active(f(g(X), Y)) → mark(f(X, f(g(X), Y)))
mark(f(X1, X2)) → active(f(mark(X1), X2))
mark(g(X)) → active(g(mark(X)))
f(mark(X1), X2) → f(X1, X2)
f(X1, mark(X2)) → f(X1, X2)
f(active(X1), X2) → f(X1, X2)
f(X1, active(X2)) → f(X1, X2)
g(mark(X)) → g(X)
g(active(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
active(f(g(X), Y)) → mark(f(X, f(g(X), Y)))
mark(f(X1, X2)) → active(f(mark(X1), X2))
mark(g(X)) → active(g(mark(X)))
f(mark(X1), X2) → f(X1, X2)
f(X1, mark(X2)) → f(X1, X2)
f(active(X1), X2) → f(X1, X2)
f(X1, active(X2)) → f(X1, X2)
g(mark(X)) → g(X)
g(active(X)) → g(X)
ACTIVE(f(g(X), Y)) → MARK(f(X, f(g(X), Y)))
F(active(X1), X2) → F(X1, X2)
F(X1, mark(X2)) → F(X1, X2)
MARK(g(X)) → ACTIVE(g(mark(X)))
G(active(X)) → G(X)
G(mark(X)) → G(X)
MARK(g(X)) → G(mark(X))
MARK(g(X)) → MARK(X)
ACTIVE(f(g(X), Y)) → F(X, f(g(X), Y))
MARK(f(X1, X2)) → MARK(X1)
MARK(f(X1, X2)) → F(mark(X1), X2)
MARK(f(X1, X2)) → ACTIVE(f(mark(X1), X2))
F(mark(X1), X2) → F(X1, X2)
F(X1, active(X2)) → F(X1, X2)
active(f(g(X), Y)) → mark(f(X, f(g(X), Y)))
mark(f(X1, X2)) → active(f(mark(X1), X2))
mark(g(X)) → active(g(mark(X)))
f(mark(X1), X2) → f(X1, X2)
f(X1, mark(X2)) → f(X1, X2)
f(active(X1), X2) → f(X1, X2)
f(X1, active(X2)) → f(X1, X2)
g(mark(X)) → g(X)
g(active(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
ACTIVE(f(g(X), Y)) → MARK(f(X, f(g(X), Y)))
F(active(X1), X2) → F(X1, X2)
F(X1, mark(X2)) → F(X1, X2)
MARK(g(X)) → ACTIVE(g(mark(X)))
G(active(X)) → G(X)
G(mark(X)) → G(X)
MARK(g(X)) → G(mark(X))
MARK(g(X)) → MARK(X)
ACTIVE(f(g(X), Y)) → F(X, f(g(X), Y))
MARK(f(X1, X2)) → MARK(X1)
MARK(f(X1, X2)) → F(mark(X1), X2)
MARK(f(X1, X2)) → ACTIVE(f(mark(X1), X2))
F(mark(X1), X2) → F(X1, X2)
F(X1, active(X2)) → F(X1, X2)
active(f(g(X), Y)) → mark(f(X, f(g(X), Y)))
mark(f(X1, X2)) → active(f(mark(X1), X2))
mark(g(X)) → active(g(mark(X)))
f(mark(X1), X2) → f(X1, X2)
f(X1, mark(X2)) → f(X1, X2)
f(active(X1), X2) → f(X1, X2)
f(X1, active(X2)) → f(X1, X2)
g(mark(X)) → g(X)
g(active(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
G(active(X)) → G(X)
G(mark(X)) → G(X)
active(f(g(X), Y)) → mark(f(X, f(g(X), Y)))
mark(f(X1, X2)) → active(f(mark(X1), X2))
mark(g(X)) → active(g(mark(X)))
f(mark(X1), X2) → f(X1, X2)
f(X1, mark(X2)) → f(X1, X2)
f(active(X1), X2) → f(X1, X2)
f(X1, active(X2)) → f(X1, X2)
g(mark(X)) → g(X)
g(active(X)) → g(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
G(active(X)) → G(X)
G(mark(X)) → G(X)
The value of delta used in the strict ordering is 1/4.
