TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60001 ms.

The following DP Processors were used


Problem 1 remains open; application of the following processors failed [DependencyGraph (57ms), SubtermCriterion (1ms), DependencyGraph (26ms), PolynomialLinearRange4iUR (1633ms), DependencyGraph (24ms), PolynomialLinearRange8NegiUR (4580ms), DependencyGraph (19ms), ReductionPairSAT (timeout)].

The following open problems remain:

Open Dependency Pair Problem 1

Dependency Pairs

app#(app(filter, f), app(app(cons, x), xs)) → app#(filter, f)app#(app(filter, f), app(app(cons, x), xs)) → app#(app(app(if, app(f, x)), app(app(cons, x), app(app(filter, f), xs))), app(app(filter, f), xs))
app#(app(filter, f), app(app(cons, x), xs)) → app#(app(filter, f), xs)app#(app(filter, f), app(app(cons, x), xs)) → app#(app(cons, x), app(app(filter, f), xs))
app#(app(filter, f), app(app(cons, x), xs)) → app#(app(if, app(f, x)), app(app(cons, x), app(app(filter, f), xs)))app#(app(filter, f), app(app(cons, x), xs)) → app#(f, x)
app#(app(filter, f), app(app(cons, x), xs)) → app#(if, app(f, x))app#(app(filter, f), app(app(cons, x), xs)) → app#(cons, x)

Rewrite Rules

app(app(app(if, true), x), y) → xapp(app(app(if, false), x), y) → y
app(app(filter, f), nil) → nilapp(app(filter, f), app(app(cons, x), xs)) → app(app(app(if, app(f, x)), app(app(cons, x), app(app(filter, f), xs))), app(app(filter, f), xs))

Original Signature

Termination of terms over the following signature is verified: app, if, false, true, filter, cons, nil