Termination w.r.t. Q proof of /tmp/tmpipxyZo/jambox5.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:

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

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

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

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

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

The TRS R consists of the following rules:

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

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

The TRS R consists of the following rules:

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

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