YES
The TRS could be proven terminating. The proof took 55 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (2ms).
| – Problem 2 was processed with processor SubtermCriterion (0ms).
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| f#(s(x)) | → | g#(f(x)) | | f#(s(x)) | → | f#(x) |
Rewrite Rules
| f(0) | → | 1 | | f(s(x)) | → | g(f(x)) |
| g(x) | → | +(x, s(x)) | | f(s(x)) | → | +(f(x), s(f(x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, 1, 0, s, +
Strategy
The following SCCs where found
Problem 2: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
Rewrite Rules
| f(0) | → | 1 | | f(s(x)) | → | g(f(x)) |
| g(x) | → | +(x, s(x)) | | f(s(x)) | → | +(f(x), s(f(x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, 1, 0, s, +
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed: