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.