(VAR X Y Z X1 X2 X3) (RULES active(primes) -> mark(sieve(from(s(s(0))))) active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,Y))) -> mark(X) active(tail(cons(X,Y))) -> mark(Y) active(if(true,X,Y)) -> mark(X) active(if(false,X,Y)) -> mark(Y) active(filter(s(s(X)),cons(Y,Z))) -> mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))) active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y)))) mark(primes) -> active(primes) mark(sieve(X)) -> active(sieve(mark(X))) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) mark(0) -> active(0) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(head(X)) -> active(head(mark(X))) mark(tail(X)) -> active(tail(mark(X))) mark(if(X1,X2,X3)) -> active(if(mark(X1),X2,X3)) mark(true) -> active(true) mark(false) -> active(false) mark(filter(X1,X2)) -> active(filter(mark(X1),mark(X2))) mark(divides(X1,X2)) -> active(divides(mark(X1),mark(X2))) sieve(mark(X)) -> sieve(X) sieve(active(X)) -> sieve(X) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) head(mark(X)) -> head(X) head(active(X)) -> head(X) tail(mark(X)) -> tail(X) tail(active(X)) -> tail(X) if(mark(X1),X2,X3) -> if(X1,X2,X3) if(X1,mark(X2),X3) -> if(X1,X2,X3) if(X1,X2,mark(X3)) -> if(X1,X2,X3) if(active(X1),X2,X3) -> if(X1,X2,X3) if(X1,active(X2),X3) -> if(X1,X2,X3) if(X1,X2,active(X3)) -> if(X1,X2,X3) filter(mark(X1),X2) -> filter(X1,X2) filter(X1,mark(X2)) -> filter(X1,X2) filter(active(X1),X2) -> filter(X1,X2) filter(X1,active(X2)) -> filter(X1,X2) divides(mark(X1),X2) -> divides(X1,X2) divides(X1,mark(X2)) -> divides(X1,X2) divides(active(X1),X2) -> divides(X1,X2) divides(X1,active(X2)) -> divides(X1,X2) )