YES
The TRS could be proven terminating. The proof took 27 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (7ms).
| – Problem 2 was processed with processor SubtermCriterion (0ms).
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| f#(a) | → | f#(c(a)) | | f#(a) | → | f#(d(a)) |
| f#(c(a)) | → | f#(d(b)) | | f#(c(b)) | → | f#(d(a)) |
| e#(g(X)) | → | e#(X) |
Rewrite Rules
| f(a) | → | f(c(a)) | | f(c(X)) | → | X |
| f(c(a)) | → | f(d(b)) | | f(a) | → | f(d(a)) |
| f(d(X)) | → | X | | f(c(b)) | → | f(d(a)) |
| e(g(X)) | → | e(X) |
Original Signature
Termination of terms over the following signature is verified: f, g, d, e, b, c, a
Strategy
The following SCCs where found
Problem 2: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
Rewrite Rules
| f(a) | → | f(c(a)) | | f(c(X)) | → | X |
| f(c(a)) | → | f(d(b)) | | f(a) | → | f(d(a)) |
| f(d(X)) | → | X | | f(c(b)) | → | f(d(a)) |
| e(g(X)) | → | e(X) |
Original Signature
Termination of terms over the following signature is verified: f, g, d, e, b, c, a
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed: