f(f(x1)) → b(b(b(x1)))
a(f(x1)) → f(a(a(x1)))
b(b(x1)) → c(c(a(c(x1))))
d(b(x1)) → d(a(b(x1)))
c(c(x1)) → d(d(d(x1)))
b(d(x1)) → d(b(x1))
c(d(d(x1))) → f(x1)
↳ QTRS
↳ DependencyPairsProof
f(f(x1)) → b(b(b(x1)))
a(f(x1)) → f(a(a(x1)))
b(b(x1)) → c(c(a(c(x1))))
d(b(x1)) → d(a(b(x1)))
c(c(x1)) → d(d(d(x1)))
b(d(x1)) → d(b(x1))
c(d(d(x1))) → f(x1)
A(f(x1)) → A(x1)
B(d(x1)) → D(b(x1))
C(c(x1)) → D(d(d(x1)))
C(d(d(x1))) → F(x1)
C(c(x1)) → D(x1)
A(f(x1)) → A(a(x1))
A(f(x1)) → F(a(a(x1)))
C(c(x1)) → D(d(x1))
D(b(x1)) → D(a(b(x1)))
F(f(x1)) → B(b(x1))
F(f(x1)) → B(x1)
B(b(x1)) → C(x1)
B(b(x1)) → C(a(c(x1)))
B(d(x1)) → B(x1)
F(f(x1)) → B(b(b(x1)))
B(b(x1)) → C(c(a(c(x1))))
B(b(x1)) → A(c(x1))
D(b(x1)) → A(b(x1))
f(f(x1)) → b(b(b(x1)))
a(f(x1)) → f(a(a(x1)))
b(b(x1)) → c(c(a(c(x1))))
d(b(x1)) → d(a(b(x1)))
c(c(x1)) → d(d(d(x1)))
b(d(x1)) → d(b(x1))
c(d(d(x1))) → f(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
A(f(x1)) → A(x1)
B(d(x1)) → D(b(x1))
C(c(x1)) → D(d(d(x1)))
C(d(d(x1))) → F(x1)
C(c(x1)) → D(x1)
A(f(x1)) → A(a(x1))
A(f(x1)) → F(a(a(x1)))
C(c(x1)) → D(d(x1))
D(b(x1)) → D(a(b(x1)))
F(f(x1)) → B(b(x1))
F(f(x1)) → B(x1)
B(b(x1)) → C(x1)
B(b(x1)) → C(a(c(x1)))
B(d(x1)) → B(x1)
F(f(x1)) → B(b(b(x1)))
B(b(x1)) → C(c(a(c(x1))))
B(b(x1)) → A(c(x1))
D(b(x1)) → A(b(x1))
f(f(x1)) → b(b(b(x1)))
a(f(x1)) → f(a(a(x1)))
b(b(x1)) → c(c(a(c(x1))))
d(b(x1)) → d(a(b(x1)))
c(c(x1)) → d(d(d(x1)))
b(d(x1)) → d(b(x1))
c(d(d(x1))) → f(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(f(x1)) → A(x1)
B(d(x1)) → D(b(x1))
C(c(x1)) → D(x1)
A(f(x1)) → A(a(x1))
A(f(x1)) → F(a(a(x1)))
C(c(x1)) → D(d(x1))
F(f(x1)) → B(b(x1))
F(f(x1)) → B(x1)
B(b(x1)) → C(x1)
B(b(x1)) → C(a(c(x1)))
B(d(x1)) → B(x1)
B(b(x1)) → C(c(a(c(x1))))
B(b(x1)) → A(c(x1))
D(b(x1)) → A(b(x1))
Used ordering: Polynomial interpretation [25,35]:
C(c(x1)) → D(d(d(x1)))
C(d(d(x1))) → F(x1)
D(b(x1)) → D(a(b(x1)))
F(f(x1)) → B(b(b(x1)))
The value of delta used in the strict ordering is 1/8.
POL(C(x1)) = 2 + (1/2)x_1
POL(f(x1)) = 7/2 + x_1
POL(c(x1)) = 3/2 + x_1
POL(B(x1)) = 5/2 + (1/2)x_1
POL(D(x1)) = 7/4 + (1/2)x_1
POL(a(x1)) = x_1
POL(A(x1)) = 3/2 + (1/2)x_1
POL(d(x1)) = 1 + x_1
POL(b(x1)) = 9/4 + x_1
POL(F(x1)) = 3 + (1/2)x_1
b(b(x1)) → c(c(a(c(x1))))
c(d(d(x1))) → f(x1)
f(f(x1)) → b(b(b(x1)))
a(f(x1)) → f(a(a(x1)))
c(c(x1)) → d(d(d(x1)))
d(b(x1)) → d(a(b(x1)))
b(d(x1)) → d(b(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
C(c(x1)) → D(d(d(x1)))
C(d(d(x1))) → F(x1)
D(b(x1)) → D(a(b(x1)))
F(f(x1)) → B(b(b(x1)))
f(f(x1)) → b(b(b(x1)))
a(f(x1)) → f(a(a(x1)))
b(b(x1)) → c(c(a(c(x1))))
d(b(x1)) → d(a(b(x1)))
c(c(x1)) → d(d(d(x1)))
b(d(x1)) → d(b(x1))
c(d(d(x1))) → f(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
D(b(x1)) → D(a(b(x1)))
f(f(x1)) → b(b(b(x1)))
a(f(x1)) → f(a(a(x1)))
b(b(x1)) → c(c(a(c(x1))))
d(b(x1)) → d(a(b(x1)))
c(c(x1)) → d(d(d(x1)))
b(d(x1)) → d(b(x1))
c(d(d(x1))) → f(x1)