Termination w.r.t. Q of the following Term Rewriting System could be proven:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(f(x, y, z), u, f(x, y, v)) → f(x, y, f(z, u, v))
f(x, y, y) → y
f(x, y, g(y)) → x
f(x, x, y) → x
f(g(x), x, y) → y
Q is empty.
↳ QTRS
↳ DirectTerminationProof
Q restricted rewrite system:
The TRS R consists of the following rules:
f(f(x, y, z), u, f(x, y, v)) → f(x, y, f(z, u, v))
f(x, y, y) → y
f(x, y, g(y)) → x
f(x, x, y) → x
f(g(x), x, y) → y
Q is empty.
We use [23] with the following order to prove termination.
Recursive path order with status [2].
Precedence:
trivial
Status:
f3: [1,2,3]