MAYBE
Termination w.r.t. Q proof of ../tpdb/TRS/higher-order/Lifantsev/Ex2PrimRec.trs
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(rec, h), app(g, 0)) → g
app(app(rec, h), app(g, app(s, x))) → app(app(h, x), app(app(rec, h), app(g, x)))
Q is empty.
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
app(app(rec, h), app(g, 0)) → g
app(app(rec, h), app(g, app(s, x))) → app(app(h, x), app(app(rec, h), app(g, 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(rec, h), app(g, app(s, x))) → APP(app(h, x), app(app(rec, h), app(g, x)))
APP(app(rec, h), app(g, app(s, x))) → APP(g, x)
APP(app(rec, h), app(g, app(s, x))) → APP(h, x)
APP(app(rec, h), app(g, app(s, x))) → APP(app(rec, h), app(g, x))
The TRS R consists of the following rules:
app(app(rec, h), app(g, 0)) → g
app(app(rec, h), app(g, app(s, x))) → app(app(h, x), app(app(rec, h), app(g, 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(rec, h), app(g, app(s, x))) → APP(app(h, x), app(app(rec, h), app(g, x)))
APP(app(rec, h), app(g, app(s, x))) → APP(g, x)
APP(app(rec, h), app(g, app(s, x))) → APP(h, x)
APP(app(rec, h), app(g, app(s, x))) → APP(app(rec, h), app(g, x))
The TRS R consists of the following rules:
app(app(rec, h), app(g, 0)) → g
app(app(rec, h), app(g, app(s, x))) → app(app(h, x), app(app(rec, h), app(g, x)))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.