MAYBE
The TRS could not be proven terminating. The proof attempt took 1540 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 (2ms), PolynomialLinearRange4iUR (161ms), DependencyGraph (1ms), PolynomialLinearRange8NegiUR (673ms), DependencyGraph (1ms), ReductionPairSAT (451ms), DependencyGraph (1ms), SizeChangePrinciple (4ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| f#(n__a, X, X) | → | f#(activate(X), b, n__b) |
Rewrite Rules
| f(n__a, X, X) | → | f(activate(X), b, n__b) | | b | → | a |
| a | → | n__a | | b | → | n__b |
| activate(n__a) | → | a | | activate(n__b) | → | b |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: f, activate, n__b, b, n__a, a
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| activate#(n__a) | → | a# | | f#(n__a, X, X) | → | b# |
| activate#(n__b) | → | b# | | f#(n__a, X, X) | → | f#(activate(X), b, n__b) |
| f#(n__a, X, X) | → | activate#(X) | | b# | → | a# |
Rewrite Rules
| f(n__a, X, X) | → | f(activate(X), b, n__b) | | b | → | a |
| a | → | n__a | | b | → | n__b |
| activate(n__a) | → | a | | activate(n__b) | → | b |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: activate, f, n__b, b, n__a, a
Strategy
The following SCCs where found
| f#(n__a, X, X) → f#(activate(X), b, n__b) |