/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/Ex26_Luc03b_C.trs

The program

(VAR N X Y Z X1 X2)
(RULES 
active(terms(N)) -> mark(cons(recip(sqr(N)),terms(s(N))))
active(sqr(0)) -> mark(0)
active(sqr(s(X))) -> mark(s(add(sqr(X),dbl(X))))
active(dbl(0)) -> mark(0)
active(dbl(s(X))) -> mark(s(s(dbl(X))))
active(add(0,X)) -> mark(X)
active(add(s(X),Y)) -> mark(s(add(X,Y)))
active(first(0,X)) -> mark(nil)
active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
active(terms(X)) -> terms(active(X))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(recip(X)) -> recip(active(X))
active(sqr(X)) -> sqr(active(X))
active(add(X1,X2)) -> add(active(X1),X2)
active(add(X1,X2)) -> add(X1,active(X2))
active(dbl(X)) -> dbl(active(X))
active(first(X1,X2)) -> first(active(X1),X2)
active(first(X1,X2)) -> first(X1,active(X2))
terms(mark(X)) -> mark(terms(X))
cons(mark(X1),X2) -> mark(cons(X1,X2))
recip(mark(X)) -> mark(recip(X))
sqr(mark(X)) -> mark(sqr(X))
add(mark(X1),X2) -> mark(add(X1,X2))
add(X1,mark(X2)) -> mark(add(X1,X2))
dbl(mark(X)) -> mark(dbl(X))
first(mark(X1),X2) -> mark(first(X1,X2))
first(X1,mark(X2)) -> mark(first(X1,X2))
proper(terms(X)) -> terms(proper(X))
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(recip(X)) -> recip(proper(X))
proper(sqr(X)) -> sqr(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(add(X1,X2)) -> add(proper(X1),proper(X2))
proper(dbl(X)) -> dbl(proper(X))
proper(first(X1,X2)) -> first(proper(X1),proper(X2))
proper(nil) -> ok(nil)
terms(ok(X)) -> ok(terms(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
recip(ok(X)) -> ok(recip(X))
sqr(ok(X)) -> ok(sqr(X))
s(ok(X)) -> ok(s(X))
add(ok(X1),ok(X2)) -> ok(add(X1,X2))
dbl(ok(X)) -> ok(dbl(X))
first(ok(X1),ok(X2)) -> ok(first(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)

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