POL(active(x1)) = 1/2 + (3/2)x_1
POL(mark(x1)) = 9/4 + x_1
POL(G(x1)) = (1/2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
active(f(g(X), Y)) → mark(f(X, f(g(X), Y)))
mark(f(X1, X2)) → active(f(mark(X1), X2))
mark(g(X)) → active(g(mark(X)))
f(mark(X1), X2) → f(X1, X2)
f(X1, mark(X2)) → f(X1, X2)
f(active(X1), X2) → f(X1, X2)
f(X1, active(X2)) → f(X1, X2)
g(mark(X)) → g(X)
g(active(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
F(active(X1), X2) → F(X1, X2)
F(X1, mark(X2)) → F(X1, X2)
F(X1, active(X2)) → F(X1, X2)
F(mark(X1), X2) → F(X1, X2)
active(f(g(X), Y)) → mark(f(X, f(g(X), Y)))
mark(f(X1, X2)) → active(f(mark(X1), X2))
mark(g(X)) → active(g(mark(X)))
f(mark(X1), X2) → f(X1, X2)
f(X1, mark(X2)) → f(X1, X2)
f(active(X1), X2) → f(X1, X2)
f(X1, active(X2)) → f(X1, X2)
g(mark(X)) → g(X)
g(active(X)) → g(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(active(X1), X2) → F(X1, X2)
F(X1, mark(X2)) → F(X1, X2)
F(X1, active(X2)) → F(X1, X2)
F(mark(X1), X2) → F(X1, X2)
The value of delta used in the strict ordering is 7/16.
POL(active(x1)) = 13/4 + (2)x_1
POL(mark(x1)) = 7/4 + x_1
POL(F(x1, x2)) = (1/4)x_1 + (1/2)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
active(f(g(X), Y)) → mark(f(X, f(g(X), Y)))
mark(f(X1, X2)) → active(f(mark(X1), X2))
mark(g(X)) → active(g(mark(X)))
f(mark(X1), X2) → f(X1, X2)
f(X1, mark(X2)) → f(X1, X2)
f(active(X1), X2) → f(X1, X2)
f(X1, active(X2)) → f(X1, X2)
g(mark(X)) → g(X)
g(active(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
ACTIVE(f(g(X), Y)) → MARK(f(X, f(g(X), Y)))
MARK(f(X1, X2)) → MARK(X1)
MARK(g(X)) → ACTIVE(g(mark(X)))
MARK(f(X1, X2)) → ACTIVE(f(mark(X1), X2))
MARK(g(X)) → MARK(X)
active(f(g(X), Y)) → mark(f(X, f(g(X), Y)))
mark(f(X1, X2)) → active(f(mark(X1), X2))
mark(g(X)) → active(g(mark(X)))
f(mark(X1), X2) → f(X1, X2)
f(X1, mark(X2)) → f(X1, X2)
f(active(X1), X2) → f(X1, X2)
f(X1, active(X2)) → f(X1, X2)
g(mark(X)) → g(X)
g(active(X)) → g(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(g(X)) → ACTIVE(g(mark(X)))
Used ordering: Polynomial interpretation [25,35]:
ACTIVE(f(g(X), Y)) → MARK(f(X, f(g(X), Y)))
MARK(f(X1, X2)) → MARK(X1)
MARK(f(X1, X2)) → ACTIVE(f(mark(X1), X2))
MARK(g(X)) → MARK(X)
The value of delta used in the strict ordering is 4.
