+(p1, p1) → p2
+(p1, +(p2, p2)) → p5
+(p5, p5) → p10
+(+(x, y), z) → +(x, +(y, z))
+(p1, +(p1, x)) → +(p2, x)
+(p1, +(p2, +(p2, x))) → +(p5, x)
+(p2, p1) → +(p1, p2)
+(p2, +(p1, x)) → +(p1, +(p2, x))
+(p2, +(p2, p2)) → +(p1, p5)
+(p2, +(p2, +(p2, x))) → +(p1, +(p5, x))
+(p5, p1) → +(p1, p5)
+(p5, +(p1, x)) → +(p1, +(p5, x))
+(p5, p2) → +(p2, p5)
+(p5, +(p2, x)) → +(p2, +(p5, x))
+(p5, +(p5, x)) → +(p10, x)
+(p10, p1) → +(p1, p10)
+(p10, +(p1, x)) → +(p1, +(p10, x))
+(p10, p2) → +(p2, p10)
+(p10, +(p2, x)) → +(p2, +(p10, x))
+(p10, p5) → +(p5, p10)
+(p10, +(p5, x)) → +(p5, +(p10, x))
↳ QTRS
↳ DependencyPairsProof
+(p1, p1) → p2
+(p1, +(p2, p2)) → p5
+(p5, p5) → p10
+(+(x, y), z) → +(x, +(y, z))
+(p1, +(p1, x)) → +(p2, x)
+(p1, +(p2, +(p2, x))) → +(p5, x)
+(p2, p1) → +(p1, p2)
+(p2, +(p1, x)) → +(p1, +(p2, x))
+(p2, +(p2, p2)) → +(p1, p5)
+(p2, +(p2, +(p2, x))) → +(p1, +(p5, x))
+(p5, p1) → +(p1, p5)
+(p5, +(p1, x)) → +(p1, +(p5, x))
+(p5, p2) → +(p2, p5)
+(p5, +(p2, x)) → +(p2, +(p5, x))
+(p5, +(p5, x)) → +(p10, x)
+(p10, p1) → +(p1, p10)
+(p10, +(p1, x)) → +(p1, +(p10, x))
+(p10, p2) → +(p2, p10)
+(p10, +(p2, x)) → +(p2, +(p10, x))
+(p10, p5) → +(p5, p10)
+(p10, +(p5, x)) → +(p5, +(p10, x))
+1(p5, +(p2, x)) → +1(p5, x)
+1(p2, p1) → +1(p1, p2)
+1(p10, p2) → +1(p2, p10)
+1(p5, +(p2, x)) → +1(p2, +(p5, x))
+1(+(x, y), z) → +1(x, +(y, z))
+1(p2, +(p2, p2)) → +1(p1, p5)
+1(p10, p5) → +1(p5, p10)
+1(p10, +(p2, x)) → +1(p10, x)
+1(p10, +(p1, x)) → +1(p1, +(p10, x))
+1(p5, p2) → +1(p2, p5)
+1(p5, p1) → +1(p1, p5)
+1(p10, p1) → +1(p1, p10)
+1(p10, +(p2, x)) → +1(p2, +(p10, x))
+1(p2, +(p2, +(p2, x))) → +1(p5, x)
+1(p5, +(p1, x)) → +1(p5, x)
+1(p10, +(p1, x)) → +1(p10, x)
+1(p1, +(p1, x)) → +1(p2, x)
+1(p10, +(p5, x)) → +1(p5, +(p10, x))
+1(p2, +(p1, x)) → +1(p1, +(p2, x))
+1(p2, +(p1, x)) → +1(p2, x)
+1(p2, +(p2, +(p2, x))) → +1(p1, +(p5, x))
+1(p1, +(p2, +(p2, x))) → +1(p5, x)
+1(p10, +(p5, x)) → +1(p10, x)
+1(p5, +(p5, x)) → +1(p10, x)
+1(p5, +(p1, x)) → +1(p1, +(p5, x))
+1(+(x, y), z) → +1(y, z)
+(p1, p1) → p2
+(p1, +(p2, p2)) → p5
+(p5, p5) → p10
+(+(x, y), z) → +(x, +(y, z))
+(p1, +(p1, x)) → +(p2, x)
+(p1, +(p2, +(p2, x))) → +(p5, x)
+(p2, p1) → +(p1, p2)
+(p2, +(p1, x)) → +(p1, +(p2, x))
+(p2, +(p2, p2)) → +(p1, p5)
