/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/Ex6_15_AEL02_C.trs

The program

(VAR X Y Z X1 X2)
(RULES 
active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
active(sel(0,cons(X,Z))) -> mark(X)
active(first(0,Z)) -> mark(nil)
active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
active(from(X)) -> mark(cons(X,from(s(X))))
active(sel1(s(X),cons(Y,Z))) -> mark(sel1(X,Z))
active(sel1(0,cons(X,Z))) -> mark(quote(X))
active(first1(0,Z)) -> mark(nil1)
active(first1(s(X),cons(Y,Z))) -> mark(cons1(quote(Y),first1(X,Z)))
active(quote(0)) -> mark(01)
active(quote1(cons(X,Z))) -> mark(cons1(quote(X),quote1(Z)))
active(quote1(nil)) -> mark(nil1)
active(quote(s(X))) -> mark(s1(quote(X)))
active(quote(sel(X,Z))) -> mark(sel1(X,Z))
active(quote1(first(X,Z))) -> mark(first1(X,Z))
active(unquote(01)) -> mark(0)
active(unquote(s1(X))) -> mark(s(unquote(X)))
active(unquote1(nil1)) -> mark(nil)
active(unquote1(cons1(X,Z))) -> mark(fcons(unquote(X),unquote1(Z)))
active(fcons(X,Z)) -> mark(cons(X,Z))
active(sel(X1,X2)) -> sel(active(X1),X2)
active(sel(X1,X2)) -> sel(X1,active(X2))
active(s(X)) -> s(active(X))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(first(X1,X2)) -> first(active(X1),X2)
active(first(X1,X2)) -> first(X1,active(X2))
active(from(X)) -> from(active(X))
active(sel1(X1,X2)) -> sel1(active(X1),X2)
active(sel1(X1,X2)) -> sel1(X1,active(X2))
active(first1(X1,X2)) -> first1(active(X1),X2)
active(first1(X1,X2)) -> first1(X1,active(X2))
active(cons1(X1,X2)) -> cons1(active(X1),X2)
active(cons1(X1,X2)) -> cons1(X1,active(X2))
active(s1(X)) -> s1(active(X))
active(unquote(X)) -> unquote(active(X))
active(unquote1(X)) -> unquote1(active(X))
active(fcons(X1,X2)) -> fcons(active(X1),X2)
active(fcons(X1,X2)) -> fcons(X1,active(X2))
sel(mark(X1),X2) -> mark(sel(X1,X2))
sel(X1,mark(X2)) -> mark(sel(X1,X2))
s(mark(X)) -> mark(s(X))
cons(mark(X1),X2) -> mark(cons(X1,X2))
first(mark(X1),X2) -> mark(first(X1,X2))
first(X1,mark(X2)) -> mark(first(X1,X2))
from(mark(X)) -> mark(from(X))
sel1(mark(X1),X2) -> mark(sel1(X1,X2))
sel1(X1,mark(X2)) -> mark(sel1(X1,X2))
first1(mark(X1),X2) -> mark(first1(X1,X2))
first1(X1,mark(X2)) -> mark(first1(X1,X2))
cons1(mark(X1),X2) -> mark(cons1(X1,X2))
cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
s1(mark(X)) -> mark(s1(X))
unquote(mark(X)) -> mark(unquote(X))
unquote1(mark(X)) -> mark(unquote1(X))
fcons(mark(X1),X2) -> mark(fcons(X1,X2))
fcons(X1,mark(X2)) -> mark(fcons(X1,X2))
proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
proper(s(X)) -> s(proper(X))
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(0) -> ok(0)
proper(first(X1,X2)) -> first(proper(X1),proper(X2))
proper(nil) -> ok(nil)
proper(from(X)) -> from(proper(X))
proper(sel1(X1,X2)) -> sel1(proper(X1),proper(X2))
proper(quote(X)) -> quote(proper(X))
proper(first1(X1,X2)) -> first1(proper(X1),proper(X2))
proper(nil1) -> ok(nil1)
proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
proper(01) -> ok(01)
proper(quote1(X)) -> quote1(proper(X))
proper(s1(X)) -> s1(proper(X))
proper(unquote(X)) -> unquote(proper(X))
proper(unquote1(X)) -> unquote1(proper(X))
proper(fcons(X1,X2)) -> fcons(proper(X1),proper(X2))
sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
s(ok(X)) -> ok(s(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
first(ok(X1),ok(X2)) -> ok(first(X1,X2))
from(ok(X)) -> ok(from(X))
sel1(ok(X1),ok(X2)) -> ok(sel1(X1,X2))
quote(ok(X)) -> ok(quote(X))
first1(ok(X1),ok(X2)) -> ok(first1(X1,X2))
cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
quote1(ok(X)) -> ok(quote1(X))
s1(ok(X)) -> ok(s1(X))
unquote(ok(X)) -> ok(unquote(X))
unquote1(ok(X)) -> ok(unquote1(X))
fcons(ok(X1),ok(X2)) -> ok(fcons(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)

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