POL(active(x1)) = 3 + (1/4)x_1
POL(MARK(x1)) = 4
POL(f(x1, x2)) = 4
POL(g(x1)) = 0
POL(mark(x1)) = 4
POL(ACTIVE(x1)) = x_1
f(X1, active(X2)) → f(X1, X2)
f(X1, mark(X2)) → f(X1, X2)
f(mark(X1), X2) → f(X1, X2)
f(active(X1), X2) → f(X1, X2)
g(active(X)) → g(X)
g(mark(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
ACTIVE(f(g(X), Y)) → MARK(f(X, f(g(X), Y)))
MARK(f(X1, X2)) → MARK(X1)
MARK(f(X1, X2)) → ACTIVE(f(mark(X1), X2))
MARK(g(X)) → MARK(X)
active(f(g(X), Y)) → mark(f(X, f(g(X), Y)))
mark(f(X1, X2)) → active(f(mark(X1), X2))
mark(g(X)) → active(g(mark(X)))
f(mark(X1), X2) → f(X1, X2)
f(X1, mark(X2)) → f(X1, X2)
f(active(X1), X2) → f(X1, X2)
f(X1, active(X2)) → f(X1, X2)
g(mark(X)) → g(X)
g(active(X)) → g(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(f(g(X), Y)) → MARK(f(X, f(g(X), Y)))
MARK(g(X)) → MARK(X)
Used ordering: Polynomial interpretation [25,35]:
MARK(f(X1, X2)) → MARK(X1)
MARK(f(X1, X2)) → ACTIVE(f(mark(X1), X2))
The value of delta used in the strict ordering is 13/32.
POL(active(x1)) = x_1
POL(MARK(x1)) = (1/4)x_1
POL(f(x1, x2)) = (2)x_1 + (3/4)x_2
POL(g(x1)) = 13/4 + (4)x_1
POL(mark(x1)) = x_1
POL(ACTIVE(x1)) = (1/4)x_1
mark(g(X)) → active(g(mark(X)))
mark(f(X1, X2)) → active(f(mark(X1), X2))
active(f(g(X), Y)) → mark(f(X, f(g(X), Y)))
f(X1, active(X2)) → f(X1, X2)
f(X1, mark(X2)) → f(X1, X2)
f(mark(X1), X2) → f(X1, X2)
f(active(X1), X2) → f(X1, X2)
g(active(X)) → g(X)
g(mark(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
MARK(f(X1, X2)) → MARK(X1)
MARK(f(X1, X2)) → ACTIVE(f(mark(X1), X2))
active(f(g(X), Y)) → mark(f(X, f(g(X), Y)))
mark(f(X1, X2)) → active(f(mark(X1), X2))
mark(g(X)) → active(g(mark(X)))
f(mark(X1), X2) → f(X1, X2)
f(X1, mark(X2)) → f(X1, X2)
f(active(X1), X2) → f(X1, X2)
f(X1, active(X2)) → f(X1, X2)
g(mark(X)) → g(X)
g(active(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
MARK(f(X1, X2)) → MARK(X1)
active(f(g(X), Y)) → mark(f(X, f(g(X), Y)))
mark(f(X1, X2)) → active(f(mark(X1), X2))
mark(g(X)) → active(g(mark(X)))
f(mark(X1), X2) → f(X1, X2)
f(X1, mark(X2)) → f(X1, X2)
f(active(X1), X2) → f(X1, X2)
f(X1, active(X2)) → f(X1, X2)
g(mark(X)) → g(X)
g(active(X)) → g(X)
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)
The value of delta used in the strict ordering is 1/2.
POL(MARK(x1)) = (2)x_1
POL(f(x1, x2)) = 1/4 + (7/2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
active(f(g(X), Y)) → mark(f(X, f(g(X), Y)))
mark(f(X1, X2)) → active(f(mark(X1), X2))
mark(g(X)) → active(g(mark(X)))
f(mark(X1), X2) → f(X1, X2)
f(X1, mark(X2)) → f(X1, X2)
f(active(X1), X2) → f(X1, X2)
f(X1, active(X2)) → f(X1, X2)
g(mark(X)) → g(X)
g(active(X)) → g(X)