+(p2, +(p2, +(p2, x))) → +(p1, +(p5, x))
+(p5, p1) → +(p1, p5)
+(p5, +(p1, x)) → +(p1, +(p5, x))
+(p5, p2) → +(p2, p5)
+(p5, +(p2, x)) → +(p2, +(p5, x))
+(p5, +(p5, x)) → +(p10, x)
+(p10, p1) → +(p1, p10)
+(p10, +(p1, x)) → +(p1, +(p10, x))
+(p10, p2) → +(p2, p10)
+(p10, +(p2, x)) → +(p2, +(p10, x))
+(p10, p5) → +(p5, p10)
+(p10, +(p5, x)) → +(p5, +(p10, x))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
+1(p5, +(p2, x)) → +1(p5, x)
+1(p2, p1) → +1(p1, p2)
+1(p10, p2) → +1(p2, p10)
+1(p5, +(p2, x)) → +1(p2, +(p5, x))
+1(+(x, y), z) → +1(x, +(y, z))
+1(p2, +(p2, p2)) → +1(p1, p5)
+1(p10, p5) → +1(p5, p10)
+1(p10, +(p2, x)) → +1(p10, x)
+1(p10, +(p1, x)) → +1(p1, +(p10, x))
+1(p5, p2) → +1(p2, p5)
+1(p5, p1) → +1(p1, p5)
+1(p10, p1) → +1(p1, p10)
+1(p10, +(p2, x)) → +1(p2, +(p10, x))
+1(p2, +(p2, +(p2, x))) → +1(p5, x)
+1(p5, +(p1, x)) → +1(p5, x)
+1(p10, +(p1, x)) → +1(p10, x)
+1(p1, +(p1, x)) → +1(p2, x)
+1(p10, +(p5, x)) → +1(p5, +(p10, x))
+1(p2, +(p1, x)) → +1(p1, +(p2, x))
+1(p2, +(p1, x)) → +1(p2, x)
+1(p2, +(p2, +(p2, x))) → +1(p1, +(p5, x))
+1(p1, +(p2, +(p2, x))) → +1(p5, x)
+1(p10, +(p5, x)) → +1(p10, x)
+1(p5, +(p5, x)) → +1(p10, x)
+1(p5, +(p1, x)) → +1(p1, +(p5, x))
+1(+(x, y), z) → +1(y, z)
+(p1, p1) → p2
+(p1, +(p2, p2)) → p5
+(p5, p5) → p10
+(+(x, y), z) → +(x, +(y, z))
+(p1, +(p1, x)) → +(p2, x)
+(p1, +(p2, +(p2, x))) → +(p5, x)
+(p2, p1) → +(p1, p2)
+(p2, +(p1, x)) → +(p1, +(p2, x))
+(p2, +(p2, p2)) → +(p1, p5)
+(p2, +(p2, +(p2, x))) → +(p1, +(p5, x))
+(p5, p1) → +(p1, p5)
+(p5, +(p1, x)) → +(p1, +(p5, x))
+(p5, p2) → +(p2, p5)
+(p5, +(p2, x)) → +(p2, +(p5, x))
+(p5, +(p5, x)) → +(p10, x)
+(p10, p1) → +(p1, p10)
+(p10, +(p1, x)) → +(p1, +(p10, x))
+(p10, p2) → +(p2, p10)
+(p10, +(p2, x)) → +(p2, +(p10, x))
+(p10, p5) → +(p5, p10)
+(p10, +(p5, x)) → +(p5, +(p10, x))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
+1(p10, +(p2, x)) → +1(p2, +(p10, x))
+1(p5, +(p2, x)) → +1(p5, x)
+1(p2, +(p2, +(p2, x))) → +1(p5, x)
+1(p5, +(p1, x)) → +1(p5, x)
+1(p10, +(p1, x)) → +1(p10, x)
+1(p1, +(p1, x)) → +1(p2, x)
+1(p5, +(p2, x)) → +1(p2, +(p5, x))
+1(p10, +(p5, x)) → +1(p5, +(p10, x))
+1(p10, +(p2, x)) → +1(p10, x)
+1(p2, +(p1, x)) → +1(p1, +(p2, x))
+1(p10, +(p1, x)) → +1(p1, +(p10, x))
+1(p2, +(p1, x)) → +1(p2, x)
