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:
r(e(x1)) → w(r(x1))
i(t(x1)) → e(r(x1))
e(w(x1)) → r(i(x1))
t(e(x1)) → r(e(x1))
w(r(x1)) → i(t(x1))
e(r(x1)) → e(w(x1))
r(i(t(e(r(x1))))) → e(w(r(i(t(e(x1))))))
Q is empty.
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
r(e(x1)) → w(r(x1))
i(t(x1)) → e(r(x1))
e(w(x1)) → r(i(x1))
t(e(x1)) → r(e(x1))
w(r(x1)) → i(t(x1))
e(r(x1)) → e(w(x1))
r(i(t(e(r(x1))))) → e(w(r(i(t(e(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:
E(w(x1)) → R(i(x1))
E(r(x1)) → W(x1)
R(i(t(e(r(x1))))) → W(r(i(t(e(x1)))))
R(i(t(e(r(x1))))) → I(t(e(x1)))
R(e(x1)) → W(r(x1))
W(r(x1)) → T(x1)
E(w(x1)) → I(x1)
R(i(t(e(r(x1))))) → E(w(r(i(t(e(x1))))))
I(t(x1)) → R(x1)
R(i(t(e(r(x1))))) → T(e(x1))
W(r(x1)) → I(t(x1))
I(t(x1)) → E(r(x1))
R(e(x1)) → R(x1)
R(i(t(e(r(x1))))) → R(i(t(e(x1))))
R(i(t(e(r(x1))))) → E(x1)
E(r(x1)) → E(w(x1))
T(e(x1)) → R(e(x1))
The TRS R consists of the following rules:
r(e(x1)) → w(r(x1))
i(t(x1)) → e(r(x1))
e(w(x1)) → r(i(x1))
t(e(x1)) → r(e(x1))
w(r(x1)) → i(t(x1))
e(r(x1)) → e(w(x1))
r(i(t(e(r(x1))))) → e(w(r(i(t(e(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:
E(w(x1)) → R(i(x1))
E(r(x1)) → W(x1)
R(i(t(e(r(x1))))) → W(r(i(t(e(x1)))))
R(i(t(e(r(x1))))) → I(t(e(x1)))
R(e(x1)) → W(r(x1))
W(r(x1)) → T(x1)
E(w(x1)) → I(x1)
R(i(t(e(r(x1))))) → E(w(r(i(t(e(x1))))))
I(t(x1)) → R(x1)
R(i(t(e(r(x1))))) → T(e(x1))
W(r(x1)) → I(t(x1))
I(t(x1)) → E(r(x1))
R(e(x1)) → R(x1)
R(i(t(e(r(x1))))) → R(i(t(e(x1))))
R(i(t(e(r(x1))))) → E(x1)
E(r(x1)) → E(w(x1))
T(e(x1)) → R(e(x1))
The TRS R consists of the following rules:
r(e(x1)) → w(r(x1))
i(t(x1)) → e(r(x1))
e(w(x1)) → r(i(x1))
t(e(x1)) → r(e(x1))
w(r(x1)) → i(t(x1))
e(r(x1)) → e(w(x1))
r(i(t(e(r(x1))))) → e(w(r(i(t(e(x1))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.