The rewrite relation of the following TRS is considered.
U71(tt) | → | s(length(L)) | (1) |
U91(tt) | → | cons(N) | (2) |
and(tt) | → | X | (3) |
zeros | → | cons(0) | (4) |
U11(tt) | → | U12(isNatList) | (5) |
U12(tt) | → | tt | (6) |
U21(tt) | → | U22(isNat) | (7) |
U22(tt) | → | tt | (8) |
U31(tt) | → | U32(isNatList) | (9) |
U32(tt) | → | tt | (10) |
U41(tt) | → | U42(isNat) | (11) |
U42(tt) | → | U43(isNatIList) | (12) |
U43(tt) | → | tt | (13) |
U51(tt) | → | U52(isNat) | (14) |
U52(tt) | → | U53(isNatList) | (15) |
U53(tt) | → | tt | (16) |
U61(tt) | → | U62(isNat) | (17) |
U62(tt) | → | U63(isNatIList) | (18) |
U63(tt) | → | tt | (19) |
U81(tt) | → | nil | (20) |
isNat | → | tt | (21) |
isNat | → | U11(isNatIListKind) | (22) |
isNat | → | U21(isNatKind) | (23) |
isNatIList | → | U31(isNatIListKind) | (24) |
isNatIList | → | tt | (25) |
isNatIList | → | U41(and(isNatKind)) | (26) |
isNatIListKind | → | tt | (27) |
isNatIListKind | → | and(isNatKind) | (28) |
isNatKind | → | tt | (29) |
isNatKind | → | isNatIListKind | (30) |
isNatKind | → | isNatKind | (31) |
isNatList | → | tt | (32) |
isNatList | → | U51(and(isNatKind)) | (33) |
isNatList | → | U61(and(isNatKind)) | (34) |
length(nil) | → | 0 | (35) |
length(cons(N)) | → | U71(and(and(isNatList))) | (36) |
take(0,IL) | → | U81(and(isNatIList)) | (37) |
take(s(M),cons(N)) | → | U91(and(and(isNatIList))) | (38) |
The TRS violates one of the two variable conditions. Thus, it is not terminating.