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:

a1(b1(x)) -> b1(a1(a1(x)))
b1(c1(x)) -> c1(b1(b1(x)))
c1(a1(x)) -> a1(c1(c1(x)))
u1(a1(x)) -> x
v1(b1(x)) -> x
w1(c1(x)) -> x
a1(u1(x)) -> x
b1(v1(x)) -> x
c1(w1(x)) -> x

Q is empty.


QTRS
  ↳ DependencyPairsProof

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

a1(b1(x)) -> b1(a1(a1(x)))
b1(c1(x)) -> c1(b1(b1(x)))
c1(a1(x)) -> a1(c1(c1(x)))
u1(a1(x)) -> x
v1(b1(x)) -> x
w1(c1(x)) -> x
a1(u1(x)) -> x
b1(v1(x)) -> x
c1(w1(x)) -> x

Q is empty.

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

A1(b1(x)) -> B1(a1(a1(x)))
B1(c1(x)) -> B1(b1(x))
C1(a1(x)) -> C1(x)
B1(c1(x)) -> C1(b1(b1(x)))
C1(a1(x)) -> C1(c1(x))
A1(b1(x)) -> A1(a1(x))
C1(a1(x)) -> A1(c1(c1(x)))
A1(b1(x)) -> A1(x)
B1(c1(x)) -> B1(x)

The TRS R consists of the following rules:

a1(b1(x)) -> b1(a1(a1(x)))
b1(c1(x)) -> c1(b1(b1(x)))
c1(a1(x)) -> a1(c1(c1(x)))
u1(a1(x)) -> x
v1(b1(x)) -> x
w1(c1(x)) -> x
a1(u1(x)) -> x
b1(v1(x)) -> x
c1(w1(x)) -> x

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:

A1(b1(x)) -> B1(a1(a1(x)))
B1(c1(x)) -> B1(b1(x))
C1(a1(x)) -> C1(x)
B1(c1(x)) -> C1(b1(b1(x)))
C1(a1(x)) -> C1(c1(x))
A1(b1(x)) -> A1(a1(x))
C1(a1(x)) -> A1(c1(c1(x)))
A1(b1(x)) -> A1(x)
B1(c1(x)) -> B1(x)

The TRS R consists of the following rules:

a1(b1(x)) -> b1(a1(a1(x)))
b1(c1(x)) -> c1(b1(b1(x)))
c1(a1(x)) -> a1(c1(c1(x)))
u1(a1(x)) -> x
v1(b1(x)) -> x
w1(c1(x)) -> x
a1(u1(x)) -> x
b1(v1(x)) -> x
c1(w1(x)) -> x

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