+1(p2, +(p2, +(p2, x))) → +1(p1, +(p5, x))
+1(p1, +(p2, +(p2, x))) → +1(p5, x)
+1(p10, +(p5, x)) → +1(p10, x)
+1(p5, +(p5, x)) → +1(p10, x)
+1(p5, +(p1, x)) → +1(p1, +(p5, x))
+(p1, p1) → p2
+(p1, +(p2, p2)) → p5
+(p5, p5) → p10
+(+(x, y), z) → +(x, +(y, z))
+(p1, +(p1, x)) → +(p2, x)
+(p1, +(p2, +(p2, x))) → +(p5, x)
+(p2, p1) → +(p1, p2)
+(p2, +(p1, x)) → +(p1, +(p2, x))
+(p2, +(p2, p2)) → +(p1, p5)
+(p2, +(p2, +(p2, x))) → +(p1, +(p5, x))
+(p5, p1) → +(p1, p5)
+(p5, +(p1, x)) → +(p1, +(p5, x))
+(p5, p2) → +(p2, p5)
+(p5, +(p2, x)) → +(p2, +(p5, x))
+(p5, +(p5, x)) → +(p10, x)
+(p10, p1) → +(p1, p10)
+(p10, +(p1, x)) → +(p1, +(p10, x))
+(p10, p2) → +(p2, p10)
+(p10, +(p2, x)) → +(p2, +(p10, x))
+(p10, p5) → +(p5, p10)
+(p10, +(p5, x)) → +(p5, +(p10, x))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
+1(p10, +(p2, x)) → +1(p2, +(p10, x))
+1(p5, +(p2, x)) → +1(p5, x)
+1(p2, +(p2, +(p2, x))) → +1(p5, x)
+1(p5, +(p1, x)) → +1(p5, x)
+1(p10, +(p1, x)) → +1(p10, x)
+1(p1, +(p1, x)) → +1(p2, x)
+1(p5, +(p2, x)) → +1(p2, +(p5, x))
+1(p10, +(p2, x)) → +1(p10, x)
+1(p2, +(p1, x)) → +1(p1, +(p2, x))
+1(p10, +(p1, x)) → +1(p1, +(p10, x))
+1(p2, +(p1, x)) → +1(p2, x)
+1(p2, +(p2, +(p2, x))) → +1(p1, +(p5, x))
+1(p1, +(p2, +(p2, x))) → +1(p5, x)
+1(p5, +(p1, x)) → +1(p1, +(p5, x))
Used ordering: Polynomial interpretation [25,35]:
+1(p10, +(p5, x)) → +1(p5, +(p10, x))
+1(p10, +(p5, x)) → +1(p10, x)
+1(p5, +(p5, x)) → +1(p10, x)
The value of delta used in the strict ordering is 1/4.
POL(p1) = 1
POL(p10) = 0
POL(p5) = 0
POL(+1(x1, x2)) = (4)x_2
POL(p2) = 1/4
POL(+(x1, x2)) = (1/4)x_1 + (4)x_2
+(p2, +(p2, p2)) → +(p1, p5)
+(p2, p1) → +(p1, p2)
+(p5, p2) → +(p2, p5)
+(p5, p1) → +(p1, p5)
+(p10, p1) → +(p1, p10)
+(p10, p5) → +(p5, p10)
+(p10, p2) → +(p2, p10)
+(p1, p1) → p2
+(p5, p5) → p10
+(p1, +(p2, p2)) → p5
+(p1, +(p2, +(p2, x))) → +(p5, x)
+(p10, +(p1, x)) → +(p1, +(p10, x))
+(p1, +(p1, x)) → +(p2, x)
+(p2, +(p1, x)) → +(p1, +(p2, x))
+(p10, +(p2, x)) → +(p2, +(p10, x))
+(p10, +(p5, x)) → +(p5, +(p10, x))
+(p5, +(p1, x)) → +(p1, +(p5, x))
+(p5, +(p2, x)) → +(p2, +(p5, x))
+(p2, +(p2, +(p2, x))) → +(p1, +(p5, x))
+(p5, +(p5, x)) → +(p10, x)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
+1(p10, +(p5, x)) → +1(p10, x)
