active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
↳ QTRS
↳ DependencyPairsProof
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
H(active(X)) → H(X)
ACTIVE(f(f(X))) → C(f(g(f(X))))
C(active(X)) → C(X)
MARK(c(X)) → ACTIVE(c(X))
ACTIVE(h(X)) → D(X)
C(mark(X)) → C(X)
ACTIVE(h(X)) → C(d(X))
D(active(X)) → D(X)
MARK(f(X)) → MARK(X)
F(active(X)) → F(X)
MARK(h(X)) → ACTIVE(h(mark(X)))
F(mark(X)) → F(X)
ACTIVE(c(X)) → D(X)
ACTIVE(c(X)) → MARK(d(X))
ACTIVE(f(f(X))) → G(f(X))
ACTIVE(f(f(X))) → MARK(c(f(g(f(X)))))
G(active(X)) → G(X)
D(mark(X)) → D(X)
G(mark(X)) → G(X)
MARK(f(X)) → ACTIVE(f(mark(X)))
ACTIVE(h(X)) → MARK(c(d(X)))
MARK(h(X)) → MARK(X)
MARK(d(X)) → ACTIVE(d(X))
MARK(f(X)) → F(mark(X))
MARK(g(X)) → ACTIVE(g(X))
H(mark(X)) → H(X)
ACTIVE(f(f(X))) → F(g(f(X)))
MARK(h(X)) → H(mark(X))
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
H(active(X)) → H(X)
ACTIVE(f(f(X))) → C(f(g(f(X))))
C(active(X)) → C(X)
MARK(c(X)) → ACTIVE(c(X))
ACTIVE(h(X)) → D(X)
C(mark(X)) → C(X)
ACTIVE(h(X)) → C(d(X))
D(active(X)) → D(X)
MARK(f(X)) → MARK(X)
F(active(X)) → F(X)
MARK(h(X)) → ACTIVE(h(mark(X)))
F(mark(X)) → F(X)
ACTIVE(c(X)) → D(X)
ACTIVE(c(X)) → MARK(d(X))
ACTIVE(f(f(X))) → G(f(X))
ACTIVE(f(f(X))) → MARK(c(f(g(f(X)))))
G(active(X)) → G(X)
D(mark(X)) → D(X)
G(mark(X)) → G(X)
MARK(f(X)) → ACTIVE(f(mark(X)))
ACTIVE(h(X)) → MARK(c(d(X)))
MARK(h(X)) → MARK(X)
MARK(d(X)) → ACTIVE(d(X))
MARK(f(X)) → F(mark(X))
MARK(g(X)) → ACTIVE(g(X))
H(mark(X)) → H(X)
ACTIVE(f(f(X))) → F(g(f(X)))
MARK(h(X)) → H(mark(X))
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
H(active(X)) → H(X)
H(mark(X)) → H(X)
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(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)
H(mark(X)) → H(X)
The value of delta used in the strict ordering is 16.
POL(active(x1)) = 4 + x_1
POL(H(x1)) = (4)x_1
POL(mark(x1)) = 4 + (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
D(mark(X)) → D(X)
D(active(X)) → D(X)
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(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.
D(mark(X)) → D(X)
D(active(X)) → D(X)
The value of delta used in the strict ordering is 16.
POL(active(x1)) = 4 + (4)x_1
POL(D(x1)) = (4)x_1
POL(mark(x1)) = 4 + x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
G(active(X)) → G(X)
G(mark(X)) → G(X)
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(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 16.
POL(active(x1)) = 4 + (4)x_1
POL(mark(x1)) = 4 + x_1
POL(G(x1)) = (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
↳ QDP
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
C(active(X)) → C(X)
C(mark(X)) → C(X)
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(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.
C(active(X)) → C(X)
C(mark(X)) → C(X)
The value of delta used in the strict ordering is 16.
POL(C(x1)) = (4)x_1
POL(active(x1)) = 4 + x_1
POL(mark(x1)) = 4 + (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
F(mark(X)) → F(X)
F(active(X)) → F(X)
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(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 16.
