The rewrite relation of the following TRS is considered.
| U94(tt) | → | s(length(L)) | (1) |
| zeros | → | cons(0) | (2) |
| U11(tt) | → | U12(isNatIListKind) | (3) |
| U12(tt) | → | U13(isNatList) | (4) |
| U13(tt) | → | tt | (5) |
| U21(tt) | → | U22(isNatKind) | (6) |
| U22(tt) | → | U23(isNat) | (7) |
| U23(tt) | → | tt | (8) |
| U31(tt) | → | U32(isNatIListKind) | (9) |
| U32(tt) | → | U33(isNatList) | (10) |
| U33(tt) | → | tt | (11) |
| U41(tt) | → | U42(isNatKind) | (12) |
| U42(tt) | → | U43(isNatIListKind) | (13) |
| U43(tt) | → | U44(isNatIListKind) | (14) |
| U44(tt) | → | U45(isNat) | (15) |
| U45(tt) | → | U46(isNatIList) | (16) |
| U46(tt) | → | tt | (17) |
| U51(tt) | → | U52(isNatIListKind) | (18) |
| U52(tt) | → | tt | (19) |
| U61(tt) | → | tt | (20) |
| U71(tt) | → | tt | (21) |
| U81(tt) | → | U82(isNatKind) | (22) |
| U82(tt) | → | U83(isNatIListKind) | (23) |
| U83(tt) | → | U84(isNatIListKind) | (24) |
| U84(tt) | → | U85(isNat) | (25) |
| U85(tt) | → | U86(isNatList) | (26) |
| U86(tt) | → | tt | (27) |
| U91(tt) | → | U92(isNatIListKind) | (28) |
| U92(tt) | → | U93(isNat) | (29) |
| U93(tt) | → | U94(isNatKind) | (30) |
| isNat | → | tt | (31) |
| isNat | → | U11(isNatIListKind) | (32) |
| isNat | → | U21(isNatKind) | (33) |
| isNatIList | → | U31(isNatIListKind) | (34) |
| isNatIList | → | tt | (35) |
| isNatIList | → | U41(isNatKind) | (36) |
| isNatIListKind | → | tt | (37) |
| isNatIListKind | → | U51(isNatKind) | (38) |
| isNatKind | → | tt | (39) |
| isNatKind | → | U61(isNatIListKind) | (40) |
| isNatKind | → | U71(isNatKind) | (41) |
| isNatList | → | tt | (42) |
| isNatList | → | U81(isNatKind) | (43) |
| length(nil) | → | 0 | (44) |
| length(cons(N)) | → | U91(isNatList) | (45) |
The TRS violates one of the two variable conditions. Thus, it is not terminating.