f(f(X)) → c(n__f(n__g(n__f(X))))
c(X) → d(activate(X))
h(X) → c(n__d(X))
f(X) → n__f(X)
g(X) → n__g(X)
d(X) → n__d(X)
activate(n__f(X)) → f(activate(X))
activate(n__g(X)) → g(X)
activate(n__d(X)) → d(X)
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
f(f(X)) → c(n__f(n__g(n__f(X))))
c(X) → d(activate(X))
h(X) → c(n__d(X))
f(X) → n__f(X)
g(X) → n__g(X)
d(X) → n__d(X)
activate(n__f(X)) → f(activate(X))
activate(n__g(X)) → g(X)
activate(n__d(X)) → d(X)
activate(X) → X
ACTIVATE(n__d(X)) → D(X)
ACTIVATE(n__f(X)) → F(activate(X))
ACTIVATE(n__f(X)) → ACTIVATE(X)
ACTIVATE(n__g(X)) → G(X)
F(f(X)) → C(n__f(n__g(n__f(X))))
H(X) → C(n__d(X))
C(X) → ACTIVATE(X)
C(X) → D(activate(X))
f(f(X)) → c(n__f(n__g(n__f(X))))
c(X) → d(activate(X))
h(X) → c(n__d(X))
f(X) → n__f(X)
g(X) → n__g(X)
d(X) → n__d(X)
activate(n__f(X)) → f(activate(X))
activate(n__g(X)) → g(X)
activate(n__d(X)) → d(X)
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
ACTIVATE(n__d(X)) → D(X)
ACTIVATE(n__f(X)) → F(activate(X))
ACTIVATE(n__f(X)) → ACTIVATE(X)
ACTIVATE(n__g(X)) → G(X)
F(f(X)) → C(n__f(n__g(n__f(X))))
H(X) → C(n__d(X))
C(X) → ACTIVATE(X)
C(X) → D(activate(X))
f(f(X)) → c(n__f(n__g(n__f(X))))
c(X) → d(activate(X))
h(X) → c(n__d(X))
f(X) → n__f(X)
g(X) → n__g(X)
d(X) → n__d(X)
activate(n__f(X)) → f(activate(X))
activate(n__g(X)) → g(X)
activate(n__d(X)) → d(X)
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
ACTIVATE(n__f(X)) → F(activate(X))
ACTIVATE(n__f(X)) → ACTIVATE(X)
F(f(X)) → C(n__f(n__g(n__f(X))))
C(X) → ACTIVATE(X)
f(f(X)) → c(n__f(n__g(n__f(X))))
c(X) → d(activate(X))
h(X) → c(n__d(X))
f(X) → n__f(X)
g(X) → n__g(X)
d(X) → n__d(X)
activate(n__f(X)) → f(activate(X))
activate(n__g(X)) → g(X)
activate(n__d(X)) → d(X)
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVATE(n__f(X)) → ACTIVATE(X)
Used ordering: Polynomial interpretation [25,35]:
ACTIVATE(n__f(X)) → F(activate(X))
F(f(X)) → C(n__f(n__g(n__f(X))))
C(X) → ACTIVATE(X)
The value of delta used in the strict ordering is 1.
POL(C(x1)) = x_1
POL(f(x1)) = (2)x_1
POL(c(x1)) = 1
POL(n__g(x1)) = 0
POL(g(x1)) = 1 + (3)x_1
POL(n__f(x1)) = 1 + (4)x_1
POL(activate(x1)) = 0
POL(d(x1)) = 3 + (3)x_1
POL(n__d(x1)) = 3
POL(ACTIVATE(x1)) = x_1
POL(F(x1)) = 1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
ACTIVATE(n__f(X)) → F(activate(X))
F(f(X)) → C(n__f(n__g(n__f(X))))
C(X) → ACTIVATE(X)
f(f(X)) → c(n__f(n__g(n__f(X))))
c(X) → d(activate(X))
h(X) → c(n__d(X))
f(X) → n__f(X)
g(X) → n__g(X)
d(X) → n__d(X)
activate(n__f(X)) → f(activate(X))
activate(n__g(X)) → g(X)
activate(n__d(X)) → d(X)
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVATE(n__f(X)) → F(activate(X))
F(f(X)) → C(n__f(n__g(n__f(X))))
Used ordering: Polynomial interpretation [25,35]:
C(X) → ACTIVATE(X)
The value of delta used in the strict ordering is 1.
POL(C(x1)) = x_1
POL(f(x1)) = 1 + (2)x_1
POL(c(x1)) = 0
POL(n__g(x1)) = 0
POL(g(x1)) = 0
POL(n__f(x1)) = 1 + (2)x_1
POL(activate(x1)) = x_1
POL(d(x1)) = 0
POL(n__d(x1)) = 0
POL(ACTIVATE(x1)) = x_1
POL(F(x1)) = (2)x_1
activate(n__d(X)) → d(X)
activate(n__g(X)) → g(X)
activate(X) → X
f(f(X)) → c(n__f(n__g(n__f(X))))
c(X) → d(activate(X))
f(X) → n__f(X)
g(X) → n__g(X)
d(X) → n__d(X)
activate(n__f(X)) → f(activate(X))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
C(X) → ACTIVATE(X)
f(f(X)) → c(n__f(n__g(n__f(X))))
c(X) → d(activate(X))
h(X) → c(n__d(X))
f(X) → n__f(X)
g(X) → n__g(X)
d(X) → n__d(X)
activate(n__f(X)) → f(activate(X))
activate(n__g(X)) → g(X)
activate(n__d(X)) → d(X)
activate(X) → X