TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60002 ms.

The following DP Processors were used


Problem 1 remains open; application of the following processors failed [DependencyGraph (200ms), SubtermCriterion (1ms), DependencyGraph (157ms), PolynomialLinearRange4iUR (3572ms), DependencyGraph (144ms), PolynomialLinearRange8NegiUR (10133ms), DependencyGraph (142ms), ReductionPairSAT (timeout)].

The following open problems remain:

Open Dependency Pair Problem 1

Dependency Pairs

app#(app(takeWhile, p), app(app(cons, x), xs)) → app#(app(if, app(p, x)), app(app(cons, x), app(app(takeWhile, p), xs)))app#(app(dropWhile, p), app(app(cons, x), xs)) → app#(cons, x)
app#(app(takeWhile, p), app(app(cons, x), xs)) → app#(if, app(p, x))app#(app(takeWhile, p), app(app(cons, x), xs)) → app#(cons, x)
app#(app(dropWhile, p), app(app(cons, x), xs)) → app#(app(if, app(p, x)), app(app(dropWhile, p), xs))app#(app(dropWhile, p), app(app(cons, x), xs)) → app#(app(cons, x), xs)
app#(app(takeWhile, p), app(app(cons, x), xs)) → app#(app(cons, x), app(app(takeWhile, p), xs))app#(app(dropWhile, p), app(app(cons, x), xs)) → app#(app(dropWhile, p), xs)
app#(app(takeWhile, p), app(app(cons, x), xs)) → app#(takeWhile, p)app#(app(takeWhile, p), app(app(cons, x), xs)) → app#(app(app(if, app(p, x)), app(app(cons, x), app(app(takeWhile, p), xs))), nil)
app#(app(takeWhile, p), app(app(cons, x), xs)) → app#(app(takeWhile, p), xs)app#(app(dropWhile, p), app(app(cons, x), xs)) → app#(p, x)
app#(app(takeWhile, p), app(app(cons, x), xs)) → app#(p, x)app#(app(dropWhile, p), app(app(cons, x), xs)) → app#(app(app(if, app(p, x)), app(app(dropWhile, p), xs)), app(app(cons, x), xs))
app#(app(dropWhile, p), app(app(cons, x), xs)) → app#(dropWhile, p)app#(app(dropWhile, p), app(app(cons, x), xs)) → app#(if, app(p, x))

Rewrite Rules

app(app(app(if, true), x), y) → xapp(app(app(if, true), x), y) → y
app(app(takeWhile, p), nil) → nilapp(app(takeWhile, p), app(app(cons, x), xs)) → app(app(app(if, app(p, x)), app(app(cons, x), app(app(takeWhile, p), xs))), nil)
app(app(dropWhile, p), nil) → nilapp(app(dropWhile, p), app(app(cons, x), xs)) → app(app(app(if, app(p, x)), app(app(dropWhile, p), xs)), app(app(cons, x), xs))

Original Signature

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