/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/Ex1_Luc02b_C.trs

The program

(VAR X Z Y X1 X2)
(RULES 
active(from(X)) -> mark(cons(X,from(s(X))))
active(first(0,Z)) -> mark(nil)
active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
active(sel(0,cons(X,Z))) -> mark(X)
active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
active(from(X)) -> from(active(X))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(s(X)) -> s(active(X))
active(first(X1,X2)) -> first(active(X1),X2)
active(first(X1,X2)) -> first(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))
first(mark(X1),X2) -> mark(first(X1,X2))
first(X1,mark(X2)) -> mark(first(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(first(X1,X2)) -> first(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))
first(ok(X1),ok(X2)) -> ok(first(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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