The rewrite relation of the following TRS is considered.
| U104(tt) | → | plus(x(N,M),N) | (1) |
| U72(tt) | → | N | (2) |
| U84(tt) | → | s(plus(N,M)) | (3) |
| U101(tt) | → | U102(isNatKind) | (4) |
| U102(tt) | → | U103(isNat) | (5) |
| U103(tt) | → | U104(isNatKind) | (6) |
| U11(tt) | → | U12(isNatKind) | (7) |
| U12(tt) | → | U13(isNatKind) | (8) |
| U13(tt) | → | U14(isNatKind) | (9) |
| U14(tt) | → | U15(isNat) | (10) |
| U15(tt) | → | U16(isNat) | (11) |
| U16(tt) | → | tt | (12) |
| U21(tt) | → | U22(isNatKind) | (13) |
| U22(tt) | → | U23(isNat) | (14) |
| U23(tt) | → | tt | (15) |
| U31(tt) | → | U32(isNatKind) | (16) |
| U32(tt) | → | U33(isNatKind) | (17) |
| U33(tt) | → | U34(isNatKind) | (18) |
| U34(tt) | → | U35(isNat) | (19) |
| U35(tt) | → | U36(isNat) | (20) |
| U36(tt) | → | tt | (21) |
| U41(tt) | → | U42(isNatKind) | (22) |
| U42(tt) | → | tt | (23) |
| U51(tt) | → | tt | (24) |
| U61(tt) | → | U62(isNatKind) | (25) |
| U62(tt) | → | tt | (26) |
| U71(tt) | → | U72(isNatKind) | (27) |
| U81(tt) | → | U82(isNatKind) | (28) |
| U82(tt) | → | U83(isNat) | (29) |
| U83(tt) | → | U84(isNatKind) | (30) |
| U91(tt) | → | U92(isNatKind) | (31) |
| U92(tt) | → | 0 | (32) |
| isNat | → | tt | (33) |
| isNat | → | U11(isNatKind) | (34) |
| isNat | → | U21(isNatKind) | (35) |
| isNat | → | U31(isNatKind) | (36) |
| isNatKind | → | tt | (37) |
| isNatKind | → | U41(isNatKind) | (38) |
| isNatKind | → | U51(isNatKind) | (39) |
| isNatKind | → | U61(isNatKind) | (40) |
| plus(N,0) | → | U71(isNat) | (41) |
| plus(N,s(M)) | → | U81(isNat) | (42) |
| x(N,0) | → | U91(isNat) | (43) |
| x(N,s(M)) | → | U101(isNat) | (44) |
The TRS violates one of the two variable conditions. Thus, it is not terminating.