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
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) |
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) |