+1(p5, +(p5, x)) → +1(p10, x)
+1(p10, +(p5, x)) → +1(p5, +(p10, x))
+(p1, p1) → p2
+(p1, +(p2, p2)) → p5
+(p5, p5) → p10
+(+(x, y), z) → +(x, +(y, z))
+(p1, +(p1, x)) → +(p2, x)
+(p1, +(p2, +(p2, x))) → +(p5, x)
+(p2, p1) → +(p1, p2)
+(p2, +(p1, x)) → +(p1, +(p2, x))
+(p2, +(p2, p2)) → +(p1, p5)
+(p2, +(p2, +(p2, x))) → +(p1, +(p5, x))
+(p5, p1) → +(p1, p5)
+(p5, +(p1, x)) → +(p1, +(p5, x))
+(p5, p2) → +(p2, p5)
+(p5, +(p2, x)) → +(p2, +(p5, x))
+(p5, +(p5, x)) → +(p10, x)
+(p10, p1) → +(p1, p10)
+(p10, +(p1, x)) → +(p1, +(p10, x))
+(p10, p2) → +(p2, p10)
+(p10, +(p2, x)) → +(p2, +(p10, x))
+(p10, p5) → +(p5, p10)
+(p10, +(p5, x)) → +(p5, +(p10, x))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
+1(p10, +(p5, x)) → +1(p10, x)
+1(p5, +(p5, x)) → +1(p10, x)
Used ordering: Polynomial interpretation [25,35]:
+1(p10, +(p5, x)) → +1(p5, +(p10, x))
The value of delta used in the strict ordering is 16.
POL(p1) = 0
POL(p10) = 0
POL(p5) = 0
POL(+1(x1, x2)) = (4)x_1 + (4)x_2
POL(p2) = 0
POL(+(x1, x2)) = 4 + (4)x_1 + (4)x_2
+(p2, +(p2, p2)) → +(p1, p5)
+(p2, p1) → +(p1, p2)
+(p5, p2) → +(p2, p5)
+(p5, p1) → +(p1, p5)
+(p10, p1) → +(p1, p10)
+(p1, p1) → p2
+(p5, p5) → p10
+(p10, p5) → +(p5, p10)
+(p1, +(p2, p2)) → p5
+(p10, p2) → +(p2, p10)
+(p1, +(p2, +(p2, x))) → +(p5, x)
+(p10, +(p1, x)) → +(p1, +(p10, x))
+(p1, +(p1, x)) → +(p2, x)
+(p2, +(p1, x)) → +(p1, +(p2, x))
+(p10, +(p2, x)) → +(p2, +(p10, x))
+(p10, +(p5, x)) → +(p5, +(p10, x))
+(p5, +(p1, x)) → +(p1, +(p5, x))
+(p5, +(p2, x)) → +(p2, +(p5, x))
+(p2, +(p2, +(p2, x))) → +(p1, +(p5, x))
+(p5, +(p5, x)) → +(p10, x)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
+1(p10, +(p5, x)) → +1(p5, +(p10, x))
+(p1, p1) → p2
+(p1, +(p2, p2)) → p5
+(p5, p5) → p10
+(+(x, y), z) → +(x, +(y, z))
+(p1, +(p1, x)) → +(p2, x)
+(p1, +(p2, +(p2, x))) → +(p5, x)
+(p2, p1) → +(p1, p2)
+(p2, +(p1, x)) → +(p1, +(p2, x))
+(p2, +(p2, p2)) → +(p1, p5)
+(p2, +(p2, +(p2, x))) → +(p1, +(p5, x))
+(p5, p1) → +(p1, p5)
+(p5, +(p1, x)) → +(p1, +(p5, x))
+(p5, p2) → +(p2, p5)
+(p5, +(p2, x)) → +(p2, +(p5, x))
+(p5, +(p5, x)) → +(p10, x)
+(p10, p1) → +(p1, p10)
+(p10, +(p1, x)) → +(p1, +(p10, x))
+(p10, p2) → +(p2, p10)
+(p10, +(p2, x)) → +(p2, +(p10, x))
+(p10, p5) → +(p5, p10)
+(p10, +(p5, x)) → +(p5, +(p10, x))