f(true, x, y, z) → g(gt(x, y), x, y, z)
g(true, x, y, z) → f(gt(x, z), x, s(y), z)
g(true, x, y, z) → f(gt(x, z), x, y, s(z))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)
↳ QTRS
↳ DependencyPairsProof
f(true, x, y, z) → g(gt(x, y), x, y, z)
g(true, x, y, z) → f(gt(x, z), x, s(y), z)
g(true, x, y, z) → f(gt(x, z), x, y, s(z))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)
G(true, x, y, z) → F(gt(x, z), x, y, s(z))
F(true, x, y, z) → GT(x, y)
GT(s(u), s(v)) → GT(u, v)
G(true, x, y, z) → F(gt(x, z), x, s(y), z)
G(true, x, y, z) → GT(x, z)
F(true, x, y, z) → G(gt(x, y), x, y, z)
f(true, x, y, z) → g(gt(x, y), x, y, z)
g(true, x, y, z) → f(gt(x, z), x, s(y), z)
g(true, x, y, z) → f(gt(x, z), x, y, s(z))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
G(true, x, y, z) → F(gt(x, z), x, y, s(z))
F(true, x, y, z) → GT(x, y)
GT(s(u), s(v)) → GT(u, v)
G(true, x, y, z) → F(gt(x, z), x, s(y), z)
G(true, x, y, z) → GT(x, z)
F(true, x, y, z) → G(gt(x, y), x, y, z)
f(true, x, y, z) → g(gt(x, y), x, y, z)
g(true, x, y, z) → f(gt(x, z), x, s(y), z)
g(true, x, y, z) → f(gt(x, z), x, y, s(z))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
GT(s(u), s(v)) → GT(u, v)
f(true, x, y, z) → g(gt(x, y), x, y, z)
g(true, x, y, z) → f(gt(x, z), x, s(y), z)
g(true, x, y, z) → f(gt(x, z), x, y, s(z))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
GT(s(u), s(v)) → GT(u, v)
The value of delta used in the strict ordering is 1.
POL(s(x1)) = 1 + x_1
POL(GT(x1, x2)) = x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
f(true, x, y, z) → g(gt(x, y), x, y, z)
g(true, x, y, z) → f(gt(x, z), x, s(y), z)
g(true, x, y, z) → f(gt(x, z), x, y, s(z))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
G(true, x, y, z) → F(gt(x, z), x, y, s(z))
G(true, x, y, z) → F(gt(x, z), x, s(y), z)
F(true, x, y, z) → G(gt(x, y), x, y, z)
f(true, x, y, z) → g(gt(x, y), x, y, z)
g(true, x, y, z) → f(gt(x, z), x, s(y), z)
g(true, x, y, z) → f(gt(x, z), x, y, s(z))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)