The rewrite relation of the following TRS is considered.
| U114(tt) | → | s(length(L)) | (1) |
| U136(tt) | → | cons(N) | (2) |
| zeros | → | cons(0) | (3) |
| U101(tt) | → | U102(isNatKind) | (4) |
| U102(tt) | → | U103(isNatIListKind) | (5) |
| U103(tt) | → | U104(isNatIListKind) | (6) |
| U104(tt) | → | U105(isNat) | (7) |
| U105(tt) | → | U106(isNatIList) | (8) |
| U106(tt) | → | tt | (9) |
| U11(tt) | → | U12(isNatIListKind) | (10) |
| U111(tt) | → | U112(isNatIListKind) | (11) |
| U112(tt) | → | U113(isNat) | (12) |
| U113(tt) | → | U114(isNatKind) | (13) |
| U12(tt) | → | U13(isNatList) | (14) |
| U121(tt) | → | U122(isNatIListKind) | (15) |
| U122(tt) | → | nil | (16) |
| U13(tt) | → | tt | (17) |
| U131(tt) | → | U132(isNatIListKind) | (18) |
| U132(tt) | → | U133(isNat) | (19) |
| U133(tt) | → | U134(isNatKind) | (20) |
| U134(tt) | → | U135(isNat) | (21) |
| U135(tt) | → | U136(isNatKind) | (22) |
| U21(tt) | → | U22(isNatKind) | (23) |
| U22(tt) | → | U23(isNat) | (24) |
| U23(tt) | → | tt | (25) |
| U31(tt) | → | U32(isNatIListKind) | (26) |
| U32(tt) | → | U33(isNatList) | (27) |
| U33(tt) | → | tt | (28) |
| U41(tt) | → | U42(isNatKind) | (29) |
| U42(tt) | → | U43(isNatIListKind) | (30) |
| U43(tt) | → | U44(isNatIListKind) | (31) |
| U44(tt) | → | U45(isNat) | (32) |
| U45(tt) | → | U46(isNatIList) | (33) |
| U46(tt) | → | tt | (34) |
| U51(tt) | → | U52(isNatIListKind) | (35) |
| U52(tt) | → | tt | (36) |
| U61(tt) | → | U62(isNatIListKind) | (37) |
| U62(tt) | → | tt | (38) |
| U71(tt) | → | tt | (39) |
| U81(tt) | → | tt | (40) |
| U91(tt) | → | U92(isNatKind) | (41) |
| U92(tt) | → | U93(isNatIListKind) | (42) |
| U93(tt) | → | U94(isNatIListKind) | (43) |
| U94(tt) | → | U95(isNat) | (44) |
| U95(tt) | → | U96(isNatList) | (45) |
| U96(tt) | → | tt | (46) |
| isNat | → | tt | (47) |
| isNat | → | U11(isNatIListKind) | (48) |
| isNat | → | U21(isNatKind) | (49) |
| isNatIList | → | U31(isNatIListKind) | (50) |
| isNatIList | → | tt | (51) |
| isNatIList | → | U41(isNatKind) | (52) |
| isNatIListKind | → | tt | (53) |
| isNatIListKind | → | U51(isNatKind) | (54) |
| isNatIListKind | → | U61(isNatKind) | (55) |
| isNatKind | → | tt | (56) |
| isNatKind | → | U71(isNatIListKind) | (57) |
| isNatKind | → | U81(isNatKind) | (58) |
| isNatList | → | tt | (59) |
| isNatList | → | U91(isNatKind) | (60) |
| isNatList | → | U101(isNatKind) | (61) |
| length(nil) | → | 0 | (62) |
| length(cons(N)) | → | U111(isNatList) | (63) |
| take(0,IL) | → | U121(isNatIList) | (64) |
| take(s(M),cons(N)) | → | U131(isNatIList) | (65) |
The TRS violates one of the two variable conditions. Thus, it is not terminating.