/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/Ex7_BLR02_C.trs

The program

(VAR X XS N X1 X2)
(RULES 
active(from(X)) -> mark(cons(X,from(s(X))))
active(head(cons(X,XS))) -> mark(X)
active(2nd(cons(X,XS))) -> mark(head(XS))
active(take(0,XS)) -> mark(nil)
active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS)))
active(sel(0,cons(X,XS))) -> mark(X)
active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS))
active(from(X)) -> from(active(X))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(s(X)) -> s(active(X))
active(head(X)) -> head(active(X))
active(2nd(X)) -> 2nd(active(X))
active(take(X1,X2)) -> take(active(X1),X2)
active(take(X1,X2)) -> take(X1,active(X2))
active(sel(X1,X2)) -> sel(active(X1),X2)
active(sel(X1,X2)) -> sel(X1,active(X2))
from(mark(X)) -> mark(from(X))
cons(mark(X1),X2) -> mark(cons(X1,X2))
s(mark(X)) -> mark(s(X))
head(mark(X)) -> mark(head(X))
2nd(mark(X)) -> mark(2nd(X))
take(mark(X1),X2) -> mark(take(X1,X2))
take(X1,mark(X2)) -> mark(take(X1,X2))
sel(mark(X1),X2) -> mark(sel(X1,X2))
sel(X1,mark(X2)) -> mark(sel(X1,X2))
proper(from(X)) -> from(proper(X))
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(s(X)) -> s(proper(X))
proper(head(X)) -> head(proper(X))
proper(2nd(X)) -> 2nd(proper(X))
proper(take(X1,X2)) -> take(proper(X1),proper(X2))
proper(0) -> ok(0)
proper(nil) -> ok(nil)
proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
from(ok(X)) -> ok(from(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
s(ok(X)) -> ok(s(X))
head(ok(X)) -> ok(head(X))
2nd(ok(X)) -> ok(2nd(X))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)

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