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(0, x), 1) → f(g(f(x, x)), x)
f(g(x), y) → g(f(x, y))
Q is empty.
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
f(f(0, x), 1) → f(g(f(x, x)), x)
f(g(x), y) → g(f(x, 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(f(0, x), 1) → F(g(f(x, x)), x)
F(f(0, x), 1) → F(x, x)
F(g(x), y) → F(x, y)
The TRS R consists of the following rules:
f(f(0, x), 1) → f(g(f(x, x)), x)
f(g(x), y) → g(f(x, 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(f(0, x), 1) → F(g(f(x, x)), x)
F(f(0, x), 1) → F(x, x)
F(g(x), y) → F(x, y)
The TRS R consists of the following rules:
f(f(0, x), 1) → f(g(f(x, x)), x)
f(g(x), y) → g(f(x, y))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.