Termination w.r.t. Q proof of /tmp/tmpKQ967U/z104.srs

Termination w.r.t. Q of the following Term Rewriting System could not be shown:

Q restricted rewrite system:
The TRS R consists of the following rules:

c(c(c(a(x1)))) → d(d(x1))
d(b(x1)) → c(c(x1))
c(x1) → a(a(a(a(x1))))
d(x1) → b(b(b(b(x1))))
b(d(x1)) → c(c(x1))
a(c(c(c(x1)))) → d(d(x1))

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

Q restricted rewrite system:
The TRS R consists of the following rules:

c(c(c(a(x1)))) → d(d(x1))
d(b(x1)) → c(c(x1))
c(x1) → a(a(a(a(x1))))
d(x1) → b(b(b(b(x1))))
b(d(x1)) → c(c(x1))
a(c(c(c(x1)))) → d(d(x1))

Q is empty.

Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

B(d(x1)) → C(x1)
C(c(c(a(x1)))) → D(x1)
D(x1) → B(x1)
D(x1) → B(b(b(b(x1))))
A(c(c(c(x1)))) → D(x1)
D(b(x1)) → C(c(x1))
D(x1) → B(b(x1))
C(c(c(a(x1)))) → D(d(x1))
D(x1) → B(b(b(x1)))
B(d(x1)) → C(c(x1))
C(x1) → A(x1)
C(x1) → A(a(x1))
C(x1) → A(a(a(a(x1))))
C(x1) → A(a(a(x1)))
A(c(c(c(x1)))) → D(d(x1))
D(b(x1)) → C(x1)

The TRS R consists of the following rules:

c(c(c(a(x1)))) → d(d(x1))
d(b(x1)) → c(c(x1))
c(x1) → a(a(a(a(x1))))
d(x1) → b(b(b(b(x1))))
b(d(x1)) → c(c(x1))
a(c(c(c(x1)))) → d(d(x1))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B(d(x1)) → C(x1)
C(c(c(a(x1)))) → D(x1)
D(x1) → B(x1)
D(x1) → B(b(b(b(x1))))
A(c(c(c(x1)))) → D(x1)
D(b(x1)) → C(c(x1))
D(x1) → B(b(x1))
C(c(c(a(x1)))) → D(d(x1))
D(x1) → B(b(b(x1)))
B(d(x1)) → C(c(x1))
C(x1) → A(x1)
C(x1) → A(a(x1))
C(x1) → A(a(a(a(x1))))
C(x1) → A(a(a(x1)))
A(c(c(c(x1)))) → D(d(x1))
D(b(x1)) → C(x1)

The TRS R consists of the following rules:

c(c(c(a(x1)))) → d(d(x1))
d(b(x1)) → c(c(x1))
c(x1) → a(a(a(a(x1))))
d(x1) → b(b(b(b(x1))))
b(d(x1)) → c(c(x1))
a(c(c(c(x1)))) → d(d(x1))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.