MAYBE Time: 1.113892 TRS: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), filter(X1, X2, mark X3) -> mark filter(X1, X2, X3), filter(X1, mark X2, X3) -> mark filter(X1, X2, X3), filter(mark X1, X2, X3) -> mark filter(X1, X2, X3), filter(ok X1, ok X2, ok X3) -> ok filter(X1, X2, X3), active cons(X1, X2) -> cons(active X1, X2), active filter(X1, X2, X3) -> filter(X1, X2, active X3), active filter(X1, X2, X3) -> filter(X1, active X2, X3), active filter(X1, X2, X3) -> filter(active X1, X2, X3), active filter(cons(X, Y), 0(), M) -> mark cons(0(), filter(Y, M, M)), active filter(cons(X, Y), s N, M) -> mark cons(X, filter(Y, N, M)), active s X -> s active X, active sieve X -> sieve active X, active sieve cons(0(), Y) -> mark cons(0(), sieve Y), active sieve cons(s N, Y) -> mark cons(s N, sieve filter(Y, N, N)), active nats X -> nats active X, active nats N -> mark cons(N, nats s N), active zprimes() -> mark sieve nats s s 0(), s mark X -> mark s X, s ok X -> ok s X, sieve mark X -> mark sieve X, sieve ok X -> ok sieve X, nats mark X -> mark nats X, nats ok X -> ok nats X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper filter(X1, X2, X3) -> filter(proper X1, proper X2, proper X3), proper s X -> s proper X, proper sieve X -> sieve proper X, proper nats X -> nats proper X, proper zprimes() -> ok zprimes(), top mark X -> top proper X, top ok X -> top active X} DP: DP: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3), active# cons(X1, X2) -> cons#(active X1, X2), active# cons(X1, X2) -> active# X1, active# filter(X1, X2, X3) -> filter#(X1, X2, active X3), active# filter(X1, X2, X3) -> filter#(X1, active X2, X3), active# filter(X1, X2, X3) -> filter#(active X1, X2, X3), active# filter(X1, X2, X3) -> active# X1, active# filter(X1, X2, X3) -> active# X2, active# filter(X1, X2, X3) -> active# X3, active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M)), active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M), active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M)), active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M), active# s X -> active# X, active# s X -> s# active X, active# sieve X -> active# X, active# sieve X -> sieve# active X, active# sieve cons(0(), Y) -> cons#(0(), sieve Y), active# sieve cons(0(), Y) -> sieve# Y, active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N)), active# sieve cons(s N, Y) -> filter#(Y, N, N), active# sieve cons(s N, Y) -> sieve# filter(Y, N, N), active# nats X -> active# X, active# nats X -> nats# active X, active# nats N -> cons#(N, nats s N), active# nats N -> s# N, active# nats N -> nats# s N, active# zprimes() -> s# 0(), active# zprimes() -> s# s 0(), active# zprimes() -> sieve# nats s s 0(), active# zprimes() -> nats# s s 0(), s# mark X -> s# X, s# ok X -> s# X, sieve# mark X -> sieve# X, sieve# ok X -> sieve# X, nats# mark X -> nats# X, nats# ok X -> nats# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2), proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3), proper# filter(X1, X2, X3) -> proper# X1, proper# filter(X1, X2, X3) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X3, proper# s X -> s# proper X, proper# s X -> proper# X, proper# sieve X -> sieve# proper X, proper# sieve X -> proper# X, proper# nats X -> nats# proper X, proper# nats X -> proper# X, top# mark X -> proper# X, top# mark X -> top# proper X, top# ok X -> active# X, top# ok X -> top# active X} TRS: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), filter(X1, X2, mark X3) -> mark filter(X1, X2, X3), filter(X1, mark X2, X3) -> mark filter(X1, X2, X3), filter(mark X1, X2, X3) -> mark filter(X1, X2, X3), filter(ok X1, ok X2, ok X3) -> ok filter(X1, X2, X3), active cons(X1, X2) -> cons(active X1, X2), active filter(X1, X2, X3) -> filter(X1, X2, active X3), active filter(X1, X2, X3) -> filter(X1, active X2, X3), active filter(X1, X2, X3) -> filter(active X1, X2, X3), active filter(cons(X, Y), 0(), M) -> mark cons(0(), filter(Y, M, M)), active filter(cons(X, Y), s N, M) -> mark cons(X, filter(Y, N, M)), active s X -> s active X, active sieve X -> sieve active X, active sieve cons(0(), Y) -> mark cons(0(), sieve Y), active sieve cons(s N, Y) -> mark cons(s N, sieve filter(Y, N, N)), active nats X -> nats active X, active nats N -> mark cons(N, nats s N), active zprimes() -> mark sieve nats s s 0(), s mark X -> mark s X, s ok X -> ok s X, sieve mark X -> mark sieve X, sieve ok X -> ok sieve X, nats mark X -> mark nats X, nats ok X -> ok nats X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper filter(X1, X2, X3) -> filter(proper X1, proper X2, proper X3), proper s X -> s proper X, proper sieve X -> sieve proper X, proper nats X -> nats proper X, proper zprimes() -> ok zprimes(), top mark X -> top proper X, top ok X -> top active X} UR: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), filter(X1, X2, mark X3) -> mark filter(X1, X2, X3), filter(X1, mark X2, X3) -> mark filter(X1, X2, X3), filter(mark X1, X2, X3) -> mark filter(X1, X2, X3), filter(ok X1, ok X2, ok X3) -> ok filter(X1, X2, X3), active cons(X1, X2) -> cons(active X1, X2), active filter(X1, X2, X3) -> filter(X1, X2, active X3), active filter(X1, X2, X3) -> filter(X1, active X2, X3), active filter(X1, X2, X3) -> filter(active X1, X2, X3), active filter(cons(X, Y), 0(), M) -> mark cons(0(), filter(Y, M, M)), active filter(cons(X, Y), s N, M) -> mark cons(X, filter(Y, N, M)), active s X -> s active X, active sieve X -> sieve active X, active sieve cons(0(), Y) -> mark cons(0(), sieve Y), active sieve cons(s N, Y) -> mark cons(s N, sieve filter(Y, N, N)), active nats X -> nats active X, active nats N -> mark cons(N, nats s N), active zprimes() -> mark sieve nats s s 0(), s mark X -> mark s X, s ok X -> ok s X, sieve mark X -> mark sieve X, sieve ok X -> ok sieve X, nats mark X -> mark nats X, nats ok X -> ok nats X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper filter(X1, X2, X3) -> filter(proper X1, proper X2, proper X3), proper s X -> s proper X, proper sieve X -> sieve proper X, proper nats X -> nats proper X, proper zprimes() -> ok zprimes()} EDG: { (active# zprimes() -> nats# s s 0(), nats# ok X -> nats# X) (active# zprimes() -> nats# s s 0(), nats# mark X -> nats# X) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3)) (active# sieve cons(s N, Y) -> sieve# filter(Y, N, N), sieve# ok X -> sieve# X) (active# sieve cons(s N, Y) -> sieve# filter(Y, N, N), sieve# mark X -> sieve# X) (active# sieve cons(0(), Y) -> sieve# Y, sieve# ok X -> sieve# X) (active# sieve cons(0(), Y) -> sieve# Y, sieve# mark X -> sieve# X) (active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N)), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N)), cons#(mark X1, X2) -> cons#(X1, X2)) (filter#(X1, X2, mark X3) -> filter#(X1, X2, X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (filter#(X1, X2, mark X3) -> filter#(X1, X2, X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (filter#(X1, X2, mark X3) -> filter#(X1, X2, X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (filter#(X1, X2, mark X3) -> filter#(X1, X2, X3), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3)) (filter#(mark X1, X2, X3) -> filter#(X1, X2, X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (filter#(mark X1, X2, X3) -> filter#(X1, X2, X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (filter#(mark X1, X2, X3) -> filter#(X1, X2, X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (filter#(mark X1, X2, X3) -> filter#(X1, X2, X3), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(active X1, X2, X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(active X1, X2, X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(active X1, X2, X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(active