The rewrite relation of the following TRS is considered.
| sel(0,cons) | → | X | (1) |
| sel(s,cons) | → | sel(X,Z) | (2) |
| dbl1(s) | → | s1(s1(dbl1(X))) | (3) |
| sel1(0,cons) | → | X | (4) |
| sel1(s,cons) | → | sel1(X,Z) | (5) |
| quote(s) | → | s1(quote(X)) | (6) |
| dbl(0) | → | 0 | (7) |
| dbl(s) | → | s | (8) |
| dbls(nil) | → | nil | (9) |
| dbls(cons) | → | cons | (10) |
| indx(nil) | → | nil | (11) |
| indx(cons) | → | cons | (12) |
| from | → | cons | (13) |
| dbl1(0) | → | 01 | (14) |
| quote(0) | → | 01 | (15) |
| quote(dbl(X)) | → | dbl1(X) | (16) |
| quote(sel(X,Y)) | → | sel1(X,Y) | (17) |
The TRS violates one of the two variable conditions. Thus, it is not terminating.