active(f(f(a))) → mark(f(g(f(a))))
mark(f(X)) → active(f(X))
mark(a) → active(a)
mark(g(X)) → active(g(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
active(f(f(a))) → mark(f(g(f(a))))
mark(f(X)) → active(f(X))
mark(a) → active(a)
mark(g(X)) → active(g(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
F(mark(X)) → F(X)
MARK(a) → ACTIVE(a)
MARK(f(X)) → ACTIVE(f(X))
ACTIVE(f(f(a))) → G(f(a))
ACTIVE(f(f(a))) → MARK(f(g(f(a))))
MARK(g(X)) → ACTIVE(g(mark(X)))
G(active(X)) → G(X)
G(mark(X)) → G(X)
ACTIVE(f(f(a))) → F(g(f(a)))
F(active(X)) → F(X)
MARK(g(X)) → MARK(X)
MARK(g(X)) → G(mark(X))
active(f(f(a))) → mark(f(g(f(a))))
mark(f(X)) → active(f(X))
mark(a) → active(a)
mark(g(X)) → active(g(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
F(mark(X)) → F(X)
MARK(a) → ACTIVE(a)
MARK(f(X)) → ACTIVE(f(X))
ACTIVE(f(f(a))) → G(f(a))
ACTIVE(f(f(a))) → MARK(f(g(f(a))))
MARK(g(X)) → ACTIVE(g(mark(X)))
G(active(X)) → G(X)
G(mark(X)) → G(X)
ACTIVE(f(f(a))) → F(g(f(a)))
F(active(X)) → F(X)
MARK(g(X)) → MARK(X)
MARK(g(X)) → G(mark(X))
active(f(f(a))) → mark(f(g(f(a))))
mark(f(X)) → active(f(X))
mark(a) → active(a)
mark(g(X)) → active(g(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
G(active(X)) → G(X)
G(mark(X)) → G(X)
active(f(f(a))) → mark(f(g(f(a))))
mark(f(X)) → active(f(X))
mark(a) → active(a)
mark(g(X)) → active(g(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
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(mark(X)) → G(X)
Used ordering: Polynomial interpretation [25,35]:
G(active(X)) → G(X)
The value of delta used in the strict ordering is 8.
POL(active(x1)) = (2)x_1
POL(mark(x1)) = 4 + (2)x_1
POL(G(x1)) = (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
G(active(X)) → G(X)
active(f(f(a))) → mark(f(g(f(a))))
mark(f(X)) → active(f(X))
mark(a) → active(a)
mark(g(X)) → active(g(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
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)
The value of delta used in the strict ordering is 8.
POL(active(x1)) = 4 + (4)x_1
POL(G(x1)) = (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
↳ QDP
active(f(f(a))) → mark(f(g(f(a))))
mark(f(X)) → active(f(X))
mark(a) → active(a)
mark(g(X)) → active(g(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
F(mark(X)) → F(X)
F(active(X)) → F(X)
active(f(f(a))) → mark(f(g(f(a))))
mark(f(X)) → active(f(X))
mark(a) → active(a)
mark(g(X)) → active(g(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
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(X)) → F(X)
Used ordering: Polynomial interpretation [25,35]:
F(mark(X)) → F(X)
The value of delta used in the strict ordering is 8.
POL(active(x1)) = 4 + (2)x_1
POL(mark(x1)) = (2)x_1
POL(F(x1)) = (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
F(mark(X)) → F(X)
active(f(f(a))) → mark(f(g(f(a))))
mark(f(X)) → active(f(X))
mark(a) → active(a)
mark(g(X)) → active(g(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
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(mark(X)) → F(X)
The value of delta used in the strict ordering is 8.
POL(mark(x1)) = 4 + (4)x_1
POL(F(x1)) = (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
active(f(f(a))) → mark(f(g(f(a))))
mark(f(X)) → active(f(X))
mark(a) → active(a)
mark(g(X)) → active(g(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
MARK(f(X)) → ACTIVE(f(X))
ACTIVE(f(f(a))) → MARK(f(g(f(a))))
active(f(f(a))) → mark(f(g(f(a))))
mark(f(X)) → active(f(X))
mark(a) → active(a)
mark(g(X)) → active(g(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
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(f(a))) → MARK(f(g(f(a))))
Used ordering: Polynomial interpretation [25,35]:
MARK(f(X)) → ACTIVE(f(X))
The value of delta used in the strict ordering is 2.
POL(active(x1)) = (4)x_1
POL(MARK(x1)) = (1/4)x_1
POL(f(x1)) = (4)x_1
POL(a) = 1/2
POL(g(x1)) = 0
POL(mark(x1)) = 1 + (2)x_1
POL(ACTIVE(x1)) = (1/4)x_1
f(mark(X)) → f(X)
f(active(X)) → f(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
MARK(f(X)) → ACTIVE(f(X))
active(f(f(a))) → mark(f(g(f(a))))
mark(f(X)) → active(f(X))
mark(a) → active(a)
mark(g(X)) → active(g(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
MARK(g(X)) → MARK(X)
active(f(f(a))) → mark(f(g(f(a))))
mark(f(X)) → active(f(X))
mark(a) → active(a)
mark(g(X)) → active(g(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
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)) → MARK(X)
The value of delta used in the strict ordering is 8.
POL(MARK(x1)) = (2)x_1
POL(g(x1)) = 4 + (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
active(f(f(a))) → mark(f(g(f(a))))
mark(f(X)) → active(f(X))
mark(a) → active(a)
mark(g(X)) → active(g(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)