TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60000 ms.

The following DP Processors were used


Problem 1 remains open; application of the following processors failed [DependencyGraph (333ms), SubtermCriterion (1ms), DependencyGraph (290ms), PolynomialLinearRange4iUR (4819ms), DependencyGraph (319ms), PolynomialLinearRange8NegiUR (17054ms), DependencyGraph (334ms), ReductionPairSAT (timeout)].

The following open problems remain:



Open Dependency Pair Problem 1

Dependency Pairs

app#(app(app(app(rec, t), u), v), app(s, x)) → app#(app(app(rec, t), u), v)app#(app(app(app(rec, t), u), v), app(s, x)) → app#(app(app(app(rec, t), u), v), x)
app#(app(app(app(rec, t), u), v), app(lim, f)) → app#(app(app(rectuv, t), u), v)app#(app(app(app(rectuv, t), u), v), n) → app#(rec, t)
app#(app(app(app(rectuv, t), u), v), n) → app#(app(rec, t), u)app#(app(app(app(rec, t), u), v), app(lim, f)) → app#(rectuv, t)
app#(app(app(app(rec, t), u), v), app(lim, f)) → app#(f, n)app#(app(app(app(rectuv, t), u), v), n) → app#(app(app(rec, t), u), v)
app#(app(app(app(rec, t), u), v), app(lim, f)) → app#(app(v, f), app(app(app(app(rectuv, t), u), v), app(f, n)))app#(app(app(app(rec, t), u), v), app(s, x)) → app#(u, x)
app#(app(app(app(rec, t), u), v), app(s, x)) → app#(rec, t)app#(app(app(app(rec, t), u), v), app(lim, f)) → app#(app(rectuv, t), u)
app#(app(app(app(rectuv, t), u), v), n) → app#(app(app(app(rec, t), u), v), n)app#(app(app(app(rec, t), u), v), app(s, x)) → app#(app(u, x), app(app(app(app(rec, t), u), v), x))
app#(app(app(app(rec, t), u), v), app(lim, f)) → app#(v, f)app#(app(app(app(rec, t), u), v), app(lim, f)) → app#(app(app(app(rectuv, t), u), v), app(f, n))
app#(app(app(app(rec, t), u), v), app(s, x)) → app#(app(rec, t), u)

Rewrite Rules

app(app(app(app(rec, t), u), v), 0) → tapp(app(app(app(rec, t), u), v), app(s, x)) → app(app(u, x), app(app(app(app(rec, t), u), v), x))
app(app(app(app(rec, t), u), v), app(lim, f)) → app(app(v, f), app(app(app(app(rectuv, t), u), v), app(f, n)))app(app(app(app(rectuv, t), u), v), n) → app(app(app(app(rec, t), u), v), n)

Original Signature

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