The rewrite relation of the following TRS is considered.
| tail(cons(X)) | → | L | (1) |
| incr(nil) | → | nil | (2) |
| incr(cons(X)) | → | cons(s(X)) | (3) |
| adx(nil) | → | nil | (4) |
| adx(cons(X)) | → | incr(cons(X)) | (5) |
| nats | → | adx(zeros) | (6) |
| zeros | → | cons(0) | (7) |
| head(cons(X)) | → | X | (8) |
The TRS violates one of the two variable conditions. Thus, it is not terminating.