MAYBE

The TRS could not be proven terminating. The proof attempt took 285 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (0ms).
 | – Problem 2 remains open; application of the following processors failed [SubtermCriterion (0ms), DependencyGraph (1ms), PolynomialLinearRange4iUR (57ms), DependencyGraph (2ms), PolynomialLinearRange8NegiUR (37ms), DependencyGraph (1ms), ReductionPairSAT (16ms), DependencyGraph (1ms), SizeChangePrinciple (6ms)].
 | – Problem 3 was processed with processor SubtermCriterion (0ms).

The following open problems remain:



Open Dependency Pair Problem 2

Dependency Pairs

from#(X)from#(s(X))

Rewrite Rules

from(X)cons(X, from(s(X)))after(0, XS)XS
after(s(N), cons(X, XS))after(N, XS)

Original Signature

Termination of terms over the following signature is verified: after, 0, s, from, cons


Problem 1: DependencyGraph



Dependency Pair Problem

Dependency Pairs

after#(s(N), cons(X, XS))after#(N, XS)from#(X)from#(s(X))

Rewrite Rules

from(X)cons(X, from(s(X)))after(0, XS)XS
after(s(N), cons(X, XS))after(N, XS)

Original Signature

Termination of terms over the following signature is verified: after, 0, s, from, cons

Strategy


The following SCCs where found

after#(s(N), cons(X, XS)) → after#(N, XS)

from#(X) → from#(s(X))

Problem 3: SubtermCriterion



Dependency Pair Problem

Dependency Pairs

after#(s(N), cons(X, XS))after#(N, XS)

Rewrite Rules

from(X)cons(X, from(s(X)))after(0, XS)XS
after(s(N), cons(X, XS))after(N, XS)

Original Signature

Termination of terms over the following signature is verified: after, 0, s, from, cons

Strategy


Projection

The following projection was used:

Thus, the following dependency pairs are removed:

after#(s(N), cons(X, XS))after#(N, XS)