active(f(X)) → mark(g(h(f(X))))
mark(f(X)) → active(f(mark(X)))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
↳ QTRS
↳ DependencyPairsProof
active(f(X)) → mark(g(h(f(X))))
mark(f(X)) → active(f(mark(X)))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
MARK(h(X)) → ACTIVE(h(mark(X)))
F(mark(X)) → F(X)
H(active(X)) → H(X)
ACTIVE(f(X)) → H(f(X))
G(active(X)) → G(X)
G(mark(X)) → G(X)
MARK(f(X)) → ACTIVE(f(mark(X)))
MARK(h(X)) → MARK(X)
ACTIVE(f(X)) → G(h(f(X)))
MARK(f(X)) → F(mark(X))
MARK(g(X)) → ACTIVE(g(X))
ACTIVE(f(X)) → MARK(g(h(f(X))))
H(mark(X)) → H(X)
MARK(h(X)) → H(mark(X))
MARK(f(X)) → MARK(X)
F(active(X)) → F(X)
active(f(X)) → mark(g(h(f(X))))
mark(f(X)) → active(f(mark(X)))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
MARK(h(X)) → ACTIVE(h(mark(X)))
F(mark(X)) → F(X)
H(active(X)) → H(X)
ACTIVE(f(X)) → H(f(X))
G(active(X)) → G(X)
G(mark(X)) → G(X)
MARK(f(X)) → ACTIVE(f(mark(X)))
MARK(h(X)) → MARK(X)
ACTIVE(f(X)) → G(h(f(X)))
MARK(f(X)) → F(mark(X))
MARK(g(X)) → ACTIVE(g(X))
ACTIVE(f(X)) → MARK(g(h(f(X))))
H(mark(X)) → H(X)
MARK(h(X)) → H(mark(X))
MARK(f(X)) → MARK(X)
F(active(X)) → F(X)
active(f(X)) → mark(g(h(f(X))))
mark(f(X)) → active(f(mark(X)))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
H(active(X)) → H(X)
H(mark(X)) → H(X)
active(f(X)) → mark(g(h(f(X))))
mark(f(X)) → active(f(mark(X)))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
H(active(X)) → H(X)
Used ordering: Polynomial interpretation [25,35]:
H(mark(X)) → H(X)
The value of delta used in the strict ordering is 8.
POL(active(x1)) = 4 + (2)x_1
POL(H(x1)) = (2)x_1
POL(mark(x1)) = (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
H(mark(X)) → H(X)
active(f(X)) → mark(g(h(f(X))))
mark(f(X)) → active(f(mark(X)))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
H(mark(X)) → H(X)
The value of delta used in the strict ordering is 8.
POL(H(x1)) = (2)x_1
POL(mark(x1)) = 4 + (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
↳ QDP
active(f(X)) → mark(g(h(f(X))))
mark(f(X)) → active(f(mark(X)))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
G(active(X)) → G(X)
G(mark(X)) → G(X)
active(f(X)) → mark(g(h(f(X))))
mark(f(X)) → active(f(mark(X)))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(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 4.
POL(active(x1)) = 4 + (4)x_1
POL(mark(x1)) = 1 + x_1
POL(G(x1)) = (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
active(f(X)) → mark(g(h(f(X))))
mark(f(X)) → active(f(mark(X)))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
F(mark(X)) → F(X)
F(active(X)) → F(X)
active(f(X)) → mark(g(h(f(X))))
mark(f(X)) → active(f(mark(X)))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(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)
F(active(X)) → F(X)
The value of delta used in the strict ordering is 4.
POL(active(x1)) = 4 + (4)x_1
POL(mark(x1)) = 1 + x_1
POL(F(x1)) = (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
active(f(X)) → mark(g(h(f(X))))
mark(f(X)) → active(f(mark(X)))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
MARK(h(X)) → ACTIVE(h(mark(X)))
MARK(h(X)) → MARK(X)
MARK(g(X)) → ACTIVE(g(X))
ACTIVE(f(X)) → MARK(g(h(f(X))))
MARK(f(X)) → MARK(X)
MARK(f(X)) → ACTIVE(f(mark(X)))
active(f(X)) → mark(g(h(f(X))))
mark(f(X)) → active(f(mark(X)))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(h(X)) → ACTIVE(h(mark(X)))
MARK(h(X)) → MARK(X)
Used ordering: Polynomial interpretation [25,35]:
MARK(g(X)) → ACTIVE(g(X))
ACTIVE(f(X)) → MARK(g(h(f(X))))
MARK(f(X)) → MARK(X)
MARK(f(X)) → ACTIVE(f(mark(X)))
The value of delta used in the strict ordering is 1.
POL(active(x1)) = 0
POL(MARK(x1)) = (1/2)x_1
POL(f(x1)) = (4)x_1
POL(g(x1)) = 0
POL(h(x1)) = 2 + x_1
POL(mark(x1)) = 0
POL(ACTIVE(x1)) = 0
g(active(X)) → g(X)
g(mark(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
MARK(g(X)) → ACTIVE(g(X))
ACTIVE(f(X)) → MARK(g(h(f(X))))
MARK(f(X)) → ACTIVE(f(mark(X)))
MARK(f(X)) → MARK(X)
active(f(X)) → mark(g(h(f(X))))
mark(f(X)) → active(f(mark(X)))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(f(X)) → ACTIVE(f(mark(X)))
MARK(f(X)) → MARK(X)
Used ordering: Polynomial interpretation [25,35]:
MARK(g(X)) → ACTIVE(g(X))
ACTIVE(f(X)) → MARK(g(h(f(X))))
The value of delta used in the strict ordering is 1.
POL(active(x1)) = 0
POL(MARK(x1)) = (4)x_1
POL(f(x1)) = 1/4 + (2)x_1
POL(g(x1)) = 0
POL(h(x1)) = 0
POL(mark(x1)) = 0
POL(ACTIVE(x1)) = 0
g(active(X)) → g(X)
g(mark(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
MARK(g(X)) → ACTIVE(g(X))
ACTIVE(f(X)) → MARK(g(h(f(X))))
active(f(X)) → mark(g(h(f(X))))
mark(f(X)) → active(f(mark(X)))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(f(X)) → MARK(g(h(f(X))))
Used ordering: Polynomial interpretation [25,35]:
MARK(g(X)) → ACTIVE(g(X))
The value of delta used in the strict ordering is 1/2.
POL(active(x1)) = 1/2 + (4)x_1
POL(MARK(x1)) = 0
POL(f(x1)) = 1/2 + x_1
POL(g(x1)) = 0
POL(h(x1)) = x_1
POL(mark(x1)) = (2)x_1
POL(ACTIVE(x1)) = x_1
g(active(X)) → g(X)
g(mark(X)) → g(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
MARK(g(X)) → ACTIVE(g(X))
active(f(X)) → mark(g(h(f(X))))
mark(f(X)) → active(f(mark(X)))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)