The rewrite relation of the following TRS is considered.
U11(tt) | → | U12(splitAt(N,XS)) | (1) |
U12(pair(YS,ZS)) | → | pair(cons(X),ZS) | (2) |
and(tt) | → | X | (3) |
tail(cons(N)) | → | XS | (4) |
afterNth(N,XS) | → | snd(splitAt(N,XS)) | (5) |
fst(pair(X,Y)) | → | X | (6) |
head(cons(N)) | → | N | (7) |
natsFrom(N) | → | cons(N) | (8) |
sel(N,XS) | → | head(afterNth(N,XS)) | (9) |
snd(pair(X,Y)) | → | Y | (10) |
splitAt(0,XS) | → | pair(nil,XS) | (11) |
splitAt(s(N),cons(X)) | → | U11(tt) | (12) |
take(N,XS) | → | fst(splitAt(N,XS)) | (13) |
t0 | = | U11(tt) |
→ | U12(splitAt(U11(tt),U11(tt))) | |
= | t1 |