minus(X, 0) → X
minus(s(X), s(Y)) → p(minus(X, Y))
p(s(X)) → X
div(0, s(Y)) → 0
div(s(X), s(Y)) → s(div(minus(X, Y), s(Y)))
↳ QTRS
↳ DependencyPairsProof
minus(X, 0) → X
minus(s(X), s(Y)) → p(minus(X, Y))
p(s(X)) → X
div(0, s(Y)) → 0
div(s(X), s(Y)) → s(div(minus(X, Y), s(Y)))
DIV(s(X), s(Y)) → DIV(minus(X, Y), s(Y))
MINUS(s(X), s(Y)) → MINUS(X, Y)
MINUS(s(X), s(Y)) → P(minus(X, Y))
DIV(s(X), s(Y)) → MINUS(X, Y)
minus(X, 0) → X
minus(s(X), s(Y)) → p(minus(X, Y))
p(s(X)) → X
div(0, s(Y)) → 0
div(s(X), s(Y)) → s(div(minus(X, Y), s(Y)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
DIV(s(X), s(Y)) → DIV(minus(X, Y), s(Y))
MINUS(s(X), s(Y)) → MINUS(X, Y)
MINUS(s(X), s(Y)) → P(minus(X, Y))
DIV(s(X), s(Y)) → MINUS(X, Y)
minus(X, 0) → X
minus(s(X), s(Y)) → p(minus(X, Y))
p(s(X)) → X
div(0, s(Y)) → 0
div(s(X), s(Y)) → s(div(minus(X, Y), s(Y)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
MINUS(s(X), s(Y)) → MINUS(X, Y)
minus(X, 0) → X
minus(s(X), s(Y)) → p(minus(X, Y))
p(s(X)) → X
div(0, s(Y)) → 0
div(s(X), s(Y)) → s(div(minus(X, Y), s(Y)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MINUS(s(X), s(Y)) → MINUS(X, Y)
The value of delta used in the strict ordering is 15/8.
POL(MINUS(x1, x2)) = (15/4)x_2
POL(s(x1)) = 1/2 + (13/4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
minus(X, 0) → X
minus(s(X), s(Y)) → p(minus(X, Y))
p(s(X)) → X
div(0, s(Y)) → 0
div(s(X), s(Y)) → s(div(minus(X, Y), s(Y)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
DIV(s(X), s(Y)) → DIV(minus(X, Y), s(Y))
minus(X, 0) → X
minus(s(X), s(Y)) → p(minus(X, Y))
p(s(X)) → X
div(0, s(Y)) → 0
div(s(X), s(Y)) → s(div(minus(X, Y), s(Y)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
DIV(s(X), s(Y)) → DIV(minus(X, Y), s(Y))
The value of delta used in the strict ordering is 9/16.
POL(minus(x1, x2)) = 1/4 + x_1
POL(DIV(x1, x2)) = (1/4)x_1
POL(s(x1)) = 5/2 + (7/2)x_1
POL(p(x1)) = 3/4 + (1/2)x_1
POL(0) = 0
minus(X, 0) → X
minus(s(X), s(Y)) → p(minus(X, Y))
p(s(X)) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
minus(X, 0) → X
minus(s(X), s(Y)) → p(minus(X, Y))
p(s(X)) → X
div(0, s(Y)) → 0
div(s(X), s(Y)) → s(div(minus(X, Y), s(Y)))