MAYBE
The TRS could not be proven terminating. The proof attempt took 1744 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (0ms).
| – Problem 2 was processed with processor SubtermCriterion (0ms).
| – Problem 3 remains open; application of the following processors failed [SubtermCriterion (2ms), DependencyGraph (2ms), PolynomialLinearRange4iUR (209ms), DependencyGraph (1ms), PolynomialLinearRange8NegiUR (450ms), DependencyGraph (1ms), ReductionPairSAT (920ms), DependencyGraph (1ms), SizeChangePrinciple (15ms)].
The following open problems remain:
Open Dependency Pair Problem 3
Dependency Pairs
| f#(X, n__g(X), Y) | → | f#(activate(Y), activate(Y), activate(Y)) |
Rewrite Rules
| f(X, n__g(X), Y) | → | f(activate(Y), activate(Y), activate(Y)) | | g(b) | → | c |
| b | → | c | | g(X) | → | n__g(X) |
| activate(n__g(X)) | → | g(activate(X)) | | activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: f, activate, g, b, c, n__g
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| activate#(n__g(X)) | → | activate#(X) | | f#(X, n__g(X), Y) | → | f#(activate(Y), activate(Y), activate(Y)) |
| activate#(n__g(X)) | → | g#(activate(X)) | | f#(X, n__g(X), Y) | → | activate#(Y) |
Rewrite Rules
| f(X, n__g(X), Y) | → | f(activate(Y), activate(Y), activate(Y)) | | g(b) | → | c |
| b | → | c | | g(X) | → | n__g(X) |
| activate(n__g(X)) | → | g(activate(X)) | | activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: activate, f, g, b, c, n__g
Strategy
The following SCCs where found
| activate#(n__g(X)) → activate#(X) |
| f#(X, n__g(X), Y) → f#(activate(Y), activate(Y), activate(Y)) |
Problem 2: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| activate#(n__g(X)) | → | activate#(X) |
Rewrite Rules
| f(X, n__g(X), Y) | → | f(activate(Y), activate(Y), activate(Y)) | | g(b) | → | c |
| b | → | c | | g(X) | → | n__g(X) |
| activate(n__g(X)) | → | g(activate(X)) | | activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: activate, f, g, b, c, n__g
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| activate#(n__g(X)) | → | activate#(X) |