TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60096 ms.

The following DP Processors were used


Problem 1 remains open; application of the following processors failed [DependencyGraph (95ms), SubtermCriterion (1ms), DependencyGraph (62ms), PolynomialLinearRange4iUR (2506ms), DependencyGraph (57ms), PolynomialLinearRange8NegiUR (15987ms), DependencyGraph (44ms), ReductionPairSAT (timeout)].

The following open problems remain:



Open Dependency Pair Problem 1

Dependency Pairs

app#(app(forall, p), app(app(cons, x), xs))app#(app(and, app(p, x)), app(app(forall, p), xs))app#(app(forsome, p), app(app(cons, x), xs))app#(forsome, p)
app#(app(forsome, p), app(app(cons, x), xs))app#(app(or, app(p, x)), app(app(forsome, p), xs))app#(app(forsome, p), app(app(cons, x), xs))app#(app(forsome, p), xs)
app#(app(forall, p), app(app(cons, x), xs))app#(forall, p)app#(app(forall, p), app(app(cons, x), xs))app#(and, app(p, x))
app#(app(forall, p), app(app(cons, x), xs))app#(p, x)app#(app(forall, p), app(app(cons, x), xs))app#(app(forall, p), xs)
app#(app(forsome, p), app(app(cons, x), xs))app#(p, x)app#(app(forsome, p), app(app(cons, x), xs))app#(or, app(p, x))

Rewrite Rules

app(app(and, true), true)trueapp(app(and, true), false)false
app(app(and, false), true)falseapp(app(and, false), false)false
app(app(or, true), true)trueapp(app(or, true), false)true
app(app(or, false), true)trueapp(app(or, false), false)false
app(app(forall, p), nil)trueapp(app(forall, p), app(app(cons, x), xs))app(app(and, app(p, x)), app(app(forall, p), xs))
app(app(forsome, p), nil)falseapp(app(forsome, p), app(app(cons, x), xs))app(app(or, app(p, x)), app(app(forsome, p), xs))

Original Signature

Termination of terms over the following signature is verified: app, or, forsome, false, true, forall, cons, nil, and