minus(0) → 0
+(x, 0) → x
+(0, y) → y
+(minus(1), 1) → 0
minus(minus(x)) → x
+(x, minus(y)) → minus(+(minus(x), y))
+(x, +(y, z)) → +(+(x, y), z)
+(minus(+(x, 1)), 1) → minus(x)
↳ QTRS
↳ DependencyPairsProof
minus(0) → 0
+(x, 0) → x
+(0, y) → y
+(minus(1), 1) → 0
minus(minus(x)) → x
+(x, minus(y)) → minus(+(minus(x), y))
+(x, +(y, z)) → +(+(x, y), z)
+(minus(+(x, 1)), 1) → minus(x)
+1(x, minus(y)) → +1(minus(x), y)
+1(x, +(y, z)) → +1(x, y)
+1(x, minus(y)) → MINUS(+(minus(x), y))
+1(x, +(y, z)) → +1(+(x, y), z)
+1(x, minus(y)) → MINUS(x)
+1(minus(+(x, 1)), 1) → MINUS(x)
minus(0) → 0
+(x, 0) → x
+(0, y) → y
+(minus(1), 1) → 0
minus(minus(x)) → x
+(x, minus(y)) → minus(+(minus(x), y))
+(x, +(y, z)) → +(+(x, y), z)
+(minus(+(x, 1)), 1) → minus(x)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
+1(x, minus(y)) → +1(minus(x), y)
+1(x, +(y, z)) → +1(x, y)
+1(x, minus(y)) → MINUS(+(minus(x), y))
+1(x, +(y, z)) → +1(+(x, y), z)
+1(x, minus(y)) → MINUS(x)
+1(minus(+(x, 1)), 1) → MINUS(x)
minus(0) → 0
+(x, 0) → x
+(0, y) → y
+(minus(1), 1) → 0
minus(minus(x)) → x
+(x, minus(y)) → minus(+(minus(x), y))
+(x, +(y, z)) → +(+(x, y), z)
+(minus(+(x, 1)), 1) → minus(x)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
+1(x, minus(y)) → +1(minus(x), y)
+1(x, +(y, z)) → +1(x, y)
+1(x, +(y, z)) → +1(+(x, y), z)
minus(0) → 0
+(x, 0) → x
+(0, y) → y
+(minus(1), 1) → 0
minus(minus(x)) → x
+(x, minus(y)) → minus(+(minus(x), y))
+(x, +(y, z)) → +(+(x, y), z)
+(minus(+(x, 1)), 1) → minus(x)
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, y), z)
Used ordering: Polynomial interpretation [25,35]:
+1(x, minus(y)) → +1(minus(x), y)
The value of delta used in the strict ordering is 7/16.
POL(minus(x1)) = x_1
POL(0) = 1/4
POL(1) = 0
POL(+1(x1, x2)) = (1/2)x_1 + (9/4)x_2
POL(+(x1, x2)) = 1/4 + x_1 + (3/2)x_2
minus(0) → 0
+(x, 0) → x
+(0, y) → y
+(minus(1), 1) → 0
minus(minus(x)) → x
+(x, minus(y)) → minus(+(minus(x), y))
+(x, +(y, z)) → +(+(x, y), z)
+(minus(+(x, 1)), 1) → minus(x)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
+1(x, minus(y)) → +1(minus(x), y)
minus(0) → 0
+(x, 0) → x
+(0, y) → y
+(minus(1), 1) → 0
minus(minus(x)) → x
+(x, minus(y)) → minus(+(minus(x), y))
+(x, +(y, z)) → +(+(x, y), z)
+(minus(+(x, 1)), 1) → minus(x)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
+1(x, minus(y)) → +1(minus(x), y)
The value of delta used in the strict ordering is 9.
POL(minus(x1)) = 3 + (2)x_1
POL(0) = 1
POL(+1(x1, x2)) = (3)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
minus(0) → 0
+(x, 0) → x
+(0, y) → y
+(minus(1), 1) → 0
minus(minus(x)) → x
+(x, minus(y)) → minus(+(minus(x), y))
+(x, +(y, z)) → +(+(x, y), z)
+(minus(+(x, 1)), 1) → minus(x)