The rewrite relation of the following TRS is considered.
| sel(0,cons) | → | X | (1) |
| sel(s,cons) | → | sel(X,Z) | (2) |
| dbl(0) | → | 0 | (3) |
| dbl(s) | → | s | (4) |
| dbls(nil) | → | nil | (5) |
| dbls(cons) | → | cons | (6) |
| indx(nil) | → | nil | (7) |
| indx(cons) | → | cons | (8) |
| from | → | cons | (9) |
The TRS violates one of the two variable conditions. Thus, it is not terminating.