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:
f(f(X, Y), Z) → f(X, f(Y, Z))
f(X, f(Y, Z)) → f(Y, Y)
Q is empty.
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
f(f(X, Y), Z) → f(X, f(Y, Z))
f(X, f(Y, Z)) → f(Y, Y)
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:
F(X, f(Y, Z)) → F(Y, Y)
F(f(X, Y), Z) → F(Y, Z)
F(f(X, Y), Z) → F(X, f(Y, Z))
The TRS R consists of the following rules:
f(f(X, Y), Z) → f(X, f(Y, Z))
f(X, f(Y, Z)) → f(Y, Y)
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:
F(X, f(Y, Z)) → F(Y, Y)
F(f(X, Y), Z) → F(Y, Z)
F(f(X, Y), Z) → F(X, f(Y, Z))
The TRS R consists of the following rules:
f(f(X, Y), Z) → f(X, f(Y, Z))
f(X, f(Y, Z)) → f(Y, Y)
Q is empty.
We have to consider all minimal (P,Q,R)-chains.