The rewrite relation of the following TRS is considered.
U11(tt) | → | s(length(L)) | (1) |
U31(tt) | → | cons(N) | (2) |
and(tt) | → | X | (3) |
zeros | → | cons(0) | (4) |
U21(tt) | → | nil | (5) |
isNat | → | tt | (6) |
isNat | → | isNatList | (7) |
isNat | → | isNat | (8) |
isNatIList | → | isNatList | (9) |
isNatIList | → | tt | (10) |
isNatIList | → | and(isNat) | (11) |
isNatList | → | tt | (12) |
isNatList | → | and(isNat) | (13) |
length(nil) | → | 0 | (14) |
length(cons(N)) | → | U11(and(isNatList)) | (15) |
take(0,IL) | → | U21(isNatIList) | (16) |
take(s(M),cons(N)) | → | U31(and(isNatIList)) | (17) |
The TRS violates one of the two variable conditions. Thus, it is not terminating.