YES
The TRS could be proven terminating. The proof took 142 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (7ms).
| – Problem 2 was processed with processor PolynomialLinearRange4iUR (86ms).
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| f#(g(X), b) | → | a# | | f#(g(X), b) | → | f#(a, X) |
| a# | → | g#(c) |
Rewrite Rules
| a | → | g(c) | | g(a) | → | b |
| f(g(X), b) | → | f(a, X) |
Original Signature
Termination of terms over the following signature is verified: f, g, b, c, a
Strategy
The following SCCs where found
Problem 2: PolynomialLinearRange4iUR
Dependency Pair Problem
Dependency Pairs
Rewrite Rules
| a | → | g(c) | | g(a) | → | b |
| f(g(X), b) | → | f(a, X) |
Original Signature
Termination of terms over the following signature is verified: f, g, b, c, a
Strategy
Polynomial Interpretation
- a: 1
- b: 1
- c: 0
- f(x,y): 0
- f#(x,y): 2y + x
- g(x): 2x
Improved Usable rules
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed: