*(*(x, y), z) → *(x, *(y, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
*(x, +(y, f(z))) → *(g(x, z), +(y, y))
↳ QTRS
↳ DependencyPairsProof
*(*(x, y), z) → *(x, *(y, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
*(x, +(y, f(z))) → *(g(x, z), +(y, y))
*1(+(x, y), z) → *1(x, z)
*1(*(x, y), z) → *1(y, z)
*1(x, +(y, f(z))) → *1(g(x, z), +(y, y))
*1(*(x, y), z) → *1(x, *(y, z))
*1(+(x, y), z) → *1(y, z)
*(*(x, y), z) → *(x, *(y, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
*(x, +(y, f(z))) → *(g(x, z), +(y, y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
*1(+(x, y), z) → *1(x, z)
*1(*(x, y), z) → *1(y, z)
*1(x, +(y, f(z))) → *1(g(x, z), +(y, y))
*1(*(x, y), z) → *1(x, *(y, z))
*1(+(x, y), z) → *1(y, z)
*(*(x, y), z) → *(x, *(y, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
*(x, +(y, f(z))) → *(g(x, z), +(y, y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
*1(x, +(y, f(z))) → *1(g(x, z), +(y, y))
*(*(x, y), z) → *(x, *(y, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
*(x, +(y, f(z))) → *(g(x, z), +(y, y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
*1(+(x, y), z) → *1(x, z)
*1(*(x, y), z) → *1(y, z)
*1(*(x, y), z) → *1(x, *(y, z))
*1(+(x, y), z) → *1(y, z)
*(*(x, y), z) → *(x, *(y, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
*(x, +(y, f(z))) → *(g(x, z), +(y, y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
*1(+(x, y), z) → *1(x, z)
*1(+(x, y), z) → *1(y, z)
Used ordering: Polynomial interpretation [25,35]:
*1(*(x, y), z) → *1(y, z)
*1(*(x, y), z) → *1(x, *(y, z))
The value of delta used in the strict ordering is 8.
POL(f(x1)) = 0
POL(*1(x1, x2)) = (2)x_1
POL(g(x1, x2)) = x_1 + (4)x_2
POL(*(x1, x2)) = (4)x_1 + x_2
POL(+(x1, x2)) = 4 + (4)x_1 + (4)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
*1(*(x, y), z) → *1(y, z)
*1(*(x, y), z) → *1(x, *(y, z))
*(*(x, y), z) → *(x, *(y, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
*(x, +(y, f(z))) → *(g(x, z), +(y, y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
*1(*(x, y), z) → *1(y, z)
*1(*(x, y), z) → *1(x, *(y, z))
The value of delta used in the strict ordering is 1/16.
POL(f(x1)) = 0
POL(*1(x1, x2)) = (1/4)x_1
POL(g(x1, x2)) = 7/2 + (4)x_1 + (3/4)x_2
POL(*(x1, x2)) = 1/4 + x_1 + (2)x_2
POL(+(x1, x2)) = (1/2)x_1 + (1/2)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
*(*(x, y), z) → *(x, *(y, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
*(x, +(y, f(z))) → *(g(x, z), +(y, y))