X1, X2, X3), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3)) (active# sieve X -> active# X, active# zprimes() -> nats# s s 0()) (active# sieve X -> active# X, active# zprimes() -> sieve# nats s s 0()) (active# sieve X -> active# X, active# zprimes() -> s# s 0()) (active# sieve X -> active# X, active# zprimes() -> s# 0()) (active# sieve X -> active# X, active# nats N -> nats# s N) (active# sieve X -> active# X, active# nats N -> s# N) (active# sieve X -> active# X, active# nats N -> cons#(N, nats s N)) (active# sieve X -> active# X, active# nats X -> nats# active X) (active# sieve X -> active# X, active# nats X -> active# X) (active# sieve X -> active# X, active# sieve cons(s N, Y) -> sieve# filter(Y, N, N)) (active# sieve X -> active# X, active# sieve cons(s N, Y) -> filter#(Y, N, N)) (active# sieve X -> active# X, active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N))) (active# sieve X -> active# X, active# sieve cons(0(), Y) -> sieve# Y) (active# sieve X -> active# X, active# sieve cons(0(), Y) -> cons#(0(), sieve Y)) (active# sieve X -> active# X, active# sieve X -> sieve# active X) (active# sieve X -> active# X, active# sieve X -> active# X) (active# sieve X -> active# X, active# s X -> s# active X) (active# sieve X -> active# X, active# s X -> active# X) (active# sieve X -> active# X, active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M)) (active# sieve X -> active# X, active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M))) (active# sieve X -> active# X, active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M)) (active# sieve X -> active# X, active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M))) (active# sieve X -> active# X, active# filter(X1, X2, X3) -> active# X3) (active# sieve X -> active# X, active# filter(X1, X2, X3) -> active# X2) (active# sieve X -> active# X, active# filter(X1, X2, X3) -> active# X1) (active# sieve X -> active# X, active# filter(X1, X2, X3) -> filter#(active X1, X2, X3)) (active# sieve X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, active X2, X3)) (active# sieve X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, X2, active X3)) (active# sieve X -> active# X, active# cons(X1, X2) -> active# X1) (active# sieve X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (s# mark X -> s# X, s# ok X -> s# X) (s# mark X -> s# X, s# mark X -> s# X) (sieve# mark X -> sieve# X, sieve# ok X -> sieve# X) (sieve# mark X -> sieve# X, sieve# mark X -> sieve# X) (nats# mark X -> nats# X, nats# ok X -> nats# X) (nats# mark X -> nats# X, nats# mark X -> nats# X) (proper# s X -> proper# X, proper# nats X -> proper# X) (proper# s X -> proper# X, proper# nats X -> nats# proper X) (proper# s X -> proper# X, proper# sieve X -> proper# X) (proper# s X -> proper# X, proper# sieve X -> sieve# proper X) (proper# s X -> proper# X, proper# s X -> proper# X) (proper# s X -> proper# X, proper# s X -> s# proper X) (proper# s X -> proper# X, proper# filter(X1, X2, X3) -> proper# X3) (proper# s X -> proper# X, proper# filter(X1, X2, X3) -> proper# X2) (proper# s X -> proper# X, proper# filter(X1, X2, X3) -> proper# X1) (proper# s X -> proper# X, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# nats X -> proper# X, proper# nats X -> proper# X) (proper# nats X -> proper# X, proper# nats X -> nats# proper X) (proper# nats X -> proper# X, proper# sieve X -> proper# X) (proper# nats X -> proper# X, proper# sieve X -> sieve# proper X) (proper# nats X -> proper# X, proper# s X -> proper# X) (proper# nats X -> proper# X, proper# s X -> s# proper X) (proper# nats X -> proper# X, proper# filter(X1, X2, X3) -> proper# X3) (proper# nats X -> proper# X, proper# filter(X1, X2, X3) -> proper# X2) (proper# nats X -> proper# X, proper# filter(X1, X2, X3) -> proper# X1) (proper# nats X -> proper# X, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (proper# nats X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# nats X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# nats X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (top# ok X -> active# X, active# zprimes() -> nats# s s 0()) (top# ok X -> active# X, active# zprimes() -> sieve# nats s s 0()) (top# ok X -> active# X, active# zprimes() -> s# s 0()) (top# ok X -> active# X, active# zprimes() -> s# 0()) (top# ok X -> active# X, active# nats N -> nats# s N) (top# ok X -> active# X, active# nats N -> s# N) (top# ok X -> active# X, active# nats N -> cons#(N, nats s N)) (top# ok X -> active# X, active# nats X -> nats# active X) (top# ok X -> active# X, active# nats X -> active# X) (top# ok X -> active# X, active# sieve cons(s N, Y) -> sieve# filter(Y, N, N)) (top# ok X -> active# X, active# sieve cons(s N, Y) -> filter#(Y, N, N)) (top# ok X -> active# X, active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N))) (top# ok X -> active# X, active# sieve cons(0(), Y) -> sieve# Y) (top# ok X -> active# X, active# sieve cons(0(), Y) -> cons#(0(), sieve Y)) (top# ok X -> active# X, active# sieve X -> sieve# active X) (top# ok X -> active# X, active# sieve X -> active# X) (top# ok X -> active# X, active# s X -> s# active X) (top# ok X -> active# X, active# s X -> active# X) (top# ok X -> active# X, active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M)) (top# ok X -> active# X, active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M))) (top# ok X -> active# X, active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M)) (top# ok X -> active# X, active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M))) (top# ok X -> active# X, active# filter(X1, X2, X3) -> active# X3) (top# ok X -> active# X, active# filter(X1, X2, X3) -> active# X2) (top# ok X -> active# X, active# filter(X1, X2, X3) -> active# X1) (top# ok X -> active# X, active# filter(X1, X2, X3) -> filter#(active X1, X2, X3)) (top# ok X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, active X2, X3)) (top# ok X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, X2, active X3)) (top# ok X -> active# X, active# cons(X1, X2) -> active# X1) (top# ok X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M)), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M)), cons#(mark X1, X2) -> cons#(X1, X2)) (active# cons(X1, X2) -> active# X1, active# zprimes() -> nats# s s 0()) (active# cons(X1, X2) -> active# X1, active# zprimes() -> sieve# nats s s 0()) (active# cons(X1, X2) -> active# X1, active# zprimes() -> s# s 0()) (active# cons(X1, X2) -> active# X1, active# zprimes() -> s# 0()) (active# cons(X1, X2) -> active# X1, active# nats N -> nats# s N) (active# cons(X1, X2) -> active# X1, active# nats N -> s# N) (active# cons(X1, X2) -> active# X1, active# nats N -> cons#(N, nats s N)) (active# cons(X1, X2) -> active# X1, active# nats X -> nats# active X) (active# cons(X1, X2) -> active# X1, active# nats X -> active# X) (active# cons(X1, X2) -> active# X1, active# sieve cons(s N, Y) -> sieve# filter(Y, N, N)) (active# cons(X1, X2) -> active# X1, active# sieve cons(s N, Y) -> filter#(Y, N, N)) (active# cons(X1, X2) -> active# X1, active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N))) (active# cons(X1, X2) -> active# X1, active# sieve cons(0(), Y) -> sieve# Y) (active# cons(X1, X2) -> active# X1, active# sieve cons(0(), Y) -> cons#(0(), sieve Y)) (active# cons(X1, X2) -> active# X1, active# sieve X -> sieve# active X) (active# cons(X1, X2) -> active# X1, active# sieve X -> active# X) (active# cons(X1, X2) -> active# X1, active# s X -> s# active X) (active# cons(X1, X2) -> active# X1, active# s X -> active# X) (active# cons(X1, X2) -> active# X1, active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M)) (active# cons(X1, X2) -> active# X1, active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M))) (active# cons(X1, X2) -> active# X1, active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M)) (active# cons(X1, X2) -> active# X1, active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M))) (active# cons(X1, X2) -> active# X1, active# filter(X1, X2, X3) -> active# X3) (active# cons(X1, X2) -> active# X1, active# filter(X1, X2, X3) -> active# X2) (active# cons(X1, X2) -> active# X1, active# filter(X1, X2, X3) -> active# X1) (active# cons(X1, X2) -> active# X1, active# filter(X1, X2, X3) -> filter#(active X1, X2, X3)) (active# cons(X1, X2) -> active# X1, active# filter(X1, X2, X3) -> filter#(X1, active X2, X3)) (active# cons(X1, X2) -> active# X1, active# filter(X1, X2, X3) -> filter#(X1, X2, active X3)) (active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (proper# cons(X1, X2) -> proper# X1, proper# nats X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# nats X -> nats# proper X) (proper# cons(X1, X2) -> proper# X1, proper# sieve X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# sieve X -> sieve# proper X) (proper# cons(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# cons(X1, X2) -> proper# X1, proper# filter(X1, X2, X3) -> proper# X3) (proper# cons(X1, X2) -> proper# X1, proper# filter(X1, X2, X3) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# filter(X1, X2, X3) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# filter(X1, X2, X3) -> active# X3, active# zprimes() -> nats# s s 0()) (active# filter(X1, X2, X3) -> active# X3, active# zprimes() -> sieve# nats s s 0()) (active# filter(X1, X2, X3) -> active# X3, active# zprimes() -> s# s 0()) (active# filter(X1, X2, X3) -> active# X3, active# zprimes() -> s# 0()) (active# filter(X1, X2, X3) -> active# X3, active# nats N -> nats# s N) (active# filter(X1, X2, X3) -> active# X3, active# nats N -> s# N) (active# filter(X1, X2, X3) -> active# X3, active# nats N -> cons#(N, nats s N)) (active# filter(X1, X2, X3) -> active# X3, active# nats X -> nats# active X) (active# filter(X1, X2, X3) -> active# X3, active# nats X -> active# X) (active# filter(X1, X2, X3) -> active# X3, active# sieve cons(s N, Y) -> sieve# filter(Y, N, N)) (active# filter(X1, X2, X3) -> active# X3, active# sieve cons(s N, Y) -> filter#(Y, N, N)) (active# filter(X1, X2, X3) -> active# X3, active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N))) (active# filter(X1, X2, X3) -> active# X3, active# sieve cons(0(), Y) -> sieve# Y) (active# filter(X1, X2, X3) -> active# X3, active# sieve cons(0(), Y) -> cons#(0(), sieve Y)) (active# filter(X1, X2, X3) -> active# X3, active# sieve X -> sieve# active X) (active# filter(X1, X2, X3) -> active# X3, active# sieve X -> active# X) (active# filter(X1, X2, X3) -> active# X3, active# s X -> s# active X) (active# filter(X1, X2, X3) -> active# X3, active# s X -> active# X) (active# filter(X1, X2, X3) -> active# X3, active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M)) (active# filter(X1, X2, X3) -> active# X3, active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M))) (active# filter(X1, X2, X3) -> active# X3, active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M)) (active# filter(X1, X2, X3) -> active# X3, active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M))) (active# filter(X1, X2, X3) -> active# X3, active# filter(X1, X2, X3) -> active# X3) (active# filter(X1, X2, X3) -> active# X3, active# filter(X1, X2, X3) -> active# X2) (active# filter(X1, X2, X3) -> active# X3, active# filter(X1, X2, X3) -> active# X1) (active# filter(X1, X2, X3) -> active# X3, active# filter(X1, X2, X3) -> filter#(active X1, X2, X3)) (active# filter(X1, X2, X3) -> active# X3, active# filter(X1, X2, X3) -> filter#(X1, active X2, X3)) (active# filter(X1, X2, X3) -> active# X3, active# filter(X1, X2, X3) -> filter#(X1, X2, active X3)) (active# filter(X1, X2, X3) -> active# X3, active# cons(X1, X2) -> active# X1) (active# filter(X1, X2, X3) -> active# X3, active# cons(X1, X2) -> cons#(active X1, X2)) (active# nats N -> cons#(N, nats s N), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# nats N -> cons#(N, nats s N), cons#(mark X1, X2) -> cons#(X1, X2)) (active# nats N -> s# N, s# ok X -> s# X) (active# nats N -> s# N, s# mark X -> s# X) (active# nats N -> nats# s N, nats# ok X -> nats# X) (active# nats N -> nats# s N, nats# mark X -> nats# X) (active# s X -> s# active X, s# ok X -> s# X) (active# s X -> s# active X, s# mark X -> s# X) (active# nats X -> nats# active X, nats# ok X -> nats# X) (active# nats X -> nats# active X, nats# mark X -> nats# X) (proper# sieve X -> sieve# proper X, sieve# ok X -> sieve# X) (proper# sieve X -> sieve# proper X, sieve# mark X -> sieve# X) (top# mark X -> top# proper X, top# ok X -> top# active X) (top# mark X -> top# proper X, top# ok X -> active# X) (top# mark X -> top# proper X, top# mark X -> top# proper X) (top# mark X -> top# proper X, top# mark X -> proper# X) (active# filter(X1, X2, X3) -> active# X2, active# zprimes() -> nats# s s 0()) (active# filter(X1, X2, X3) -> active# X2, active# zprimes() -> sieve# nats s s 0()) (active# filter(X1, X2, X3) -> active# X2, active# zprimes() -> s# s 0()) (active# filter(X1, X2, X3) -> active# X2, active# zprimes() -> s# 0()) (active# filter(X1, X2, X3) -> active# X2, active# nats N -> nats# s N) (active# filter(X1, X2, X3) -> active# X2, active# nats N -> s# N) (active# filter(X1, X2, X3) -> active# X2, active# nats N -> cons#(N, nats s N)) (active# filter(X1, X2, X3) -> active# X2, active# nats X -> nats# active X) (active# filter(X1, X2, X3) -> active# X2, active# nats X -> active# X) (active# filter(X1, X2, X3) -> active# X2, active# sieve cons(s N, Y) -> sieve# filter(Y, N, N)) (active# filter(X1, X2, X3) -> active# X2, active# sieve cons(s N, Y) -> filter#(Y, N, N)) (active# filter(X1, X2, X3) -> active# X2, active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N))) (active# filter(X1, X2, X3) -> active# X2, active# sieve cons(0(), Y) -> sieve# Y) (active# filter(X1, X2, X3) -> active# X2, active# sieve cons(0(), Y) -> cons#(0(), sieve Y)) (active# filter(X1, X2, X3) -> active# X2, active# sieve X -> sieve# active X) (active# filter(X1, X2, X3) -> active# X2, active# sieve X -> active# X) (active# filter(X1, X2, X3) -> active# X2, active# s X -> s# active X) (active# filter(X1, X2, X3) -> active# X2, active# s X -> active# X) (active# filter(X1, X2, X3) -> active# X2, active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M)) (active# filter(X1, X2, X3) -> active# X2, active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M))) (active# filter(X1, X2, X3) -> active# X2, active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M)) (active# filter(X1, X2, X3) -> active# X2, active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M))) (active# filter(X1, X2, X3) -> active# X2, active# filter(X1, X2, X3) -> active# X3) (active# filter(X1, X2, X3) -> active# X2, active# filter(X1, X2, X3) -> active# X2) (active# filter(X1, X2, X3) -> active# X2, active# filter(X1, X2, X3) -> active# X1) (active# filter(X1, X2, X3) -> active# X2, active# filter(X1, X2, X3) -> filter#(active X1, X2, X3)) (active# filter(X1, X2, X3) -> active# X2, active# filter(X1, X2, X3) -> filter#(X1, active X2, X3)) (active# filter(X1, X2, X3) -> active# X2, active# filter(X1, X2, X3) -> filter#(X1, X2, active X3)) (active# filter(X1, X2, X3) -> active# X2, active# cons(X1, X2) -> active# X1) (active# filter(X1, X2, X3) -> active# X2, active# cons(X1, X2) -> cons#(active X1, X2)) (proper# filter(X1, X2, X3) -> proper# X2, proper# nats X -> proper# X) (proper# filter(X1, X2, X3) -> proper# X2, proper# nats X -> nats# proper X) (proper# filter(X1, X2, X3) -> proper# X2, proper# sieve X -> proper# X) (proper# filter(X1, X2, X3) -> proper# X2, proper# sieve X -> sieve# proper X) (proper# filter(X1, X2, X3) -> proper# X2, proper# s X -> proper# X) (proper# filter(X1, X2, X3) -> proper# X2, proper# s X -> s# proper X) (proper# filter(X1, X2, X3) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X3) (proper# filter(X1, X2, X3) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X2) (proper# filter(X1, X2, X3) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X1) (proper# filter(X1, X2, X3) -> proper# X2, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (proper# filter(X1, X2, X3) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# filter(X1, X2, X3) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# filter(X1, X2, X3) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# cons(X1, X2) -> cons#(active X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (active# cons(X1, X2) -> cons#(active X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (proper# cons(X1, X2) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X3) (proper# cons(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# cons(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# sieve X -> sieve# proper X) (proper# cons(X1, X2) -> proper# X2, proper# sieve X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# nats X -> nats# proper X) (proper# cons(X1, X2) -> proper# X2, proper# nats X -> proper# X) (top# ok X -> top# active X, top# mark X -> proper# X) (top# ok X -> top# active X, top# mark X -> top# proper X) (top# ok X -> top# active X, top# ok X -> active# X) (top# ok X -> top# active X, top# ok X -> top# active X) (proper# nats X -> nats# proper X, nats# mark X -> nats# X) (proper# nats X -> nats# proper X, nats# ok X -> nats# X) (proper# s X -> s# proper X, s# mark X -> s# X) (proper# s X -> s# proper X, s# ok X -> s# X) (active# sieve X -> sieve# active X, sieve# mark X -> sieve# X) (active# sieve X -> sieve# active X, sieve# ok X -> sieve# X) (proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3)) (proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(X1, X2, active X3), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(X1, X2, active X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(X1, X2, active X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(X1, X2, active X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (active# sieve cons(s N, Y) -> filter#(Y, N, N), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3)) (active# sieve cons(s N, Y) -> filter#(Y, N, N), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (active# sieve cons(s N, Y) -> filter#(Y, N, N), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (active# sieve cons(s N, Y) -> filter#(Y, N, N), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (proper# filter(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# filter(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> proper# X1) (proper# filter(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> proper# X2) (proper# filter(X1, X2, X3) -> proper# X3, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (proper# filter(X1, X2, X3) -> proper# X3, proper# filter(X1, X2, X3) -> proper# X1) (proper# filter(X1, X2, X3) -> proper# X3, proper# filter(X1, X2, X3) -> proper# X2) (proper# filter(X1, X2, X3) -> proper# X3, proper# filter(X1, X2, X3) -> proper# X3) (proper# filter(X1, X2, X3) -> proper# X3, proper# s X -> s# proper X) (proper# filter(X1, X2, X3) -> proper# X3, proper# s X -> proper# X) (proper# filter(X1, X2, X3) -> proper# X3, proper# sieve X -> sieve# proper X) (proper# filter(X1, X2, X3) -> proper# X3, proper# sieve X -> proper# X) (proper# filter(X1, X2, X3) -> proper# X3, proper# nats X -> nats# proper X) (proper# filter(X1, X2, X3) -> proper# X3, proper# nats X -> proper# X) (proper# filter(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# filter(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# filter(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# filter(X1, X2, X3) -> proper# X1, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (proper# filter(X1, X2, X3) -> proper# X1, proper# filter(X1, X2, X3) -> proper# X1) (proper# filter(X1, X2, X3) -> proper# X1, proper# filter(X1, X2, X3) -> proper# X2) (proper# filter(X1, X2, X3) -> proper# X1, proper# filter(X1, X2, X3) -> proper# X3) (proper# filter(X1, X2, X3) -> proper# X1, proper# s X -> s# proper X) (proper# filter(X1, X2, X3) -> proper# X1, proper# s X -> proper# X) (proper# filter(X1, X2, X3) -> proper# X1, proper# sieve X -> sieve# proper X) (proper# filter(X1, X2, X3) -> proper# X1, proper# sieve X -> proper# X) (proper# filter(X1, X2, X3) -> proper# X1, proper# nats X -> nats# proper X) (proper# filter(X1, X2, X3) -> proper# X1, proper# nats X -> proper# X) (active# filter(X1, X2, X3) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# filter(X1, X2, X3) -> active# X1, active# cons(X1, X2) -> active# X1) (active# filter(X1, X2, X3) -> active# X1, active# filter(X1, X2, X3) -> filter#(X1, X2, active X3)) (active# filter(X1, X2, X3) -> active# X1, active# filter(X1, X2, X3) -> filter#(X1, active X2, X3)) (active# filter(X1, X2, X3) -> active# X1, active# filter(X1, X2, X3) -> filter#(active X1, X2, X3)) (active# filter(X1, X2, X3) -> active# X1, active# filter(X1, X2, X3) -> active# X1) (active# filter(X1, X2, X3) -> active# X1, active# filter(X1, X2, X3) -> active# X2) (active# filter(X1, X2, X3) -> active# X1, active# filter(X1, X2, X3) -> active# X3) (active# filter(X1, X2, X3) -> active# X1, active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M))) (active# filter(X1, X2, X3) -> active# X1, active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M)) (active# filter(X1, X2, X3) -> active# X1, active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M))) (active# filter(X1, X2, X3) -> active# X1, active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M)) (active# filter(X1, X2, X3) -> active# X1, active# s X -> active# X) (active# filter(X1, X2, X3) -> active# X1, active# s X -> s# active X) (active# filter(X1, X2, X3) -> active# X1, active# sieve X -> active# X) (active# filter(X1, X2, X3) -> active# X1, active# sieve X -> sieve# active X) (active# filter(X1, X2, X3) -> active# X1, active# sieve cons(0(), Y) -> cons#(0(), sieve Y)) (active# filter(X1, X2, X3) -> active# X1, active# sieve cons(0(), Y) -> sieve# Y) (active# filter(X1, X2, X3) -> active# X1, active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N))) (active# filter(X1, X2, X3) -> active# X1, active# sieve cons(s N, Y) -> filter#(Y, N, N)) (active# filter(X1, X2, X3) -> active# X1, active# sieve cons(s N, Y) -> sieve# filter(Y, N, N)) (active# filter(X1, X2, X3) -> active# X1, active# nats X -> active# X) (active# filter(X1, X2, X3) -> active# X1, active# nats X -> nats# active X) (active# filter(X1, X2, X3) -> active# X1, active# nats N -> cons#(N, nats s N)) (active# filter(X1, X2, X3) -> active# X1, active# nats N -> s# N) (active# filter(X1, X2, X3) -> active# X1, active# nats N -> nats# s N) (active# filter(X1, X2, X3) -> active# X1, active# zprimes() -> s# 0()) (active# filter(X1, X2, X3) -> active# X1, active# zprimes() -> s# s 0()) (active# filter(X1, X2, X3) -> active# X1, active# zprimes() -> sieve# nats s s 0()) (active# filter(X1, X2, X3) -> active# X1, active# zprimes() -> nats# s s 0()) (active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M)), cons#(mark X1, X2) -> cons#(X1, X2)) (active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M)), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# zprimes() -> s# 0(), s# mark X -> s# X) (active# zprimes() -> s# 0(), s# ok X -> s# X) (top# mark X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (top# mark X -> proper# X, proper# filter(X1, X2, X3) -> proper# X1) (top# mark X -> proper# X, proper# filter(X1, X2, X3) -> proper# X2) (top# mark X -> proper# X, proper# filter(X1, X2, X3) -> proper# X3) (top# mark X -> proper# X, proper# s X -> s# proper X) (top# mark X -> proper# X, proper# s X -> proper# X) (top# mark X -> proper# X, proper# sieve X -> sieve# proper X) (top# mark X -> proper# X, proper# sieve X -> proper# X) (top# mark X -> proper# X, proper# nats X -> nats# proper X) (top# mark X -> proper# X, proper# nats X -> proper# X) (proper# sieve X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# sieve X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# sieve X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# sieve X -> proper# X, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (proper# sieve X -> proper# X, proper# filter(X1, X2, X3) -> proper# X1) (proper# sieve X -> proper# X, proper# filter(X1, X2, X3) -> proper# X2) (proper# sieve X -> proper# X, proper# filter(X1, X2, X3) -> proper# X3) (proper# sieve X -> proper# X, proper# s X -> s# proper X) (proper# sieve X -> proper# X, proper# s X -> proper# X) (proper# sieve X -> proper# X, proper# sieve X -> sieve# proper X) (proper# sieve X -> proper# X, proper# sieve X -> proper# X) (proper# sieve X -> proper# X, proper# nats X -> nats# proper X) (proper# sieve X -> proper# X, proper# nats X -> proper# X) (nats# ok X -> nats# X, nats# mark X -> nats# X) (nats# ok X -> nats# X, nats# ok X -> nats# X) (sieve# ok X -> sieve# X, sieve# mark X -> sieve# X) (sieve# ok X -> sieve# X, sieve# ok X -> sieve# X) (s# ok X -> s# X, s# mark X -> s# X) (s# ok X -> s# X, s# ok X -> s# X) (active# nats X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# nats X -> active# X, active# cons(X1, X2) -> active# X1) (active# nats X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, X2, active X3)) (active# nats X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, active X2, X3)) (active# nats X -> active# X, active# filter(X1, X2, X3) -> filter#(active X1, X2, X3)) (active# nats X -> active# X, active# filter(X1, X2, X3) -> active# X1) (active# nats X -> active# X, active# filter(X1, X2, X3) -> active# X2) (active# nats X -> active# X, active# filter(X1, X2, X3) -> active# X3) (active# nats X -> active# X, active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M))) (active# nats X -> active# X, active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M)) (active# nats X -> active# X, active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M))) (active# nats X -> active# X, active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M)) (active# nats X -> active# X, active# s X -> active# X) (active# nats X -> active# X, active# s X -> s# active X) (active# nats X -> active# X, active# sieve X -> active# X) (active# nats X -> active# X, active# sieve X -> sieve# active X) (active# nats X -> active# X, active# sieve cons(0(), Y) -> cons#(0(), sieve Y)) (active# nats X -> active# X, active# sieve cons(0(), Y) -> sieve# Y) (active# nats X -> active# X, active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N))) (active# nats X -> active# X, active# sieve cons(s N, Y) -> filter#(Y, N, N)) (active# nats X -> active# X, active# sieve cons(s N, Y) -> sieve# filter(Y, N, N)) (active# nats X -> active# X, active# nats X -> active# X) (active# nats X -> active# X, active# nats X -> nats# active X) (active# nats X -> active# X, active# nats N -> cons#(N, nats s N)) (active# nats X -> active# X, active# nats N -> s# N) (active# nats X -> active# X, active# nats N -> nats# s N) (active# nats X -> active# X, active# zprimes() -> s# 0()) (active# nats X -> active# X, active# zprimes() -> s# s 0()) (active# nats X -> active# X, active# zprimes() -> sieve# nats s s 0()) (active# nats X -> active# X, active# zprimes() -> nats# s s 0()) (active# s X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# s X -> active# X, active# cons(X1, X2) -> active# X1) (active# s X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, X2, active X3)) (active# s X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, active X2, X3)) (active# s X -> active# X, active# filter(X1, X2, X3) -> filter#(active X1, X2, X3)) (active# s X -> active# X, active# filter(X1, X2, X3) -> active# X1) (active# s X -> active# X, active# filter(X1, X2, X3) -> active# X2) (active# s X -> active# X, active# filter(X1, X2, X3) -> active# X3) (active# s X -> active# X, active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M))) (active# s X -> active# X, active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M)) (active# s X -> active# X, active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M))) (active# s X -> active# X, active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M)) (active# s X -> active# X, active# s X -> active# X) (active# s X -> active# X, active# s X -> s# active X) (active# s X -> active# X, active# sieve X -> active# X) (active# s X -> active# X, active# sieve X -> sieve# active X) (active# s X -> active# X, active# sieve cons(0(), Y) -> cons#(0(), sieve Y)) (active# s X -> active# X, active# sieve cons(0(), Y) -> sieve# Y) (active# s X -> active# X, active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N))) (active# s X -> active# X, active# sieve cons(s N, Y) -> filter#(Y, N, N)) (active# s X -> active# X, active# sieve cons(s N, Y) -> sieve# filter(Y, N, N)) (active# s X -> active# X, active# nats X -> active# X) (active# s X -> active# X, active# nats X -> nats# active X) (active# s X -> active# X, active# nats N -> cons#(N, nats s N)) (active# s X -> active# X, active# nats N -> s# N) (active# s X -> active# X, active# nats N -> nats# s N) (active# s X -> active# X, active# zprimes() -> s# 0()) (active# s X -> active# X, active# zprimes() -> s# s 0()) (active# s X -> active# X, active# zprimes() -> sieve# nats s s 0()) (active# s X -> active# X, active# zprimes() -> nats# s s 0()) (filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3)) (filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (filter#(X1, mark X2, X3) -> filter#(X1, X2, X3), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3)) (filter#(X1, mark X2, X3) -> filter#(X1, X2, X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (filter#(X1, mark X2, X3) -> filter#(X1, X2, X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (filter#(X1, mark X2, X3) -> filter#(X1, X2, X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(X1, active X2, X3), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(X1, active X2, X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(X1, active X2, X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(X1, active X2, X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (proper# cons(X1, X2) -> cons#(proper X1, proper X2), cons#(mark X1, X2) -> cons#(X1, X2)) (proper# cons(X1, X2) -> cons#(proper X1, proper X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# sieve cons(0(), Y) -> cons#(0(), sieve Y), cons#(mark X1, X2) -> cons#(X1, X2)) (active# sieve cons(0(), Y) -> cons#(0(), sieve Y), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3)) (active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# zprimes() -> s# s 0(), s# mark X -> s# X) (active# zprimes() -> s# s 0(), s# ok X -> s# X) (active# zprimes() -> sieve# nats s s 0(), sieve# mark X -> sieve# X) (active# zprimes() -> sieve# nats s s 0(), sieve# ok X -> sieve# X) } EDG: { (cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (active# sieve cons(s N, Y) -> sieve# filter(Y, N, N), sieve# ok X -> sieve# X) (active# sieve cons(s N, Y) -> sieve# filter(Y, N, N), sieve# mark X -> sieve# X) (active# sieve cons(0(), Y) -> sieve# Y, sieve# ok X -> sieve# X) (active# sieve cons(0(), Y) -> sieve# Y, sieve# mark X -> sieve# X) (active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N)), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N)), cons#(mark X1, X2) -> cons#(X1, X2)) (filter#(X1, X2, mark