+(x, 0) → x
+(minus(x), x) → 0
minus(0) → 0
minus(minus(x)) → x
minus(+(x, y)) → +(minus(y), minus(x))
*(x, 1) → x
*(x, 0) → 0
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(x, minus(y)) → minus(*(x, y))
↳ QTRS
↳ DependencyPairsProof
+(x, 0) → x
+(minus(x), x) → 0
minus(0) → 0
minus(minus(x)) → x
minus(+(x, y)) → +(minus(y), minus(x))
*(x, 1) → x
*(x, 0) → 0
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(x, minus(y)) → minus(*(x, y))
*1(x, +(y, z)) → *1(x, y)
MINUS(+(x, y)) → +1(minus(y), minus(x))
*1(x, minus(y)) → MINUS(*(x, y))
*1(x, +(y, z)) → *1(x, z)
*1(x, minus(y)) → *1(x, y)
MINUS(+(x, y)) → MINUS(y)
MINUS(+(x, y)) → MINUS(x)
*1(x, +(y, z)) → +1(*(x, y), *(x, z))
+(x, 0) → x
+(minus(x), x) → 0
minus(0) → 0
minus(minus(x)) → x
minus(+(x, y)) → +(minus(y), minus(x))
*(x, 1) → x
*(x, 0) → 0
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(x, minus(y)) → minus(*(x, y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
*1(x, +(y, z)) → *1(x, y)
MINUS(+(x, y)) → +1(minus(y), minus(x))
*1(x, minus(y)) → MINUS(*(x, y))
*1(x, +(y, z)) → *1(x, z)
*1(x, minus(y)) → *1(x, y)
MINUS(+(x, y)) → MINUS(y)
MINUS(+(x, y)) → MINUS(x)
*1(x, +(y, z)) → +1(*(x, y), *(x, z))
+(x, 0) → x
+(minus(x), x) → 0
minus(0) → 0
minus(minus(x)) → x
minus(+(x, y)) → +(minus(y), minus(x))
*(x, 1) → x
*(x, 0) → 0
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(x, minus(y)) → minus(*(x, y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
MINUS(+(x, y)) → MINUS(y)
MINUS(+(x, y)) → MINUS(x)
+(x, 0) → x
+(minus(x), x) → 0
minus(0) → 0
minus(minus(x)) → x
minus(+(x, y)) → +(minus(y), minus(x))
*(x, 1) → x
*(x, 0) → 0
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(x, minus(y)) → minus(*(x, y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MINUS(+(x, y)) → MINUS(y)
MINUS(+(x, y)) → MINUS(x)
The value of delta used in the strict ordering is 1/2.
POL(MINUS(x1)) = (2)x_1
POL(+(x1, x2)) = 1/4 + (5/2)x_1 + (5/2)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
+(x, 0) → x
+(minus(x), x) → 0
minus(0) → 0
minus(minus(x)) → x
minus(+(x, y)) → +(minus(y), minus(x))
*(x, 1) → x
*(x, 0) → 0
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(x, minus(y)) → minus(*(x, y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
*1(x, +(y, z)) → *1(x, y)
*1(x, +(y, z)) → *1(x, z)
*1(x, minus(y)) → *1(x, y)
+(x, 0) → x
+(minus(x), x) → 0
minus(0) → 0
minus(minus(x)) → x
minus(+(x, y)) → +(minus(y), minus(x))
*(x, 1) → x
*(x, 0) → 0
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(x, minus(y)) → minus(*(x, 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, y)
*1(x, +(y, z)) → *1(x, z)
*1(x, minus(y)) → *1(x, y)
The value of delta used in the strict ordering is 1.
POL(*1(x1, x2)) = (4)x_2
POL(minus(x1)) = 1/4 + (4)x_1
POL(+(x1, x2)) = 3/2 + (4)x_1 + (11/4)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
+(x, 0) → x
+(minus(x), x) → 0
minus(0) → 0
minus(minus(x)) → x
minus(+(x, y)) → +(minus(y), minus(x))
*(x, 1) → x
*(x, 0) → 0
*(x, +(y, z)) → +(*(x, y), *(x, z))
*(x, minus(y)) → minus(*(x, y))