The rewrite relation of the following TRS is considered.
| U41(tt) | → | N | (1) |
| U51(tt) | → | s(plus(N,M)) | (2) |
| U71(tt) | → | plus(x(N,M),N) | (3) |
| and(tt) | → | X | (4) |
| U11(tt) | → | U12(isNat) | (5) |
| U12(tt) | → | U13(isNat) | (6) |
| U13(tt) | → | tt | (7) |
| U21(tt) | → | U22(isNat) | (8) |
| U22(tt) | → | tt | (9) |
| U31(tt) | → | U32(isNat) | (10) |
| U32(tt) | → | U33(isNat) | (11) |
| U33(tt) | → | tt | (12) |
| U61(tt) | → | 0 | (13) |
| isNat | → | tt | (14) |
| isNat | → | U11(and(isNatKind)) | (15) |
| isNat | → | U21(isNatKind) | (16) |
| isNat | → | U31(and(isNatKind)) | (17) |
| isNatKind | → | tt | (18) |
| isNatKind | → | and(isNatKind) | (19) |
| isNatKind | → | isNatKind | (20) |
| plus(N,0) | → | U41(and(isNat)) | (21) |
| plus(N,s(M)) | → | U51(and(and(isNat))) | (22) |
| x(N,0) | → | U61(and(isNat)) | (23) |
| x(N,s(M)) | → | U71(and(and(isNat))) | (24) |
The TRS violates one of the two variable conditions. Thus, it is not terminating.