YES
The TRS could be proven terminating. The proof took 21 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (3ms).
| – Problem 2 was processed with processor SubtermCriterion (1ms).
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| r1#(cons(x, k), a) | → | r1#(k, cons(x, a)) | | rev#(ls) | → | r1#(ls, empty) |
Rewrite Rules
| rev(ls) | → | r1(ls, empty) | | r1(empty, a) | → | a |
| r1(cons(x, k), a) | → | r1(k, cons(x, a)) |
Original Signature
Termination of terms over the following signature is verified: rev, empty, r1, cons
Strategy
The following SCCs where found
| r1#(cons(x, k), a) → r1#(k, cons(x, a)) |
Problem 2: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| r1#(cons(x, k), a) | → | r1#(k, cons(x, a)) |
Rewrite Rules
| rev(ls) | → | r1(ls, empty) | | r1(empty, a) | → | a |
| r1(cons(x, k), a) | → | r1(k, cons(x, a)) |
Original Signature
Termination of terms over the following signature is verified: rev, empty, r1, cons
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| r1#(cons(x, k), a) | → | r1#(k, cons(x, a)) |