MAYBE

The TRS could not be proven terminating. The proof attempt took 34915 ms.

The following DP Processors were used


Problem 1 remains open; application of the following processors failed [DependencyGraph (38ms), SubtermCriterion (1ms), DependencyGraph (21ms), PolynomialLinearRange4iUR (790ms), DependencyGraph (11ms), PolynomialLinearRange8NegiUR (3579ms), DependencyGraph (19ms), ReductionPairSAT (30289ms), DependencyGraph (12ms), SizeChangePrinciple (20ms)].

The following open problems remain:

Open Dependency Pair Problem 1

Dependency Pairs

app#(app(app(rec, f), x), app(s, y)) → app#(rec, f)app#(app(app(rec, f), x), app(s, y)) → app#(app(rec, f), x)
app#(app(app(rec, f), x), app(s, y)) → app#(app(app(rec, f), x), y)app#(app(app(rec, f), x), app(s, y)) → app#(s, y)
app#(app(app(rec, f), x), app(s, y)) → app#(f, app(s, y))app#(app(app(rec, f), x), app(s, y)) → app#(app(f, app(s, y)), app(app(app(rec, f), x), y))

Rewrite Rules

app(app(app(rec, f), x), 0) → xapp(app(app(rec, f), x), app(s, y)) → app(app(f, app(s, y)), app(app(app(rec, f), x), y))

Original Signature

Termination of terms over the following signature is verified: app, rec, 0, s