s(a) → a
s(s(x)) → x
s(f(x, y)) → f(s(y), s(x))
s(g(x, y)) → g(s(x), s(y))
f(x, a) → x
f(a, y) → y
f(g(x, y), g(u, v)) → g(f(x, u), f(y, v))
g(a, a) → a
↳ QTRS
↳ DependencyPairsProof
s(a) → a
s(s(x)) → x
s(f(x, y)) → f(s(y), s(x))
s(g(x, y)) → g(s(x), s(y))
f(x, a) → x
f(a, y) → y
f(g(x, y), g(u, v)) → g(f(x, u), f(y, v))
g(a, a) → a
F(g(x, y), g(u, v)) → G(f(x, u), f(y, v))
F(g(x, y), g(u, v)) → F(y, v)
S(g(x, y)) → S(x)
F(g(x, y), g(u, v)) → F(x, u)
S(g(x, y)) → S(y)
S(f(x, y)) → S(x)
S(f(x, y)) → F(s(y), s(x))
S(f(x, y)) → S(y)
S(g(x, y)) → G(s(x), s(y))
s(a) → a
s(s(x)) → x
s(f(x, y)) → f(s(y), s(x))
s(g(x, y)) → g(s(x), s(y))
f(x, a) → x
f(a, y) → y
f(g(x, y), g(u, v)) → g(f(x, u), f(y, v))
g(a, a) → a
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
F(g(x, y), g(u, v)) → G(f(x, u), f(y, v))
F(g(x, y), g(u, v)) → F(y, v)
S(g(x, y)) → S(x)
F(g(x, y), g(u, v)) → F(x, u)
S(g(x, y)) → S(y)
S(f(x, y)) → S(x)
S(f(x, y)) → F(s(y), s(x))
S(f(x, y)) → S(y)
S(g(x, y)) → G(s(x), s(y))
s(a) → a
s(s(x)) → x
s(f(x, y)) → f(s(y), s(x))
s(g(x, y)) → g(s(x), s(y))
f(x, a) → x
f(a, y) → y
f(g(x, y), g(u, v)) → g(f(x, u), f(y, v))
g(a, a) → a
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
F(g(x, y), g(u, v)) → F(y, v)
F(g(x, y), g(u, v)) → F(x, u)
s(a) → a
s(s(x)) → x
s(f(x, y)) → f(s(y), s(x))
s(g(x, y)) → g(s(x), s(y))
f(x, a) → x
f(a, y) → y
f(g(x, y), g(u, v)) → g(f(x, u), f(y, v))
g(a, a) → a
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(g(x, y), g(u, v)) → F(y, v)
F(g(x, y), g(u, v)) → F(x, u)
The value of delta used in the strict ordering is 14.
POL(g(x1, x2)) = 2 + (4)x_1 + (2)x_2
POL(F(x1, x2)) = (4)x_1 + (3)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
s(a) → a
s(s(x)) → x
s(f(x, y)) → f(s(y), s(x))
s(g(x, y)) → g(s(x), s(y))
f(x, a) → x
f(a, y) → y
f(g(x, y), g(u, v)) → g(f(x, u), f(y, v))
g(a, a) → a
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
S(g(x, y)) → S(x)
S(g(x, y)) → S(y)
S(f(x, y)) → S(x)
S(f(x, y)) → S(y)
s(a) → a
s(s(x)) → x
s(f(x, y)) → f(s(y), s(x))
s(g(x, y)) → g(s(x), s(y))
f(x, a) → x
f(a, y) → y
f(g(x, y), g(u, v)) → g(f(x, u), f(y, v))
g(a, a) → a
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
S(g(x, y)) → S(x)
S(g(x, y)) → S(y)
S(f(x, y)) → S(x)
S(f(x, y)) → S(y)
The value of delta used in the strict ordering is 8.
POL(g(x1, x2)) = 2 + (4)x_1 + (4)x_2
POL(f(x1, x2)) = 4 + (4)x_1 + (4)x_2
POL(S(x1)) = (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
s(a) → a
s(s(x)) → x
s(f(x, y)) → f(s(y), s(x))
s(g(x, y)) → g(s(x), s(y))
f(x, a) → x
f(a, y) → y
f(g(x, y), g(u, v)) → g(f(x, u), f(y, v))
g(a, a) → a