+(+(x, y), z) → +(x, +(y, z))
+(f(x), f(y)) → f(+(x, y))
+(f(x), +(f(y), z)) → +(f(+(x, y)), z)
↳ QTRS
↳ DependencyPairsProof
+(+(x, y), z) → +(x, +(y, z))
+(f(x), f(y)) → f(+(x, y))
+(f(x), +(f(y), z)) → +(f(+(x, y)), z)
+1(f(x), f(y)) → +1(x, y)
+1(+(x, y), z) → +1(y, z)
+1(+(x, y), z) → +1(x, +(y, z))
+1(f(x), +(f(y), z)) → +1(f(+(x, y)), z)
+1(f(x), +(f(y), z)) → +1(x, y)
+(+(x, y), z) → +(x, +(y, z))
+(f(x), f(y)) → f(+(x, y))
+(f(x), +(f(y), z)) → +(f(+(x, y)), z)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
+1(f(x), f(y)) → +1(x, y)
+1(+(x, y), z) → +1(y, z)
+1(+(x, y), z) → +1(x, +(y, z))
+1(f(x), +(f(y), z)) → +1(f(+(x, y)), z)
+1(f(x), +(f(y), z)) → +1(x, y)
+(+(x, y), z) → +(x, +(y, z))
+(f(x), f(y)) → f(+(x, y))
+(f(x), +(f(y), z)) → +(f(+(x, y)), z)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
+1(f(x), f(y)) → +1(x, y)
+1(f(x), +(f(y), z)) → +1(f(+(x, y)), z)
+1(f(x), +(f(y), z)) → +1(x, y)
Used ordering: Polynomial interpretation [25,35]:
+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 2.
POL(f(x1)) = 4 + x_1
POL(+1(x1, x2)) = (1/2)x_1 + (1/2)x_2
POL(+(x1, x2)) = x_1 + x_2
+(+(x, y), z) → +(x, +(y, z))
+(f(x), f(y)) → f(+(x, y))
+(f(x), +(f(y), z)) → +(f(+(x, y)), z)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
+1(+(x, y), z) → +1(y, z)
+1(+(x, y), z) → +1(x, +(y, z))
+(+(x, y), z) → +(x, +(y, z))
+(f(x), f(y)) → f(+(x, y))
+(f(x), +(f(y), z)) → +(f(+(x, 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 1/16.
POL(f(x1)) = 4
POL(+1(x1, x2)) = (1/4)x_1
POL(+(x1, x2)) = 1/4 + (4)x_1 + (4)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
+(+(x, y), z) → +(x, +(y, z))
+(f(x), f(y)) → f(+(x, y))
+(f(x), +(f(y), z)) → +(f(+(x, y)), z)