X3) -> filter#(X1, X2, X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (filter#(X1, X2, mark X3) -> filter#(X1, X2, X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (filter#(X1, X2, mark X3) -> filter#(X1, X2, X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (filter#(X1, X2, mark X3) -> filter#(X1, X2, X3), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3)) (filter#(mark X1, X2, X3) -> filter#(X1, X2, X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (filter#(mark X1, X2, X3) -> filter#(X1, X2, X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (filter#(mark X1, X2, X3) -> filter#(X1, X2, X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (filter#(mark X1, X2, X3) -> filter#(X1, X2, X3), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(active X1, X2, X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(active X1, X2, X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (active# sieve X -> active# X, active# zprimes() -> nats# s s 0()) (active# sieve X -> active# X, active# zprimes() -> sieve# nats s s 0()) (active# sieve X -> active# X, active# zprimes() -> s# s 0()) (active# sieve X -> active# X, active# zprimes() -> s# 0()) (active# sieve X -> active# X, active# nats N -> nats# s N) (active# sieve X -> active# X, active# nats N -> s# N) (active# sieve X -> active# X, active# nats N -> cons#(N, nats s N)) (active# sieve X -> active# X, active# nats X -> nats# active X) (active# sieve X -> active# X, active# nats X -> active# X) (active# sieve X -> active# X, active# sieve cons(s N, Y) -> sieve# filter(Y, N, N)) (active# sieve X -> active# X, active# sieve cons(s N, Y) -> filter#(Y, N, N)) (active# sieve X -> active# X, active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N))) (active# sieve X -> active# X, active# sieve cons(0(), Y) -> sieve# Y) (active# sieve X -> active# X, active# sieve cons(0(), Y) -> cons#(0(), sieve Y)) (active# sieve X -> active# X, active# sieve X -> sieve# active X) (active# sieve X -> active# X, active# sieve X -> active# X) (active# sieve X -> active# X, active# s X -> s# active X) (active# sieve X -> active# X, active# s X -> active# X) (active# sieve X -> active# X, active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M)) (active# sieve X -> active# X, active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M))) (active# sieve X -> active# X, active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M)) (active# sieve X -> active# X, active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M))) (active# sieve X -> active# X, active# filter(X1, X2, X3) -> active# X3) (active# sieve X -> active# X, active# filter(X1, X2, X3) -> active# X2) (active# sieve X -> active# X, active# filter(X1, X2, X3) -> active# X1) (active# sieve X -> active# X, active# filter(X1, X2, X3) -> filter#(active X1, X2, X3)) (active# sieve X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, active X2, X3)) (active# sieve X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, X2, active X3)) (active# sieve X -> active# X, active# cons(X1, X2) -> active# X1) (active# sieve X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (s# mark X -> s# X, s# ok X -> s# X) (s# mark X -> s# X, s# mark X -> s# X) (sieve# mark X -> sieve# X, sieve# ok X -> sieve# X) (sieve# mark X -> sieve# X, sieve# mark X -> sieve# X) (nats# mark X -> nats# X, nats# ok X -> nats# X) (nats# mark X -> nats# X, nats# mark X -> nats# X) (proper# s X -> proper# X, proper# nats X -> proper# X) (proper# s X -> proper# X, proper# nats X -> nats# proper X) (proper# s X -> proper# X, proper# sieve X -> proper# X) (proper# s X -> proper# X, proper# sieve X -> sieve# proper X) (proper# s X -> proper# X, proper# s X -> proper# X) (proper# s X -> proper# X, proper# s X -> s# proper X) (proper# s X -> proper# X, proper# filter(X1, X2, X3) -> proper# X3) (proper# s X -> proper# X, proper# filter(X1, X2, X3) -> proper# X2) (proper# s X -> proper# X, proper# filter(X1, X2, X3) -> proper# X1) (proper# s X -> proper# X, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# nats X -> proper# X, proper# nats X -> proper# X) (proper# nats X -> proper# X, proper# nats X -> nats# proper X) (proper# nats X -> proper# X, proper# sieve X -> proper# X) (proper# nats X -> proper# X, proper# sieve X -> sieve# proper X) (proper# nats X -> proper# X, proper# s X -> proper# X) (proper# nats X -> proper# X, proper# s X -> s# proper X) (proper# nats X -> proper# X, proper# filter(X1, X2, X3) -> proper# X3) (proper# nats X -> proper# X, proper# filter(X1, X2, X3) -> proper# X2) (proper# nats X -> proper# X, proper# filter(X1, X2, X3) -> proper# X1) (proper# nats X -> proper# X, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (proper# nats X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# nats X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# nats X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (top# ok X -> active# X, active# zprimes() -> nats# s s 0()) (top# ok X -> active# X, active# zprimes() -> sieve# nats s s 0()) (top# ok X -> active# X, active# zprimes() -> s# s 0()) (top# ok X -> active# X, active# zprimes() -> s# 0()) (top# ok X -> active# X, active# nats N -> nats# s N) (top# ok X -> active# X, active# nats N -> s# N) (top# ok X -> active# X, active# nats N -> cons#(N, nats s N)) (top# ok X -> active# X, active# nats X -> nats# active X) (top# ok X -> active# X, active# nats X -> active# X) (top# ok X -> active# X, active# sieve cons(s N, Y) -> sieve# filter(Y, N, N)) (top# ok X -> active# X, active# sieve cons(s N, Y) -> filter#(Y, N, N)) (top# ok X -> active# X, active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N))) (top# ok X -> active# X, active# sieve cons(0(), Y) -> sieve# Y) (top# ok X -> active# X, active# sieve cons(0(), Y) -> cons#(0(), sieve Y)) (top# ok X -> active# X, active# sieve X -> sieve# active X) (top# ok X -> active# X, active# sieve X -> active# X) (top# ok X -> active# X, active# s X -> s# active X) (top# ok X -> active# X, active# s X -> active# X) (top# ok X -> active# X, active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M)) (top# ok X -> active# X, active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M))) (top# ok X -> active# X, active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M)) (top# ok X -> active# X, active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M))) (top# ok X -> active# X, active# filter(X1, X2, X3) -> active# X3) (top# ok X -> active# X, active# filter(X1, X2, X3) -> active# X2) (top# ok X -> active# X, active# filter(X1, X2, X3) -> active# X1) (top# ok X -> active# X, active# filter(X1, X2, X3) -> filter#(active X1, X2, X3)) (top# ok X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, active X2, X3)) (top# ok X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, X2, active X3)) (top# ok X -> active# X, active# cons(X1, X2) -> active# X1) (top# ok X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# cons(X1, X2) -> active# X1, active# zprimes() -> nats# s s 0()) (active# cons(X1, X2) -> active# X1, active# zprimes() -> sieve# nats s s 0()) (active# cons(X1, X2) -> active# X1, active# zprimes() -> s# s 0()) (active# cons(X1, X2) -> active# X1, active# zprimes() -> s# 0()) (active# cons(X1, X2) -> active# X1, active# nats N -> nats# s N) (active# cons(X1, X2) -> active# X1, active# nats N -> s# N) (active# cons(X1, X2) -> active# X1, active# nats N -> cons#(N, nats s N)) (active# cons(X1, X2) -> active# X1, active# nats X -> nats# active X) (active# cons(X1, X2) -> active# X1, active# nats X -> active# X) (active# cons(X1, X2) -> active# X1, active# sieve cons(s N, Y) -> sieve# filter(Y, N, N)) (active# cons(X1, X2) -> active# X1, active# sieve cons(s N, Y) -> 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X3) -> filter#(X1, X2, active