YES
The TRS could be proven terminating. The proof took 125 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (3ms).
| – Problem 2 was processed with processor PolynomialLinearRange4iUR (107ms).
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| f#(a, y) | → | g#(y) | | f#(a, y) | → | f#(y, g(y)) |
Rewrite Rules
| f(a, y) | → | f(y, g(y)) | | g(a) | → | b |
| g(b) | → | b |
Original Signature
Termination of terms over the following signature is verified: f, g, b, a
Strategy
The following SCCs where found
Problem 2: PolynomialLinearRange4iUR
Dependency Pair Problem
Dependency Pairs
Rewrite Rules
| f(a, y) | → | f(y, g(y)) | | g(a) | → | b |
| g(b) | → | b |
Original Signature
Termination of terms over the following signature is verified: f, g, b, a
Strategy
Polynomial Interpretation
- a: 1
- b: 0
- f(x,y): 0
- f#(x,y): 2y + 2x
- g(x): 0
Improved Usable rules
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed: