+(x, 0) → x
+(x, i(x)) → 0
+(+(x, y), z) → +(x, +(y, z))
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
↳ QTRS
↳ DependencyPairsProof
+(x, 0) → x
+(x, i(x)) → 0
+(+(x, y), z) → +(x, +(y, z))
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
*1(x, +(y, z)) → *1(x, y)
*1(+(x, y), z) → *1(x, z)
*1(x, +(y, z)) → *1(x, z)
+1(+(x, y), z) → +1(y, z)
*1(+(x, y), z) → +1(*(x, z), *(y, z))
+1(+(x, y), z) → +1(x, +(y, z))
*1(+(x, y), z) → *1(y, z)
*1(x, +(y, z)) → +1(*(x, y), *(x, z))
+(x, 0) → x
+(x, i(x)) → 0
+(+(x, y), z) → +(x, +(y, z))
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
*1(x, +(y, z)) → *1(x, y)
*1(+(x, y), z) → *1(x, z)
*1(x, +(y, z)) → *1(x, z)
+1(+(x, y), z) → +1(y, z)
*1(+(x, y), z) → +1(*(x, z), *(y, z))
+1(+(x, y), z) → +1(x, +(y, z))
*1(+(x, y), z) → *1(y, z)
*1(x, +(y, z)) → +1(*(x, y), *(x, z))
+(x, 0) → x
+(x, i(x)) → 0
+(+(x, y), z) → +(x, +(y, z))
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
+1(+(x, y), z) → +1(y, z)
+1(+(x, y), z) → +1(x, +(y, z))
+(x, 0) → x
+(x, i(x)) → 0
+(+(x, y), z) → +(x, +(y, z))
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(+(x, y), z) → +(*(x, z), *(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)
+1(+(x, y), z) → +1(x, +(y, z))
The value of delta used in the strict ordering is 5/16.
POL(i(x1)) = 15/4
POL(0) = 5/4
POL(+1(x1, x2)) = (5/4)x_1
POL(+(x1, x2)) = 1/4 + (4)x_1 + (2)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
+(x, 0) → x
+(x, i(x)) → 0
+(+(x, y), z) → +(x, +(y, z))
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
*1(x, +(y, z)) → *1(x, y)
*1(+(x, y), z) → *1(x, z)
*1(x, +(y, z)) → *1(x, z)
*1(+(x, y), z) → *1(y, z)
+(x, 0) → x
+(x, i(x)) → 0
+(+(x, y), z) → +(x, +(y, z))
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(+(x, y), z) → +(*(x, z), *(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)
*1(x, +(y, z)) → *1(x, z)
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)) = x_2
POL(+(x1, x2)) = 4 + (5/2)x_1 + x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
*1(+(x, y), z) → *1(x, z)
*1(+(x, y), z) → *1(y, z)
+(x, 0) → x
+(x, i(x)) → 0
+(+(x, y), z) → +(x, +(y, z))
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(+(x, y), z) → +(*(x, z), *(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, 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
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
+(x, 0) → x
+(x, i(x)) → 0
+(+(x, y), z) → +(x, +(y, z))
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(+(x, y), z) → +(*(x, z), *(y, z))