a(b(x1)) → b(d(x1))
a(c(x1)) → d(d(d(x1)))
b(d(x1)) → a(c(b(x1)))
c(f(x1)) → d(d(c(x1)))
d(d(x1)) → f(x1)
f(f(x1)) → a(x1)
↳ QTRS
↳ DependencyPairsProof
a(b(x1)) → b(d(x1))
a(c(x1)) → d(d(d(x1)))
b(d(x1)) → a(c(b(x1)))
c(f(x1)) → d(d(c(x1)))
d(d(x1)) → f(x1)
f(f(x1)) → a(x1)
A(c(x1)) → D(d(d(x1)))
F(f(x1)) → A(x1)
A(b(x1)) → B(d(x1))
C(f(x1)) → C(x1)
A(b(x1)) → D(x1)
B(d(x1)) → A(c(b(x1)))
A(c(x1)) → D(x1)
B(d(x1)) → C(b(x1))
C(f(x1)) → D(d(c(x1)))
A(c(x1)) → D(d(x1))
D(d(x1)) → F(x1)
B(d(x1)) → B(x1)
C(f(x1)) → D(c(x1))
a(b(x1)) → b(d(x1))
a(c(x1)) → d(d(d(x1)))
b(d(x1)) → a(c(b(x1)))
c(f(x1)) → d(d(c(x1)))
d(d(x1)) → f(x1)
f(f(x1)) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
A(c(x1)) → D(d(d(x1)))
F(f(x1)) → A(x1)
A(b(x1)) → B(d(x1))
C(f(x1)) → C(x1)
A(b(x1)) → D(x1)
B(d(x1)) → A(c(b(x1)))
A(c(x1)) → D(x1)
B(d(x1)) → C(b(x1))
C(f(x1)) → D(d(c(x1)))
A(c(x1)) → D(d(x1))
D(d(x1)) → F(x1)
B(d(x1)) → B(x1)
C(f(x1)) → D(c(x1))
a(b(x1)) → b(d(x1))
a(c(x1)) → d(d(d(x1)))
b(d(x1)) → a(c(b(x1)))
c(f(x1)) → d(d(c(x1)))
d(d(x1)) → f(x1)
f(f(x1)) → a(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(b(x1)) → D(x1)
Used ordering: Polynomial interpretation [25,35]:
A(c(x1)) → D(d(d(x1)))
F(f(x1)) → A(x1)
A(b(x1)) → B(d(x1))
C(f(x1)) → C(x1)
B(d(x1)) → A(c(b(x1)))
A(c(x1)) → D(x1)
B(d(x1)) → C(b(x1))
C(f(x1)) → D(d(c(x1)))
A(c(x1)) → D(d(x1))
D(d(x1)) → F(x1)
B(d(x1)) → B(x1)
C(f(x1)) → D(c(x1))
The value of delta used in the strict ordering is 1/4.
POL(C(x1)) = x_1
POL(c(x1)) = x_1
POL(f(x1)) = x_1
POL(D(x1)) = x_1
POL(B(x1)) = 1/4 + (4)x_1
POL(a(x1)) = x_1
POL(A(x1)) = x_1
POL(d(x1)) = x_1
POL(b(x1)) = 1/4 + (4)x_1
POL(F(x1)) = x_1
c(f(x1)) → d(d(c(x1)))
a(c(x1)) → d(d(d(x1)))
d(d(x1)) → f(x1)
b(d(x1)) → a(c(b(x1)))
a(b(x1)) → b(d(x1))
f(f(x1)) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
B(d(x1)) → C(b(x1))
C(f(x1)) → D(d(c(x1)))
A(c(x1)) → D(d(x1))
F(f(x1)) → A(x1)
A(c(x1)) → D(d(d(x1)))
A(b(x1)) → B(d(x1))
D(d(x1)) → F(x1)
C(f(x1)) → C(x1)
B(d(x1)) → B(x1)
B(d(x1)) → A(c(b(x1)))
A(c(x1)) → D(x1)
C(f(x1)) → D(c(x1))
a(b(x1)) → b(d(x1))
a(c(x1)) → d(d(d(x1)))
b(d(x1)) → a(c(b(x1)))
c(f(x1)) → d(d(c(x1)))
d(d(x1)) → f(x1)
f(f(x1)) → a(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(f(x1)) → D(d(c(x1)))
A(c(x1)) → D(d(x1))
A(c(x1)) → D(d(d(x1)))
C(f(x1)) → C(x1)
B(d(x1)) → B(x1)
A(c(x1)) → D(x1)
C(f(x1)) → D(c(x1))
Used ordering: Polynomial interpretation [25,35]:
B(d(x1)) → C(b(x1))
F(f(x1)) → A(x1)
A(b(x1)) → B(d(x1))
D(d(x1)) → F(x1)
B(d(x1)) → A(c(b(x1)))
The value of delta used in the strict ordering is 1/4.
POL(C(x1)) = 15/4 + x_1
POL(f(x1)) = 1/2 + x_1
POL(c(x1)) = x_1
POL(B(x1)) = 3 + (3)x_1
POL(D(x1)) = 3 + x_1
POL(a(x1)) = 3/4 + x_1
POL(A(x1)) = 15/4 + x_1
POL(d(x1)) = 1/4 + x_1
POL(b(x1)) = (3)x_1
POL(F(x1)) = 13/4 + x_1
c(f(x1)) → d(d(c(x1)))
a(c(x1)) → d(d(d(x1)))
d(d(x1)) → f(x1)
b(d(x1)) → a(c(b(x1)))
a(b(x1)) → b(d(x1))
f(f(x1)) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
B(d(x1)) → C(b(x1))
F(f(x1)) → A(x1)
A(b(x1)) → B(d(x1))
D(d(x1)) → F(x1)
B(d(x1)) → A(c(b(x1)))
a(b(x1)) → b(d(x1))
a(c(x1)) → d(d(d(x1)))
b(d(x1)) → a(c(b(x1)))
c(f(x1)) → d(d(c(x1)))
d(d(x1)) → f(x1)
f(f(x1)) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
A(b(x1)) → B(d(x1))
B(d(x1)) → A(c(b(x1)))
a(b(x1)) → b(d(x1))
a(c(x1)) → d(d(d(x1)))
b(d(x1)) → a(c(b(x1)))
c(f(x1)) → d(d(c(x1)))
d(d(x1)) → f(x1)
f(f(x1)) → a(x1)