TIMEOUT
The TRS could not be proven terminating. The proof attempt took 60001 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (20ms).
| – Problem 2 remains open; application of the following processors failed [SubtermCriterion (3ms), DependencyGraph (1ms), PolynomialLinearRange4iUR (99ms), DependencyGraph (1ms), PolynomialLinearRange8NegiUR (232ms), DependencyGraph (2ms), ReductionPairSAT (339ms), DependencyGraph (1ms), SizeChangePrinciple (6ms), ForwardNarrowing (0ms), BackwardInstantiation (0ms), ForwardInstantiation (2ms), Propagation (1ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| f#(n__b, X, n__c) | → | f#(X, c, X) |
Rewrite Rules
| f(n__b, X, n__c) | → | f(X, c, X) | | c | → | b |
| b | → | n__b | | c | → | n__c |
| activate(n__b) | → | b | | activate(n__c) | → | c |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: activate, f, n__b, n__c, b, c
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| f#(n__b, X, n__c) | → | f#(X, c, X) | | f#(n__b, X, n__c) | → | c# |
| activate#(n__b) | → | b# | | c# | → | b# |
| activate#(n__c) | → | c# |
Rewrite Rules
| f(n__b, X, n__c) | → | f(X, c, X) | | c | → | b |
| b | → | n__b | | c | → | n__c |
| activate(n__b) | → | b | | activate(n__c) | → | c |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: f, activate, n__b, n__c, b, c
Strategy
The following SCCs where found
| f#(n__b, X, n__c) → f#(X, c, X) |