f(f(x)) → f(g(f(x), x))
f(f(x)) → f(h(f(x), f(x)))
g(x, y) → y
h(x, x) → g(x, 0)
↳ QTRS
↳ DependencyPairsProof
f(f(x)) → f(g(f(x), x))
f(f(x)) → f(h(f(x), f(x)))
g(x, y) → y
h(x, x) → g(x, 0)
H(x, x) → G(x, 0)
F(f(x)) → F(g(f(x), x))
F(f(x)) → H(f(x), f(x))
F(f(x)) → G(f(x), x)
F(f(x)) → F(h(f(x), f(x)))
f(f(x)) → f(g(f(x), x))
f(f(x)) → f(h(f(x), f(x)))
g(x, y) → y
h(x, x) → g(x, 0)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
H(x, x) → G(x, 0)
F(f(x)) → F(g(f(x), x))
F(f(x)) → H(f(x), f(x))
F(f(x)) → G(f(x), x)
F(f(x)) → F(h(f(x), f(x)))
f(f(x)) → f(g(f(x), x))
f(f(x)) → f(h(f(x), f(x)))
g(x, y) → y
h(x, x) → g(x, 0)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
F(f(x)) → F(g(f(x), x))
F(f(x)) → F(h(f(x), f(x)))
f(f(x)) → f(g(f(x), x))
f(f(x)) → f(h(f(x), f(x)))
g(x, y) → y
h(x, x) → g(x, 0)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(f(x)) → F(g(f(x), x))
F(f(x)) → F(h(f(x), f(x)))
The value of delta used in the strict ordering is 1/8.
POL(f(x1)) = 1 + (4)x_1
POL(g(x1, x2)) = (1/2)x_1 + (2)x_2
POL(h(x1, x2)) = (1/2)x_1
POL(0) = 0
POL(F(x1)) = (1/4)x_1
f(f(x)) → f(h(f(x), f(x)))
f(f(x)) → f(g(f(x), x))
g(x, y) → y
h(x, x) → g(x, 0)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
f(f(x)) → f(g(f(x), x))
f(f(x)) → f(h(f(x), f(x)))
g(x, y) → y
h(x, x) → g(x, 0)