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 (68ms), SubtermCriterion (1ms), DependencyGraph (51ms), PolynomialLinearRange4iUR (1092ms), DependencyGraph (9ms), PolynomialLinearRange8NegiUR (4319ms), DependencyGraph (8ms), ReductionPairSAT (timeout)].

The following open problems remain:

Open Dependency Pair Problem 1

Dependency Pairs

app#(app(F, app(app(F, f), x)), x) → app#(F, f)app#(app(F, app(app(F, f), x)), x) → app#(G, app(app(F, f), x))
app#(app(F, app(app(F, f), x)), x) → app#(app(F, app(G, app(app(F, f), x))), app(f, x))app#(app(F, app(app(F, f), x)), x) → app#(F, app(G, app(app(F, f), x)))
app#(app(F, app(app(F, f), x)), x) → app#(f, x)app#(app(F, app(app(F, f), x)), x) → app#(app(F, f), x)

Rewrite Rules

app(app(F, app(app(F, f), x)), x) → app(app(F, app(G, app(app(F, f), x))), app(f, x))

Original Signature

Termination of terms over the following signature is verified: app, F, G