X3)) (active# filter(X1, X2, X3) -> active# X3, active# cons(X1, X2) -> active# X1) (active# filter(X1, X2, X3) -> active# X3, active# cons(X1, X2) -> cons#(active X1, X2)) (active# nats N -> nats# s N, nats# ok X -> nats# X) (active# nats N -> nats# s N, nats# mark X -> nats# X) (active# s X -> s# active X, s# ok X -> s# X) (active# s X -> s# active X, s# mark X -> s# X) (active# nats X -> nats# active X, nats# ok X -> nats# X) (active# nats X -> nats# active X, nats# mark X -> nats# X) (proper# sieve X -> sieve# proper X, sieve# ok X -> sieve# X) (proper# sieve X -> sieve# proper X, sieve# mark X -> sieve# X) (top# mark X -> top# proper X, top# ok X -> top# active X) (top# mark X -> top# proper X, top# ok X -> active# X) (top# mark X -> top# proper X, top# mark X -> top# proper X) (top# mark X -> top# proper X, top# mark X -> proper# X) (active# filter(X1, X2, X3) -> active# X2, active# zprimes() -> nats# s s 0()) (active# filter(X1, X2, X3) -> active# 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(proper# filter(X1, X2, X3) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X2) (proper# filter(X1, X2, X3) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X1) (proper# filter(X1, X2, X3) -> proper# X2, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (proper# filter(X1, X2, X3) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# filter(X1, X2, X3) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# filter(X1, X2, X3) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# cons(X1, X2) -> cons#(active X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (active# cons(X1, X2) -> cons#(active X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (proper# cons(X1, X2) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X3) (proper# cons(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# cons(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# sieve X -> sieve# proper X) (proper# cons(X1, X2) -> proper# X2, proper# sieve X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# nats X -> nats# proper X) (proper# cons(X1, X2) -> proper# X2, proper# nats X -> proper# X) (top# ok X -> top# active X, top# mark X -> proper# X) (top# ok X -> top# active X, top# mark X -> top# proper X) (top# ok X -> top# active X, top# ok X -> active# X) (top# ok X -> top# active X, top# ok X -> top# active X) (proper# nats X -> nats# proper X, nats# mark X -> nats# X) (proper# nats X -> 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-> filter#(Y, N, N), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (proper# filter(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# filter(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> proper# X1) (proper# filter(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> proper# X2) (proper# filter(X1, X2, X3) -> proper# X3, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (proper# filter(X1, X2, X3) -> proper# X3, proper# filter(X1, X2, X3) -> proper# X1) (proper# filter(X1, X2, X3) -> proper# X3, proper# filter(X1, X2, X3) -> proper# X2) (proper# filter(X1, X2, X3) -> proper# X3, proper# filter(X1, X2, X3) -> proper# X3) (proper# filter(X1, X2, X3) -> proper# X3, proper# s X -> s# proper X) (proper# filter(X1, X2, X3) -> proper# X3, proper# s X -> proper# X) (proper# filter(X1, X2, X3) -> proper# X3, proper# sieve X -> sieve# proper X) (proper# filter(X1, X2, X3) -> proper# X3, proper# sieve X -> proper# X) (proper# filter(X1, X2, X3) -> proper# X3, proper# nats X -> nats# proper X) (proper# filter(X1, X2, X3) -> proper# X3, proper# nats X -> proper# X) (proper# filter(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# filter(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# filter(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# filter(X1, X2, X3) -> proper# X1, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (proper# filter(X1, X2, X3) -> proper# X1, proper# filter(X1, X2, X3) -> proper# X1) (proper# filter(X1, X2, X3) -> proper# X1, proper# filter(X1, X2, X3) -> proper# X2) (proper# filter(X1, X2, X3) -> proper# X1, proper# filter(X1, X2, X3) -> proper# X3) (proper# filter(X1, X2, X3) -> proper# X1, proper# s X -> s# proper X) (proper# filter(X1, X2, X3) -> proper# X1, proper# s X -> proper# X) (proper# filter(X1, X2, X3) -> proper# X1, proper# sieve X -> sieve# proper X) (proper# filter(X1, X2, X3) -> proper# X1, proper# sieve X -> proper# X) (proper# filter(X1, X2, X3) -> proper# X1, proper# nats X -> nats# proper X) (proper# filter(X1, X2, X3) -> proper# X1, proper# nats X -> proper# X) (active# filter(X1, X2, X3) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# filter(X1, X2, X3) -> active# X1, active# cons(X1, X2) -> active# X1) (active# filter(X1, X2, X3) -> active# X1, active# filter(X1, X2, X3) -> filter#(X1, X2, active X3)) (active# filter(X1, X2, X3) -> active# X1, active# filter(X1, X2, X3) -> filter#(X1, active X2, X3)) (active# filter(X1, X2, X3) -> active# X1, active# filter(X1, X2, X3) -> filter#(active X1, X2, X3)) (active# filter(X1, X2, X3) -> active# X1, active# filter(X1, X2, X3) -> active# X1) (active# filter(X1, X2, X3) -> active# X1, active# filter(X1, X2, X3) -> active# X2) (active# filter(X1, X2, X3) -> active# X1, active# filter(X1, X2, X3) -> active# X3) (active# filter(X1, X2, X3) -> active# X1, active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M))) (active# filter(X1, X2, X3) -> active# X1, active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M)) (active# filter(X1, X2, X3) -> active# X1, active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M))) (active# filter(X1, X2, X3) -> active# X1, active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M)) (active# filter(X1, X2, X3) -> active# X1, active# s X -> active# X) (active# filter(X1, X2, X3) -> active# X1, active# s X -> s# active X) (active# filter(X1, X2, X3) -> active# X1, active# sieve X -> active# X) (active# filter(X1, X2, X3) -> active# X1, active# sieve X -> sieve# active X) (active# filter(X1, X2, X3) -> active# X1, active# sieve cons(0(), Y) -> cons#(0(), sieve Y)) (active# filter(X1, X2, X3) -> active# X1, active# sieve cons(0(), Y) -> sieve# Y) (active# filter(X1, X2, X3) -> active# X1, active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N))) (active# filter(X1, X2, X3) -> active# X1, active# sieve cons(s N, Y) -> filter#(Y, N, N)) (active# filter(X1, X2, X3) -> active# X1, active# sieve cons(s N, Y) -> sieve# filter(Y, N, N)) (active# filter(X1, X2, X3) -> active# X1, active# nats X -> active# X) (active# filter(X1, X2, X3) -> active# X1, active# nats X -> nats# active X) (active# filter(X1, X2, X3) -> active# X1, active# nats N -> cons#(N, nats s N)) (active# filter(X1, X2, X3) -> active# X1, active# nats N -> s# N) (active# filter(X1, X2, X3) -> active# X1, active# nats N -> nats# s N) (active# filter(X1, X2, X3) -> active# X1, active# zprimes() -> s# 0()) (active# filter(X1, X2, X3) -> active# X1, active# zprimes() -> s# s 0()) (active# filter(X1, X2, X3) -> active# X1, active# zprimes() -> sieve# nats s s 0()) (active# filter(X1, X2, X3) -> active# X1, active# zprimes() -> nats# s s 0()) (active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M)), cons#(ok X1, ok X2) -> cons#(X1, X2)) (top# mark X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (top# mark X -> proper# X, proper# filter(X1, X2, X3) -> proper# X1) (top# mark X -> proper# X, proper# filter(X1, X2, X3) -> proper# X2) (top# mark X -> proper# X, proper# filter(X1, X2, X3) -> proper# X3) (top# mark X -> proper# X, proper# s X -> s# proper X) (top# mark X -> proper# X, proper# s X -> proper# X) (top# mark X -> proper# X, proper# sieve X -> sieve# proper X) (top# mark X -> proper# X, proper# sieve X -> proper# X) (top# mark X -> proper# X, proper# nats X -> nats# proper X) (top# mark