MAYBE
The TRS could not be proven terminating. The proof attempt took 384 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 (3ms), PolynomialLinearRange4iUR (0ms), DependencyGraph (2ms), PolynomialLinearRange8NegiUR (0ms), DependencyGraph (3ms), PolynomialLinearRange4 (147ms), DependencyGraph (1ms), ReductionPairSAT (104ms), DependencyGraph (1ms), SizeChangePrinciple (15ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| U21#(x, x) | → | g#(a) | | g#(x) | → | U21#(f(x), x) |
Rewrite Rules
| a | → | b | | f(a) | → | b |
| g(x) | → | U21(f(x), x) | | U21(x, x) | → | g(a) |
Original Signature
Termination of terms over the following signature is verified: f, g, b, a
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| U21#(x, x) | → | g#(a) | | g#(x) | → | f#(x) |
| g#(x) | → | U21#(f(x), x) | | U21#(x, x) | → | a# |
Rewrite Rules
| a | → | b | | f(a) | → | b |
| g(x) | → | U21(f(x), x) | | U21(x, x) | → | g(a) |
Original Signature
Termination of terms over the following signature is verified: f, g, b, a
Strategy
Context-sensitive strategy:
μ(T) = μ(b) = μ(a) = μ(a#) = ∅
μ(f) = μ(g) = μ(f#) = μ(U21#) = μ(g#) = μ(U21) = {1}
The following SCCs where found
| U21#(x, x) → g#(a) | g#(x) → U21#(f(x), x) |