+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(0, s(y)) → s(y)
s(+(0, y)) → s(y)
↳ QTRS
↳ DependencyPairsProof
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(0, s(y)) → s(y)
s(+(0, y)) → s(y)
+1(x, s(y)) → S(+(x, y))
S(+(0, y)) → S(y)
+1(x, s(y)) → +1(x, y)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(0, s(y)) → s(y)
s(+(0, y)) → s(y)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
+1(x, s(y)) → S(+(x, y))
S(+(0, y)) → S(y)
+1(x, s(y)) → +1(x, y)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(0, s(y)) → s(y)
s(+(0, y)) → s(y)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
S(+(0, y)) → S(y)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(0, s(y)) → s(y)
s(+(0, y)) → s(y)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
S(+(0, y)) → S(y)
The value of delta used in the strict ordering is 1/8.
POL(0) = 0
POL(S(x1)) = (1/2)x_1
POL(+(x1, x2)) = 1/4 + x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(0, s(y)) → s(y)
s(+(0, y)) → s(y)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
+1(x, s(y)) → +1(x, y)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(0, s(y)) → s(y)
s(+(0, y)) → s(y)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
+1(x, s(y)) → +1(x, y)
The value of delta used in the strict ordering is 8.
POL(s(x1)) = 4 + (4)x_1
POL(+1(x1, x2)) = (2)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(0, s(y)) → s(y)
s(+(0, y)) → s(y)