The rewrite relation of the following TRS is considered.
| uTake2(tt) | → | cons(N) | (1) |
| uLength(tt) | → | s(length(L)) | (2) |
| and(tt,T) | → | T | (3) |
| isNatIList | → | isNatList | (4) |
| isNat | → | tt | (5) |
| isNat | → | isNat | (6) |
| isNat | → | isNatList | (7) |
| isNatIList | → | tt | (8) |
| isNatIList | → | and(isNat,isNatIList) | (9) |
| isNatList | → | tt | (10) |
| isNatList | → | and(isNat,isNatList) | (11) |
| isNatList | → | and(isNat,isNatIList) | (12) |
| zeros | → | cons(0) | (13) |
| take(0,IL) | → | uTake1(isNatIList) | (14) |
| uTake1(tt) | → | nil | (15) |
| take(s(M),cons(N)) | → | uTake2(and(isNat,and(isNat,isNatIList))) | (16) |
| length(cons(N)) | → | uLength(and(isNat,isNatList)) | (17) |
The TRS violates one of the two variable conditions. Thus, it is not terminating.