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.