0 QTRS
↳1 DependencyPairsProof (⇔)
↳2 QDP
↳3 DependencyGraphProof (⇔)
↳4 QDP
↳5 QDPOrderProof (⇔)
↳6 QDP
↳7 QDPOrderProof (⇔)
↳8 QDP
↳9 PisEmptyProof (⇔)
↳10 TRUE
g(0, f(x, x)) → x
g(x, s(y)) → g(f(x, y), 0)
g(s(x), y) → g(f(x, y), 0)
g(f(x, y), 0) → f(g(x, 0), g(y, 0))
G(x, s(y)) → G(f(x, y), 0)
G(s(x), y) → G(f(x, y), 0)
G(f(x, y), 0) → G(x, 0)
G(f(x, y), 0) → G(y, 0)
g(0, f(x, x)) → x
g(x, s(y)) → g(f(x, y), 0)
g(s(x), y) → g(f(x, y), 0)
g(f(x, y), 0) → f(g(x, 0), g(y, 0))
G(f(x, y), 0) → G(x, 0)
G(s(x), y) → G(f(x, y), 0)
G(f(x, y), 0) → G(y, 0)
g(0, f(x, x)) → x
g(x, s(y)) → g(f(x, y), 0)
g(s(x), y) → g(f(x, y), 0)
g(f(x, y), 0) → f(g(x, 0), g(y, 0))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
G(s(x), y) → G(f(x, y), 0)
POL(0) = 0
POL(G(x1, x2)) = x1 + x2
POL(f(x1, x2)) = x1 + x2
POL(s(x1)) = 1 + x1
G(f(x, y), 0) → G(x, 0)
G(f(x, y), 0) → G(y, 0)
g(0, f(x, x)) → x
g(x, s(y)) → g(f(x, y), 0)
g(s(x), y) → g(f(x, y), 0)
g(f(x, y), 0) → f(g(x, 0), g(y, 0))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
G(f(x, y), 0) → G(x, 0)
G(f(x, y), 0) → G(y, 0)
POL(0) = 0
POL(G(x1, x2)) = x1
POL(f(x1, x2)) = 1 + x1 + x2
g(0, f(x, x)) → x
g(x, s(y)) → g(f(x, y), 0)
g(s(x), y) → g(f(x, y), 0)
g(f(x, y), 0) → f(g(x, 0), g(y, 0))