MAYBE
The TRS could not be proven terminating. The proof attempt took 550 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 (1ms), DependencyGraph (5ms), PolynomialLinearRange4iUR (90ms), DependencyGraph (3ms), PolynomialLinearRange8NegiUR (264ms), DependencyGraph (2ms), ReductionPairSAT (37ms), DependencyGraph (2ms), SizeChangePrinciple (3ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| c# | → | f#(n__g(n__c)) | | f#(n__g(X)) | → | activate#(X) |
| activate#(n__c) | → | c# |
Rewrite Rules
| c | → | f(n__g(n__c)) | | f(n__g(X)) | → | g(activate(X)) |
| g(X) | → | n__g(X) | | c | → | n__c |
| activate(n__g(X)) | → | g(X) | | activate(n__c) | → | c |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: activate, f, g, n__c, c, n__g
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| c# | → | f#(n__g(n__c)) | | f#(n__g(X)) | → | g#(activate(X)) |
| f#(n__g(X)) | → | activate#(X) | | activate#(n__g(X)) | → | g#(X) |
| activate#(n__c) | → | c# |
Rewrite Rules
| c | → | f(n__g(n__c)) | | f(n__g(X)) | → | g(activate(X)) |
| g(X) | → | n__g(X) | | c | → | n__c |
| activate(n__g(X)) | → | g(X) | | activate(n__c) | → | c |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: f, activate, g, n__c, c, n__g
Strategy
The following SCCs where found
| c# → f#(n__g(n__c)) | f#(n__g(X)) → activate#(X) |
| activate#(n__c) → c# |