*(i(x), x) → 1
*(1, y) → y
*(x, 0) → 0
*(*(x, y), z) → *(x, *(y, z))
↳ QTRS
↳ DependencyPairsProof
*(i(x), x) → 1
*(1, y) → y
*(x, 0) → 0
*(*(x, y), z) → *(x, *(y, z))
*1(*(x, y), z) → *1(y, z)
*1(*(x, y), z) → *1(x, *(y, z))
*(i(x), x) → 1
*(1, y) → y
*(x, 0) → 0
*(*(x, y), z) → *(x, *(y, z))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
*1(*(x, y), z) → *1(y, z)
*1(*(x, y), z) → *1(x, *(y, z))
*(i(x), x) → 1
*(1, y) → y
*(x, 0) → 0
*(*(x, y), z) → *(x, *(y, z))
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)
Used ordering: Polynomial interpretation [25,35]:
*1(*(x, y), z) → *1(x, *(y, z))
The value of delta used in the strict ordering is 1/2.
POL(i(x1)) = 4
POL(*1(x1, x2)) = (2)x_1 + (2)x_2
POL(*(x1, x2)) = 1/4 + x_1 + x_2
POL(1) = 1/4
POL(0) = 0
*(i(x), x) → 1
*(1, y) → y
*(x, 0) → 0
*(*(x, y), z) → *(x, *(y, z))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
*1(*(x, y), z) → *1(x, *(y, z))
*(i(x), x) → 1
*(1, y) → y
*(x, 0) → 0
*(*(x, y), z) → *(x, *(y, z))
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, *(y, z))
The value of delta used in the strict ordering is 2.
POL(i(x1)) = 0
POL(*1(x1, x2)) = (1/2)x_1
POL(*(x1, x2)) = 4 + (4)x_1
POL(1) = 0
POL(0) = 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
*(i(x), x) → 1
*(1, y) → y
*(x, 0) → 0
*(*(x, y), z) → *(x, *(y, z))