TIMEOUT
The TRS could not be proven terminating. The proof attempt took 60000 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 (1ms), DependencyGraph (2ms), PolynomialLinearRange4iUR (80ms), DependencyGraph (1ms), PolynomialLinearRange8NegiUR (49ms), DependencyGraph (1ms), ReductionPairSAT (111ms), DependencyGraph (0ms), SizeChangePrinciple (6ms), ForwardNarrowing (0ms), BackwardInstantiation (1ms), ForwardInstantiation (1ms), Propagation (0ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| f#(n__a, n__b, X) | → | f#(X, X, X) |
Rewrite Rules
| f(n__a, n__b, X) | → | f(X, X, X) | | c | → | a |
| c | → | b | | 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, c, n__a, a
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| activate#(n__a) | → | a# | | activate#(n__b) | → | b# |
| c# | → | a# | | c# | → | b# |
| f#(n__a, n__b, X) | → | f#(X, X, X) |
Rewrite Rules
| f(n__a, n__b, X) | → | f(X, X, X) | | c | → | a |
| c | → | b | | 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, c, a
Strategy
The following SCCs where found
| f#(n__a, n__b, X) → f#(X, X, X) |