YES
The TRS could be proven terminating. The proof took 236 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (4ms).
| – Problem 2 was processed with processor PolynomialLinearRange4iUR (175ms).
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| g#(a) | → | g#(b) | | b# | → | f#(a, a) |
| f#(a, a) | → | g#(d) | | g#(a) | → | b# |
Rewrite Rules
| g(a) | → | g(b) | | b | → | f(a, a) |
| f(a, a) | → | g(d) |
Original Signature
Termination of terms over the following signature is verified: f, g, d, b, a
Strategy
The following SCCs where found
Problem 2: PolynomialLinearRange4iUR
Dependency Pair Problem
Dependency Pairs
Rewrite Rules
| g(a) | → | g(b) | | b | → | f(a, a) |
| f(a, a) | → | g(d) |
Original Signature
Termination of terms over the following signature is verified: f, g, d, b, a
Strategy
Polynomial Interpretation
- a: 1
- b: 0
- d: 3
- f(x,y): 0
- g(x): 0
- g#(x): x + 1
Improved Usable rules
| b | → | f(a, a) | | f(a, a) | → | g(d) |
| g(a) | → | g(b) |
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed: