f(0, y) → y
f(x, 0) → x
f(i(x), y) → i(x)
f(f(x, y), z) → f(x, f(y, z))
f(g(x, y), z) → g(f(x, z), f(y, z))
f(1, g(x, y)) → x
f(2, g(x, y)) → y
↳ QTRS
↳ DependencyPairsProof
f(0, y) → y
f(x, 0) → x
f(i(x), y) → i(x)
f(f(x, y), z) → f(x, f(y, z))
f(g(x, y), z) → g(f(x, z), f(y, z))
f(1, g(x, y)) → x
f(2, g(x, y)) → y
F(f(x, y), z) → F(y, z)
F(g(x, y), z) → F(y, z)
F(g(x, y), z) → F(x, z)
F(f(x, y), z) → F(x, f(y, z))
f(0, y) → y
f(x, 0) → x
f(i(x), y) → i(x)
f(f(x, y), z) → f(x, f(y, z))
f(g(x, y), z) → g(f(x, z), f(y, z))
f(1, g(x, y)) → x
f(2, g(x, y)) → y
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
F(f(x, y), z) → F(y, z)
F(g(x, y), z) → F(y, z)
F(g(x, y), z) → F(x, z)
F(f(x, y), z) → F(x, f(y, z))
f(0, y) → y
f(x, 0) → x
f(i(x), y) → i(x)
f(f(x, y), z) → f(x, f(y, z))
f(g(x, y), z) → g(f(x, z), f(y, z))
f(1, g(x, y)) → x
f(2, g(x, y)) → y
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(f(x, y), z) → F(y, z)
F(f(x, y), z) → F(x, f(y, z))
Used ordering: Polynomial interpretation [25,35]:
F(g(x, y), z) → F(y, z)
F(g(x, y), z) → F(x, z)
The value of delta used in the strict ordering is 9/16.
POL(i(x1)) = 1/4 + (3)x_1
POL(g(x1, x2)) = (3/2)x_1 + (2)x_2
POL(f(x1, x2)) = 9/4 + (4)x_1 + (4)x_2
POL(2) = 0
POL(F(x1, x2)) = (1/4)x_1
POL(0) = 0
POL(1) = 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
F(g(x, y), z) → F(y, z)
F(g(x, y), z) → F(x, z)
f(0, y) → y
f(x, 0) → x
f(i(x), y) → i(x)
f(f(x, y), z) → f(x, f(y, z))
f(g(x, y), z) → g(f(x, z), f(y, z))
f(1, g(x, y)) → x
f(2, g(x, y)) → y
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(g(x, y), z) → F(y, z)
F(g(x, y), z) → F(x, z)
The value of delta used in the strict ordering is 1/2.
POL(g(x1, x2)) = 1/4 + (5/2)x_1 + (5/2)x_2
POL(F(x1, x2)) = (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
f(0, y) → y
f(x, 0) → x
f(i(x), y) → i(x)
f(f(x, y), z) → f(x, f(y, z))
f(g(x, y), z) → g(f(x, z), f(y, z))
f(1, g(x, y)) → x
f(2, g(x, y)) → y