f(c(s(x), y)) → f(c(x, s(y)))
f(c(s(x), s(y))) → g(c(x, y))
g(c(x, s(y))) → g(c(s(x), y))
g(c(s(x), s(y))) → f(c(x, y))
↳ QTRS
↳ DependencyPairsProof
f(c(s(x), y)) → f(c(x, s(y)))
f(c(s(x), s(y))) → g(c(x, y))
g(c(x, s(y))) → g(c(s(x), y))
g(c(s(x), s(y))) → f(c(x, y))
F(c(s(x), y)) → F(c(x, s(y)))
F(c(s(x), s(y))) → G(c(x, y))
G(c(s(x), s(y))) → F(c(x, y))
G(c(x, s(y))) → G(c(s(x), y))
f(c(s(x), y)) → f(c(x, s(y)))
f(c(s(x), s(y))) → g(c(x, y))
g(c(x, s(y))) → g(c(s(x), y))
g(c(s(x), s(y))) → f(c(x, y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
F(c(s(x), y)) → F(c(x, s(y)))
F(c(s(x), s(y))) → G(c(x, y))
G(c(s(x), s(y))) → F(c(x, y))
G(c(x, s(y))) → G(c(s(x), y))
f(c(s(x), y)) → f(c(x, s(y)))
f(c(s(x), s(y))) → g(c(x, y))
g(c(x, s(y))) → g(c(s(x), y))
g(c(s(x), s(y))) → f(c(x, y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(c(s(x), s(y))) → G(c(x, y))
G(c(s(x), s(y))) → F(c(x, y))
Used ordering: Polynomial interpretation [25,35]:
F(c(s(x), y)) → F(c(x, s(y)))
G(c(x, s(y))) → G(c(s(x), y))
The value of delta used in the strict ordering is 64.
POL(c(x1, x2)) = (4)x_1 + (4)x_2
POL(s(x1)) = 2 + x_1
POL(G(x1)) = (4)x_1
POL(F(x1)) = (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
F(c(s(x), y)) → F(c(x, s(y)))
G(c(x, s(y))) → G(c(s(x), y))
f(c(s(x), y)) → f(c(x, s(y)))
f(c(s(x), s(y))) → g(c(x, y))
g(c(x, s(y))) → g(c(s(x), y))
g(c(s(x), s(y))) → f(c(x, y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
G(c(x, s(y))) → G(c(s(x), y))
f(c(s(x), y)) → f(c(x, s(y)))
f(c(s(x), s(y))) → g(c(x, y))
g(c(x, s(y))) → g(c(s(x), y))
g(c(s(x), s(y))) → f(c(x, y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
G(c(x, s(y))) → G(c(s(x), y))
The value of delta used in the strict ordering is 15.
POL(c(x1, x2)) = (1/4)x_1 + (4)x_2
POL(G(x1)) = (2)x_1
POL(s(x1)) = 2 + x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
f(c(s(x), y)) → f(c(x, s(y)))
f(c(s(x), s(y))) → g(c(x, y))
g(c(x, s(y))) → g(c(s(x), y))
g(c(s(x), s(y))) → f(c(x, y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
F(c(s(x), y)) → F(c(x, s(y)))
f(c(s(x), y)) → f(c(x, s(y)))
f(c(s(x), s(y))) → g(c(x, y))
g(c(x, s(y))) → g(c(s(x), y))
g(c(s(x), s(y))) → f(c(x, y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(c(s(x), y)) → F(c(x, s(y)))
The value of delta used in the strict ordering is 64.
POL(c(x1, x2)) = (4)x_1
POL(s(x1)) = 4 + (4)x_1
POL(F(x1)) = (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
f(c(s(x), y)) → f(c(x, s(y)))
f(c(s(x), s(y))) → g(c(x, y))
g(c(x, s(y))) → g(c(s(x), y))
g(c(s(x), s(y))) → f(c(x, y))