POL(active(x1)) = 4 + x_1
POL(mark(x1)) = 4 + (4)x_1
POL(F(x1)) = (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
MARK(h(X)) → ACTIVE(h(mark(X)))
ACTIVE(c(X)) → MARK(d(X))
ACTIVE(h(X)) → MARK(c(d(X)))
MARK(h(X)) → MARK(X)
MARK(d(X)) → ACTIVE(d(X))
MARK(g(X)) → ACTIVE(g(X))
ACTIVE(f(f(X))) → MARK(c(f(g(f(X)))))
MARK(c(X)) → ACTIVE(c(X))
MARK(f(X)) → MARK(X)
MARK(f(X)) → ACTIVE(f(mark(X)))
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(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(h(X)) → MARK(c(d(X)))
MARK(h(X)) → MARK(X)
MARK(d(X)) → ACTIVE(d(X))
MARK(g(X)) → ACTIVE(g(X))
MARK(c(X)) → ACTIVE(c(X))
MARK(f(X)) → MARK(X)
Used ordering: Polynomial interpretation [25,35]:
MARK(h(X)) → ACTIVE(h(mark(X)))
ACTIVE(c(X)) → MARK(d(X))
ACTIVE(f(f(X))) → MARK(c(f(g(f(X)))))
MARK(f(X)) → ACTIVE(f(mark(X)))
The value of delta used in the strict ordering is 1.
POL(active(x1)) = x_1
POL(MARK(x1)) = 1 + x_1
POL(c(x1)) = 1
POL(f(x1)) = 1 + x_1
POL(g(x1)) = 1
POL(h(x1)) = 3 + x_1
POL(mark(x1)) = 1 + x_1
POL(d(x1)) = 0
POL(ACTIVE(x1)) = x_1
active(h(X)) → mark(c(d(X)))
mark(g(X)) → active(g(X))
active(c(X)) → mark(d(X))
mark(h(X)) → active(h(mark(X)))
mark(d(X)) → active(d(X))
mark(c(X)) → active(c(X))
active(f(f(X))) → mark(c(f(g(f(X)))))
mark(f(X)) → active(f(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(active(X)) → g(X)
g(mark(X)) → g(X)
c(active(X)) → c(X)
c(mark(X)) → c(X)
h(active(X)) → h(X)
h(mark(X)) → h(X)
d(active(X)) → d(X)
d(mark(X)) → d(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
MARK(h(X)) → ACTIVE(h(mark(X)))
ACTIVE(c(X)) → MARK(d(X))
ACTIVE(f(f(X))) → MARK(c(f(g(f(X)))))
MARK(f(X)) → ACTIVE(f(mark(X)))
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(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)))
ACTIVE(c(X)) → MARK(d(X))
MARK(f(X)) → ACTIVE(f(mark(X)))
Used ordering: Polynomial interpretation [25,35]:
ACTIVE(f(f(X))) → MARK(c(f(g(f(X)))))
The value of delta used in the strict ordering is 1.
POL(active(x1)) = x_1
POL(MARK(x1)) = 1 + (4)x_1
POL(c(x1)) = 1
POL(f(x1)) = 1 + (3)x_1
POL(g(x1)) = 0
POL(h(x1)) = 1 + (3)x_1
POL(mark(x1)) = x_1
POL(d(x1)) = 0
POL(ACTIVE(x1)) = 1 + x_1
active(h(X)) → mark(c(d(X)))
mark(g(X)) → active(g(X))
active(c(X)) → mark(d(X))
mark(h(X)) → active(h(mark(X)))
mark(d(X)) → active(d(X))
mark(c(X)) → active(c(X))
active(f(f(X))) → mark(c(f(g(f(X)))))
mark(f(X)) → active(f(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(active(X)) → g(X)
g(mark(X)) → g(X)
c(active(X)) → c(X)
c(mark(X)) → c(X)
h(active(X)) → h(X)
h(mark(X)) → h(X)
d(active(X)) → d(X)
d(mark(X)) → d(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
ACTIVE(f(f(X))) → MARK(c(f(g(f(X)))))
active(f(f(X))) → mark(c(f(g(f(X)))))
active(c(X)) → mark(d(X))
active(h(X)) → mark(c(d(X)))
mark(f(X)) → active(f(mark(X)))
mark(c(X)) → active(c(X))
mark(g(X)) → active(g(X))
mark(d(X)) → active(d(X))
mark(h(X)) → active(h(mark(X)))
f(mark(X)) → f(X)
f(active(X)) → f(X)
c(mark(X)) → c(X)
c(active(X)) → c(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
d(mark(X)) → d(X)
d(active(X)) → d(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)