+(X, 0) → X
+(X, s(Y)) → s(+(X, Y))
double(X) → +(X, X)
f(0, s(0), X) → f(X, double(X), X)
g(X, Y) → X
g(X, Y) → Y
↳ QTRS
↳ DependencyPairsProof
+(X, 0) → X
+(X, s(Y)) → s(+(X, Y))
double(X) → +(X, X)
f(0, s(0), X) → f(X, double(X), X)
g(X, Y) → X
g(X, Y) → Y
F(0, s(0), X) → F(X, double(X), X)
F(0, s(0), X) → DOUBLE(X)
+1(X, s(Y)) → +1(X, Y)
DOUBLE(X) → +1(X, X)
+(X, 0) → X
+(X, s(Y)) → s(+(X, Y))
double(X) → +(X, X)
f(0, s(0), X) → f(X, double(X), X)
g(X, Y) → X
g(X, Y) → Y
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
F(0, s(0), X) → F(X, double(X), X)
F(0, s(0), X) → DOUBLE(X)
+1(X, s(Y)) → +1(X, Y)
DOUBLE(X) → +1(X, X)
+(X, 0) → X
+(X, s(Y)) → s(+(X, Y))
double(X) → +(X, X)
f(0, s(0), X) → f(X, double(X), X)
g(X, Y) → X
g(X, Y) → Y
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
+1(X, s(Y)) → +1(X, Y)
+(X, 0) → X
+(X, s(Y)) → s(+(X, Y))
double(X) → +(X, X)
f(0, s(0), X) → f(X, double(X), X)
g(X, Y) → X
g(X, Y) → 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 4.
POL(s(x1)) = 1 + (4)x_1
POL(+1(x1, x2)) = (4)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
+(X, 0) → X
+(X, s(Y)) → s(+(X, Y))
double(X) → +(X, X)
f(0, s(0), X) → f(X, double(X), X)
g(X, Y) → X
g(X, Y) → Y
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
F(0, s(0), X) → F(X, double(X), X)
+(X, 0) → X
+(X, s(Y)) → s(+(X, Y))
double(X) → +(X, X)
f(0, s(0), X) → f(X, double(X), X)
g(X, Y) → X
g(X, Y) → Y