The rewrite relation of the following TRS is considered.
| 2ndspos(s(N),cons(X)) | → | rcons(posrecip(Y),2ndsneg(N,Z)) | (1) |
| 2ndsneg(s(N),cons(X)) | → | rcons(negrecip(Y),2ndspos(N,Z)) | (2) |
| from(X) | → | cons(X) | (3) |
| 2ndspos(0,Z) | → | rnil | (4) |
| 2ndsneg(0,Z) | → | rnil | (5) |
| pi(X) | → | 2ndspos(X,from(0)) | (6) |
| plus(0,Y) | → | Y | (7) |
| plus(s(X),Y) | → | s(plus(X,Y)) | (8) |
| times(0,Y) | → | 0 | (9) |
| times(s(X),Y) | → | plus(Y,times(X,Y)) | (10) |
| square(X) | → | times(X,X) | (11) |
The TRS violates one of the two variable conditions. Thus, it is not terminating.