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:
:2(:2(:2(:2(C, x), y), z), u) -> :2(:2(x, z), :2(:2(:2(x, y), z), u))
Q is empty.
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
:2(:2(:2(:2(C, x), y), z), u) -> :2(:2(x, z), :2(:2(:2(x, y), z), u))
Q is empty.
Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:
:12(:2(:2(:2(C, x), y), z), u) -> :12(x, z)
:12(:2(:2(:2(C, x), y), z), u) -> :12(x, y)
:12(:2(:2(:2(C, x), y), z), u) -> :12(:2(x, z), :2(:2(:2(x, y), z), u))
:12(:2(:2(:2(C, x), y), z), u) -> :12(:2(x, y), z)
:12(:2(:2(:2(C, x), y), z), u) -> :12(:2(:2(x, y), z), u)
The TRS R consists of the following rules:
:2(:2(:2(:2(C, x), y), z), u) -> :2(:2(x, z), :2(:2(:2(x, y), z), u))
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:
:12(:2(:2(:2(C, x), y), z), u) -> :12(x, z)
:12(:2(:2(:2(C, x), y), z), u) -> :12(x, y)
:12(:2(:2(:2(C, x), y), z), u) -> :12(:2(x, z), :2(:2(:2(x, y), z), u))
:12(:2(:2(:2(C, x), y), z), u) -> :12(:2(x, y), z)
:12(:2(:2(:2(C, x), y), z), u) -> :12(:2(:2(x, y), z), u)
The TRS R consists of the following rules:
:2(:2(:2(:2(C, x), y), z), u) -> :2(:2(x, z), :2(:2(:2(x, y), z), u))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.