The rewrite relation of the following TRS is considered.
| U101(tt) | → | fst(splitAt(N,XS)) | (1) |
| U11(tt) | → | snd(splitAt(N,XS)) | (2) |
| U21(tt) | → | X | (3) |
| U31(tt) | → | N | (4) |
| U41(tt) | → | cons(N) | (5) |
| U51(tt) | → | head(afterNth(N,XS)) | (6) |
| U61(tt) | → | Y | (7) |
| U71(tt) | → | pair(nil,XS) | (8) |
| U81(tt) | → | U82(splitAt(N,XS)) | (9) |
| U82(pair(YS,ZS)) | → | pair(cons(X),ZS) | (10) |
| U91(tt) | → | XS | (11) |
| and(tt) | → | X | (12) |
| afterNth(N,XS) | → | U11(and(isNatural)) | (13) |
| fst(pair(X,Y)) | → | U21(and(isLNat)) | (14) |
| head(cons(N)) | → | U31(and(isNatural)) | (15) |
| isLNat | → | tt | (16) |
| isLNat | → | and(isNatural) | (17) |
| isLNat | → | isPLNat | (18) |
| isLNat | → | isNatural | (19) |
| isLNat | → | isLNat | (20) |
| isNatural | → | tt | (21) |
| isNatural | → | isLNat | (22) |
| isNatural | → | isNatural | (23) |
| isNatural | → | and(isNatural) | (24) |
| isPLNat | → | and(isLNat) | (25) |
| isPLNat | → | and(isNatural) | (26) |
| natsFrom(N) | → | U41(isNatural) | (27) |
| sel(N,XS) | → | U51(and(isNatural)) | (28) |
| snd(pair(X,Y)) | → | U61(and(isLNat)) | (29) |
| splitAt(0,XS) | → | U71(isLNat) | (30) |
| splitAt(s(N),cons(X)) | → | U81(and(isNatural)) | (31) |
| tail(cons(N)) | → | U91(and(isNatural)) | (32) |
| take(N,XS) | → | U101(and(isNatural)) | (33) |
| t0 | = | U101(tt) |
| → | fst(splitAt(U101(tt),XS)) | |
| = | t1 |