The rewrite relation of the following TRS is considered.
| sel(s(N),cons(X)) | → | sel(N,XS) | (1) |
| from(X) | → | cons(X) | (2) |
| sel(0,cons(X)) | → | X | (3) |
| minus(X,0) | → | 0 | (4) |
| minus(s(X),s(Y)) | → | minus(X,Y) | (5) |
| quot(0,s(Y)) | → | 0 | (6) |
| quot(s(X),s(Y)) | → | s(quot(minus(X,Y),s(Y))) | (7) |
| zWquot(XS,nil) | → | nil | (8) |
| zWquot(nil,XS) | → | nil | (9) |
| zWquot(cons(X),cons(Y)) | → | cons(quot(X,Y)) | (10) |
The TRS violates one of the two variable conditions. Thus, it is not terminating.