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