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