a__f(g(X), Y) → a__f(mark(X), f(g(X), Y))
mark(f(X1, X2)) → a__f(mark(X1), X2)
mark(g(X)) → g(mark(X))
a__f(X1, X2) → f(X1, X2)
↳ QTRS
↳ DependencyPairsProof
a__f(g(X), Y) → a__f(mark(X), f(g(X), Y))
mark(f(X1, X2)) → a__f(mark(X1), X2)
mark(g(X)) → g(mark(X))
a__f(X1, X2) → f(X1, X2)
MARK(f(X1, X2)) → MARK(X1)
A__F(g(X), Y) → MARK(X)
MARK(f(X1, X2)) → A__F(mark(X1), X2)
A__F(g(X), Y) → A__F(mark(X), f(g(X), Y))
MARK(g(X)) → MARK(X)
a__f(g(X), Y) → a__f(mark(X), f(g(X), Y))
mark(f(X1, X2)) → a__f(mark(X1), X2)
mark(g(X)) → g(mark(X))
a__f(X1, X2) → f(X1, X2)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
MARK(f(X1, X2)) → MARK(X1)
A__F(g(X), Y) → MARK(X)
MARK(f(X1, X2)) → A__F(mark(X1), X2)
A__F(g(X), Y) → A__F(mark(X), f(g(X), Y))
MARK(g(X)) → MARK(X)
a__f(g(X), Y) → a__f(mark(X), f(g(X), Y))
mark(f(X1, X2)) → a__f(mark(X1), X2)
mark(g(X)) → g(mark(X))
a__f(X1, X2) → f(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(f(X1, X2)) → MARK(X1)
MARK(f(X1, X2)) → A__F(mark(X1), X2)
Used ordering: Polynomial interpretation [25,35]:
A__F(g(X), Y) → MARK(X)
A__F(g(X), Y) → A__F(mark(X), f(g(X), Y))
MARK(g(X)) → MARK(X)
The value of delta used in the strict ordering is 1.
POL(MARK(x1)) = (1/4)x_1
POL(f(x1, x2)) = 4 + (4)x_1
POL(g(x1)) = (4)x_1
POL(a__f(x1, x2)) = 4 + (4)x_1
POL(mark(x1)) = (2)x_1
POL(A__F(x1, x2)) = (1/2)x_1
a__f(g(X), Y) → a__f(mark(X), f(g(X), Y))
mark(f(X1, X2)) → a__f(mark(X1), X2)
mark(g(X)) → g(mark(X))
a__f(X1, X2) → f(X1, X2)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
A__F(g(X), Y) → MARK(X)
A__F(g(X), Y) → A__F(mark(X), f(g(X), Y))
MARK(g(X)) → MARK(X)
a__f(g(X), Y) → a__f(mark(X), f(g(X), Y))
mark(f(X1, X2)) → a__f(mark(X1), X2)
mark(g(X)) → g(mark(X))
a__f(X1, X2) → f(X1, X2)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
MARK(g(X)) → MARK(X)
a__f(g(X), Y) → a__f(mark(X), f(g(X), Y))
mark(f(X1, X2)) → a__f(mark(X1), X2)
mark(g(X)) → g(mark(X))
a__f(X1, X2) → f(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(g(X)) → MARK(X)
The value of delta used in the strict ordering is 1/16.
POL(MARK(x1)) = (1/4)x_1
POL(g(x1)) = 1/4 + (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
a__f(g(X), Y) → a__f(mark(X), f(g(X), Y))
mark(f(X1, X2)) → a__f(mark(X1), X2)
mark(g(X)) → g(mark(X))
a__f(X1, X2) → f(X1, X2)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
A__F(g(X), Y) → A__F(mark(X), f(g(X), Y))
a__f(g(X), Y) → a__f(mark(X), f(g(X), Y))
mark(f(X1, X2)) → a__f(mark(X1), X2)
mark(g(X)) → g(mark(X))
a__f(X1, X2) → f(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A__F(g(X), Y) → A__F(mark(X), f(g(X), Y))
The value of delta used in the strict ordering is 1.
POL(g(x1)) = 1/4 + (4)x_1
POL(f(x1, x2)) = 0
POL(a__f(x1, x2)) = 0
POL(mark(x1)) = (4)x_1
POL(A__F(x1, x2)) = (4)x_1
a__f(g(X), Y) → a__f(mark(X), f(g(X), Y))
mark(f(X1, X2)) → a__f(mark(X1), X2)
mark(g(X)) → g(mark(X))
a__f(X1, X2) → f(X1, X2)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
a__f(g(X), Y) → a__f(mark(X), f(g(X), Y))
mark(f(X1, X2)) → a__f(mark(X1), X2)
mark(g(X)) → g(mark(X))
a__f(X1, X2) → f(X1, X2)