MAYBE

The TRS could not be proven terminating. The proof attempt took 45069 ms.

The following DP Processors were used


Problem 1 remains open; application of the following processors failed [DependencyGraph (55ms), SubtermCriterion (1ms), DependencyGraph (21ms), PolynomialLinearRange4iUR (1132ms), DependencyGraph (20ms), PolynomialLinearRange8NegiUR (2964ms), DependencyGraph (17ms), ReductionPairSAT (40660ms), DependencyGraph (16ms), SizeChangePrinciple (22ms)].

The following open problems remain:

Open Dependency Pair Problem 1

Dependency Pairs

app#(app(app(until, p), f), x) → app#(f, x)app#(app(app(until, p), f), x) → app#(if, app(p, x))
app#(app(app(until, p), f), x) → app#(app(app(until, p), f), app(f, x))app#(app(app(until, p), f), x) → app#(app(app(if, app(p, x)), x), app(app(app(until, p), f), app(f, x)))
app#(app(app(until, p), f), x) → app#(app(until, p), f)app#(app(app(until, p), f), x) → app#(app(if, app(p, x)), x)
app#(app(app(until, p), f), x) → app#(p, x)app#(app(app(until, p), f), x) → app#(until, p)

Rewrite Rules

app(app(app(if, true), x), y) → xapp(app(app(if, false), x), y) → y
app(app(app(until, p), f), x) → app(app(app(if, app(p, x)), x), app(app(app(until, p), f), app(f, x)))

Original Signature

Termination of terms over the following signature is verified: app, if, false, true, until