)
F(h(x, y)) → F(y)
F(h(x, y)) → G(h(y, f(x)), h(x, f(y)))
f(a) → b
f(c) → d
f(g(x, y)) → g(f(x), f(y))
f(h(x, y)) → g(h(y, f(x)), h(x, f(y)))
g(x, x) → h(e, x)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
F(g(x, y)) → F(y)
F(g(x, y)) → G(f(x), f(y))
F(h(x, y)) → F(x)
F(g(x, y)) → F(x)
F(h(x, y)) → F(y)
F(h(x, y)) → G(h(y, f(x)), h(x, f(y)))
f(a) → b
f(c) → d
f(g(x, y)) → g(f(x), f(y))
f(h(x, y)) → g(h(y, f(x)), h(x, f(y)))
g(x, x) → h(e, x)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
F(g(x, y)) → F(y)
F(h(x, y)) → F(x)
F(g(x, y)) → F(x)
F(h(x, y)) → F(y)
f(a) → b
f(c) → d
f(g(x, y)) → g(f(x), f(y))
f(h(x, y)) → g(h(y, f(x)), h(x, f(y)))
g(x, x) → h(e, x)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(g(x, y)) → F(y)
F(g(x, y)) → F(x)
Used ordering: Polynomial interpretation [25,35]:
F(h(x, y)) → F(x)
F(h(x, y)) → F(y)
The value of delta used in the strict ordering is 27/8.
POL(g(x1, x2)) = 9/4 + (4)x_1 + (5/4)x_2
POL(h(x1, x2)) = x_1 + (11/4)x_2
POL(F(x1)) = (3/2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
F(h(x, y)) → F(x)
F(h(x, y)) → F(y)
f(a) → b
f(c) → d
f(g(x, y)) → g(f(x), f(y))
f(h(x, y)) → g(h(y, f(x)), h(x, f(y)))
g(x, x) → h(e, x)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(h(x, y)) → F(x)
F(h(x, y)) → F(y)
The value of delta used in the strict ordering is 1/2.
POL(h(x1, x2)) = 1/4 + (5/2)x_1 + (5/2)x_2
POL(F(x1)) = (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
f(a) → b
f(c) → d
f(g(x, y)) → g(f(x), f(y))
f(h(x, y)) → g(h(y, f(x)), h(x, f(y)))
g(x, x) → h(e, x)