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 (320ms), SubtermCriterion (1ms), DependencyGraph (271ms), PolynomialLinearRange4iUR (4421ms), DependencyGraph (243ms), PolynomialLinearRange8NegiUR (12473ms), DependencyGraph (269ms), ReductionPairSAT (timeout)].

The following open problems remain:



Open Dependency Pair Problem 1

Dependency Pairs

app#(app(map, f), app(app(append, l1), l2)) → app#(app(map, f), l2)app#(app(map, f), app(app(append, l1), l2)) → app#(app(append, app(app(map, f), l1)), app(app(map, f), l2))
app#(app(append, app(app(cons, h), t)), l) → app#(cons, h)app#(app(map, f), app(app(append, l1), l2)) → app#(app(map, f), l1)
app#(app(append, app(app(append, l1), l2)), l3) → app#(append, l1)app#(app(append, app(app(append, l1), l2)), l3) → app#(app(append, l2), l3)
app#(app(map, f), app(app(cons, h), t)) → app#(f, h)app#(app(append, app(app(cons, h), t)), l) → app#(app(append, t), l)
app#(app(map, f), app(app(append, l1), l2)) → app#(append, app(app(map, f), l1))app#(app(append, app(app(cons, h), t)), l) → app#(append, t)
app#(app(append, app(app(cons, h), t)), l) → app#(app(cons, h), app(app(append, t), l))app#(app(append, app(app(append, l1), l2)), l3) → app#(app(append, l1), app(app(append, l2), l3))
app#(app(map, f), app(app(cons, h), t)) → app#(app(cons, app(f, h)), app(app(map, f), t))app#(app(map, f), app(app(cons, h), t)) → app#(cons, app(f, h))
app#(app(map, f), app(app(append, l1), l2)) → app#(map, f)app#(app(map, f), app(app(cons, h), t)) → app#(app(map, f), t)
app#(app(map, f), app(app(cons, h), t)) → app#(map, f)app#(app(append, app(app(append, l1), l2)), l3) → app#(append, l2)

Rewrite Rules

app(app(append, nil), l) → lapp(app(append, app(app(cons, h), t)), l) → app(app(cons, h), app(app(append, t), l))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, h), t)) → app(app(cons, app(f, h)), app(app(map, f), t))
app(app(append, app(app(append, l1), l2)), l3) → app(app(append, l1), app(app(append, l2), l3))app(app(map, f), app(app(append, l1), l2)) → app(app(append, app(app(map, f), l1)), app(app(map, f), l2))

Original Signature

Termination of terms over the following signature is verified: append, app, map, cons, nil