/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/Ex26_Luc03b_GM.trs

The program

(VAR N X Y Z X1 X2)
(RULES 
a__terms(N) -> cons(recip(a__sqr(mark(N))),terms(s(N)))
a__sqr(0) -> 0
a__sqr(s(X)) -> s(add(sqr(X),dbl(X)))
a__dbl(0) -> 0
a__dbl(s(X)) -> s(s(dbl(X)))
a__add(0,X) -> mark(X)
a__add(s(X),Y) -> s(add(X,Y))
a__first(0,X) -> nil
a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
mark(terms(X)) -> a__terms(mark(X))
mark(sqr(X)) -> a__sqr(mark(X))
mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
mark(dbl(X)) -> a__dbl(mark(X))
mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(recip(X)) -> recip(mark(X))
mark(s(X)) -> s(X)
mark(0) -> 0
mark(nil) -> nil
a__terms(X) -> terms(X)
a__sqr(X) -> sqr(X)
a__add(X1,X2) -> add(X1,X2)
a__dbl(X) -> dbl(X)
a__first(X1,X2) -> first(X1,X2)
)

Submit to AProVE Web Frontend

Edit in AProVE Web Frontend