The rewrite relation of the following TRS is considered.
| U52(tt) | → | N | (1) |
| U64(tt) | → | s(plus(N,M)) | (2) |
| U11(tt) | → | U12(isNatKind) | (3) |
| U12(tt) | → | U13(isNatKind) | (4) |
| U13(tt) | → | U14(isNatKind) | (5) |
| U14(tt) | → | U15(isNat) | (6) |
| U15(tt) | → | U16(isNat) | (7) |
| U16(tt) | → | tt | (8) |
| U21(tt) | → | U22(isNatKind) | (9) |
| U22(tt) | → | U23(isNat) | (10) |
| U23(tt) | → | tt | (11) |
| U31(tt) | → | U32(isNatKind) | (12) |
| U32(tt) | → | tt | (13) |
| U41(tt) | → | tt | (14) |
| U51(tt) | → | U52(isNatKind) | (15) |
| U61(tt) | → | U62(isNatKind) | (16) |
| U62(tt) | → | U63(isNat) | (17) |
| U63(tt) | → | U64(isNatKind) | (18) |
| isNat | → | tt | (19) |
| isNat | → | U11(isNatKind) | (20) |
| isNat | → | U21(isNatKind) | (21) |
| isNatKind | → | tt | (22) |
| isNatKind | → | U31(isNatKind) | (23) |
| isNatKind | → | U41(isNatKind) | (24) |
| plus(N,0) | → | U51(isNat) | (25) |
| plus(N,s(M)) | → | U61(isNat) | (26) |
The TRS violates one of the two variable conditions. Thus, it is not terminating.