The rewrite relation of the following TRS is considered.
U41(tt) | → | N | (1) |
U52(tt) | → | s(plus(N,M)) | (2) |
U72(tt) | → | plus(x(N,M),N) | (3) |
U11(tt) | → | U12(isNat) | (4) |
U12(tt) | → | tt | (5) |
U21(tt) | → | tt | (6) |
U31(tt) | → | U32(isNat) | (7) |
U32(tt) | → | tt | (8) |
U51(tt) | → | U52(isNat) | (9) |
U61(tt) | → | 0 | (10) |
U71(tt) | → | U72(isNat) | (11) |
isNat | → | tt | (12) |
isNat | → | U11(isNat) | (13) |
isNat | → | U21(isNat) | (14) |
isNat | → | U31(isNat) | (15) |
plus(N,0) | → | U41(isNat) | (16) |
plus(N,s(M)) | → | U51(isNat) | (17) |
x(N,0) | → | U61(isNat) | (18) |
x(N,s(M)) | → | U71(isNat) | (19) |
The TRS violates one of the two variable conditions. Thus, it is not terminating.