(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)))) active(sieve(X)) -> sieve(active(X)) active(from(X)) -> from(active(X)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(head(X)) -> head(active(X)) active(tail(X)) -> tail(active(X)) active(if(X1,X2,X3)) -> if(active(X1),X2,X3) active(filter(X1,X2)) -> filter(active(X1),X2) active(filter(X1,X2)) -> filter(X1,active(X2)) active(divides(X1,X2)) -> divides(active(X1),X2) active(divides(X1,X2)) -> divides(X1,active(X2)) sieve(mark(X)) -> mark(sieve(X)) from(mark(X)) -> mark(from(X)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) head(mark(X)) -> mark(head(X)) tail(mark(X)) -> mark(tail(X)) if(mark(X1),X2,X3) -> mark(if(X1,X2,X3)) filter(mark(X1),X2) -> mark(filter(X1,X2)) filter(X1,mark(X2)) -> mark(filter(X1,X2)) divides(mark(X1),X2) -> mark(divides(X1,X2)) divides(X1,mark(X2)) -> mark(divides(X1,X2)) proper(primes) -> ok(primes) proper(sieve(X)) -> sieve(proper(X)) proper(from(X)) -> from(proper(X)) proper(s(X)) -> s(proper(X)) proper(0) -> ok(0) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(head(X)) -> head(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3)) proper(true) -> ok(true) proper(false) -> ok(false) proper(filter(X1,X2)) -> filter(proper(X1),proper(X2)) proper(divides(X1,X2)) -> divides(proper(X1),proper(X2)) sieve(ok(X)) -> ok(sieve(X)) from(ok(X)) -> ok(from(X)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) head(ok(X)) -> ok(head(X)) tail(ok(X)) -> ok(tail(X)) if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3)) filter(ok(X1),ok(X2)) -> ok(filter(X1,X2)) divides(ok(X1),ok(X2)) -> ok(divides(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) )