*(x, *(y, z)) → *(otimes(x, y), z)
*(1, y) → y
*(+(x, y), z) → oplus(*(x, z), *(y, z))
*(x, oplus(y, z)) → oplus(*(x, y), *(x, z))
↳ QTRS
↳ DependencyPairsProof
*(x, *(y, z)) → *(otimes(x, y), z)
*(1, y) → y
*(+(x, y), z) → oplus(*(x, z), *(y, z))
*(x, oplus(y, z)) → oplus(*(x, y), *(x, z))
*1(x, oplus(y, z)) → *1(x, z)
*1(+(x, y), z) → *1(x, z)
*1(x, oplus(y, z)) → *1(x, y)
*1(+(x, y), z) → *1(y, z)
*1(x, *(y, z)) → *1(otimes(x, y), z)
*(x, *(y, z)) → *(otimes(x, y), z)
*(1, y) → y
*(+(x, y), z) → oplus(*(x, z), *(y, z))
*(x, oplus(y, z)) → oplus(*(x, y), *(x, z))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
*1(x, oplus(y, z)) → *1(x, z)
*1(+(x, y), z) → *1(x, z)
*1(x, oplus(y, z)) → *1(x, y)
*1(+(x, y), z) → *1(y, z)
*1(x, *(y, z)) → *1(otimes(x, y), z)
*(x, *(y, z)) → *(otimes(x, y), z)
*(1, y) → y
*(+(x, y), z) → oplus(*(x, z), *(y, z))
*(x, oplus(y, z)) → oplus(*(x, y), *(x, 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(otimes(x, y), z)
Used ordering: Polynomial interpretation [25,35]:
*1(x, oplus(y, z)) → *1(x, z)
*1(+(x, y), z) → *1(x, z)
*1(x, oplus(y, z)) → *1(x, y)
*1(+(x, y), z) → *1(y, z)
The value of delta used in the strict ordering is 7.
POL(otimes(x1, x2)) = 3 + (13/4)x_1 + (4)x_2
POL(*1(x1, x2)) = (4)x_2
POL(*(x1, x2)) = 7/4 + (4)x_1 + (4)x_2
POL(oplus(x1, x2)) = (3/2)x_1 + (5/2)x_2
POL(+(x1, x2)) = 2 + (3/4)x_1 + (4)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
*1(+(x, y), z) → *1(x, z)
*1(x, oplus(y, z)) → *1(x, z)
*1(x, oplus(y, z)) → *1(x, y)
*1(+(x, y), z) → *1(y, z)
*(x, *(y, z)) → *(otimes(x, y), z)
*(1, y) → y
*(+(x, y), z) → oplus(*(x, z), *(y, z))
*(x, oplus(y, z)) → oplus(*(x, y), *(x, z))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
*1(x, oplus(y, z)) → *1(x, z)
*1(x, oplus(y, z)) → *1(x, y)
Used ordering: Polynomial interpretation [25,35]:
*1(+(x, y), z) → *1(x, z)
*1(+(x, y), z) → *1(y, z)
The value of delta used in the strict ordering is 4.
POL(*1(x1, x2)) = (3/2)x_1 + (4)x_2
POL(oplus(x1, x2)) = 1 + (11/4)x_1 + (7/4)x_2
POL(+(x1, x2)) = x_1 + (7/4)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
*1(+(x, y), z) → *1(x, z)
*1(+(x, y), z) → *1(y, z)
*(x, *(y, z)) → *(otimes(x, y), z)
*(1, y) → y
*(+(x, y), z) → oplus(*(x, z), *(y, z))
*(x, oplus(y, z)) → oplus(*(x, y), *(x, 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, z)
*1(+(x, y), z) → *1(y, z)
The value of delta used in the strict ordering is 1/2.
POL(*1(x1, x2)) = (2)x_1
POL(+(x1, x2)) = 1/4 + (5/2)x_1 + (5/2)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
*(x, *(y, z)) → *(otimes(x, y), z)
*(1, y) → y
*(+(x, y), z) → oplus(*(x, z), *(y, z))
*(x, oplus(y, z)) → oplus(*(x, y), *(x, z))