/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/Ex6_15_AEL02_FR.trs

The program

(VAR X Y Z X1 X2)
(RULES 
sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
sel(0,cons(X,Z)) -> X
first(0,Z) -> nil
first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
from(X) -> cons(X,n__from(n__s(X)))
sel1(s(X),cons(Y,Z)) -> sel1(X,activate(Z))
sel1(0,cons(X,Z)) -> quote(X)
first1(0,Z) -> nil1
first1(s(X),cons(Y,Z)) -> cons1(quote(Y),first1(X,activate(Z)))
quote(n__0) -> 01
quote1(n__cons(X,Z)) -> cons1(quote(activate(X)),quote1(activate(Z)))
quote1(n__nil) -> nil1
quote(n__s(X)) -> s1(quote(activate(X)))
quote(n__sel(X,Z)) -> sel1(activate(X),activate(Z))
quote1(n__first(X,Z)) -> first1(activate(X),activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X,Z)) -> fcons(unquote(X),unquote1(Z))
fcons(X,Z) -> cons(X,Z)
first(X1,X2) -> n__first(X1,X2)
from(X) -> n__from(X)
s(X) -> n__s(X)
0 -> n__0
cons(X1,X2) -> n__cons(X1,X2)
nil -> n__nil
sel(X1,X2) -> n__sel(X1,X2)
activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
activate(n__from(X)) -> from(activate(X))
activate(n__s(X)) -> s(activate(X))
activate(n__0) -> 0
activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
activate(n__nil) -> nil
activate(n__sel(X1,X2)) -> sel(activate(X1),activate(X2))
activate(X) -> X
)

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