The rewrite relation of the following TRS is considered.
| U12(tt) | → | s(plus(N,M)) | (1) |
| U22(tt) | → | plus(x(N,M),N) | (2) |
| U11(tt) | → | U12(tt) | (3) |
| U21(tt) | → | U22(tt) | (4) |
| plus(N,0) | → | N | (5) |
| plus(N,s(M)) | → | U11(tt) | (6) |
| x(N,0) | → | 0 | (7) |
| x(N,s(M)) | → | U21(tt) | (8) |
The TRS violates one of the two variable conditions. Thus, it is not terminating.