X -> proper# X, proper# nats X -> proper# X) (proper# sieve X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# sieve X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# sieve X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# sieve X -> proper# X, proper# filter(X1, X2, X3) -> filter#(proper X1, proper X2, proper X3)) (proper# sieve X -> proper# X, proper# filter(X1, X2, X3) -> proper# X1) (proper# sieve X -> proper# X, proper# filter(X1, X2, X3) -> proper# X2) (proper# sieve X -> proper# X, proper# filter(X1, X2, X3) -> proper# X3) (proper# sieve X -> proper# X, proper# s X -> s# proper X) (proper# sieve X -> proper# X, proper# s X -> proper# X) (proper# sieve X -> proper# X, proper# sieve X -> sieve# proper X) (proper# sieve X -> proper# X, proper# sieve X -> proper# X) (proper# sieve X -> proper# X, proper# nats X -> nats# proper X) (proper# sieve X -> proper# X, proper# nats X -> proper# X) (nats# ok X -> nats# X, nats# mark X -> nats# X) (nats# ok X -> nats# X, nats# ok X -> nats# X) (sieve# ok X -> sieve# X, sieve# mark X -> sieve# X) (sieve# ok X -> sieve# X, sieve# ok X -> sieve# X) (s# ok X -> s# X, s# mark X -> s# X) (s# ok X -> s# X, s# ok X -> s# X) (active# nats X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# nats X -> active# X, active# cons(X1, X2) -> active# X1) (active# nats X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, X2, active X3)) (active# nats X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, active X2, X3)) (active# nats X -> active# X, active# filter(X1, X2, X3) -> filter#(active X1, X2, X3)) (active# nats X -> active# X, active# filter(X1, X2, X3) -> active# X1) (active# nats X -> active# X, active# filter(X1, X2, X3) -> active# X2) (active# nats X -> active# X, active# filter(X1, X2, X3) -> active# X3) (active# nats X -> active# X, active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M))) (active# nats X -> active# X, active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M)) (active# nats X -> active# X, active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M))) (active# nats X -> active# X, active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M)) (active# nats X -> active# X, active# s X -> active# X) (active# nats X -> active# X, active# s X -> s# active X) (active# nats X -> active# X, active# sieve X -> active# X) (active# nats X -> active# X, active# sieve X -> sieve# active X) (active# nats X -> active# X, active# sieve cons(0(), Y) -> cons#(0(), sieve Y)) (active# nats X -> active# X, active# sieve cons(0(), Y) -> sieve# Y) (active# nats X -> active# X, active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N))) (active# nats X -> active# X, active# sieve cons(s N, Y) -> filter#(Y, N, N)) (active# nats X -> active# X, active# sieve cons(s N, Y) -> sieve# filter(Y, N, N)) (active# nats X -> active# X, active# nats X -> active# X) (active# nats X -> active# X, active# nats X -> nats# active X) (active# nats X -> active# X, active# nats N -> cons#(N, nats s N)) (active# nats X -> active# X, active# nats N -> s# N) (active# nats X -> active# X, active# nats N -> nats# s N) (active# nats X -> active# X, active# zprimes() -> s# 0()) (active# nats X -> active# X, active# zprimes() -> s# s 0()) (active# nats X -> active# X, active# zprimes() -> sieve# nats s s 0()) (active# nats X -> active# X, active# zprimes() -> nats# s s 0()) (active# s X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# s X -> active# X, active# cons(X1, X2) -> active# X1) (active# s X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, X2, active X3)) (active# s X -> active# X, active# filter(X1, X2, X3) -> filter#(X1, active X2, X3)) (active# s X -> active# X, active# filter(X1, X2, X3) -> filter#(active X1, X2, X3)) (active# s X -> active# X, active# filter(X1, X2, X3) -> active# X1) (active# s X -> active# X, active# filter(X1, X2, X3) -> active# X2) (active# s X -> active# X, active# filter(X1, X2, X3) -> active# X3) (active# s X -> active# X, active# filter(cons(X, Y), 0(), M) -> cons#(0(), filter(Y, M, M))) (active# s X -> active# X, active# filter(cons(X, Y), 0(), M) -> filter#(Y, M, M)) (active# s X -> active# X, active# filter(cons(X, Y), s N, M) -> cons#(X, filter(Y, N, M))) (active# s X -> active# X, active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M)) (active# s X -> active# X, active# s X -> active# X) (active# s X -> active# X, active# s X -> s# active X) (active# s X -> active# X, active# sieve X -> active# X) (active# s X -> active# X, active# sieve X -> sieve# active X) (active# s X -> active# X, active# sieve cons(0(), Y) -> cons#(0(), sieve Y)) (active# s X -> active# X, active# sieve cons(0(), Y) -> sieve# Y) (active# s X -> active# X, active# sieve cons(s N, Y) -> cons#(s N, sieve filter(Y, N, N))) (active# s X -> active# X, active# sieve cons(s N, Y) -> filter#(Y, N, N)) (active# s X -> active# X, active# sieve cons(s N, Y) -> sieve# filter(Y, N, N)) (active# s X -> active# X, active# nats X -> active# X) (active# s X -> active# X, active# nats X -> nats# active X) (active# s X -> active# X, active# nats N -> cons#(N, nats s N)) (active# s X -> active# X, active# nats N -> s# N) (active# s X -> active# X, active# nats N -> nats# s N) (active# s X -> active# X, active# zprimes() -> s# 0()) (active# s X -> active# X, active# zprimes() -> s# s 0()) (active# s X -> active# X, active# zprimes() -> sieve# nats s s 0()) (active# s X -> active# X, active# zprimes() -> nats# s s 0()) (filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3)) (filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (filter#(X1, mark X2, X3) -> filter#(X1, X2, X3), filter#(X1, X2, mark X3) -> filter#(X1, X2, X3)) (filter#(X1, mark X2, X3) -> filter#(X1, X2, X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (filter#(X1, mark X2, X3) -> filter#(X1, X2, X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (filter#(X1, mark X2, X3) -> filter#(X1, X2, X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(X1, active X2, X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3)) (active# filter(X1, X2, X3) -> filter#(X1, active X2, X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)) (proper# cons(X1, X2) -> cons#(proper X1, proper X2), cons#(mark X1, X2) -> cons#(X1, X2)) (proper# cons(X1, X2) -> cons#(proper X1, proper X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# filter(cons(X, Y), s N, M) -> filter#(Y, N, M), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) } STATUS: arrows: 0.874749 SCCS (8): Scc: {top# mark X -> top# proper X, top# ok X -> top# active X} Scc: { proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X1, proper# filter(X1, X2, X3) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X3, proper# s X -> proper# X, proper# sieve X -> proper# X, proper# nats X -> proper# X} Scc: { active# cons(X1, X2) -> active# X1, active# filter(X1, X2, X3) -> active# X1, active# filter(X1, X2, X3) -> active# X2, active# filter(X1, X2, X3) -> active# X3, active# s X -> active# X, active# sieve X -> active# X, active# nats X -> active# X} Scc: {nats# mark X -> nats# X, nats# ok X -> nats# X} Scc: {s# mark X -> s# X, s# ok X -> s# X} Scc: {sieve# mark X -> sieve# X, sieve# ok X -> sieve# X} Scc: { filter#(X1, X2, mark X3) -> filter#(X1, X2, X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)} Scc: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)} SCC (2): Strict: {top# mark X -> top# proper X, top# ok X -> top# active X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), filter(X1, X2, mark X3) -> mark filter(X1, X2, X3), filter(X1, mark X2, X3) -> mark filter(X1, X2, X3), filter(mark X1, X2, X3) -> mark filter(X1, X2, X3), filter(ok X1, ok X2, ok X3) -> ok filter(X1, X2, X3), active cons(X1, X2) -> cons(active X1, X2), active filter(X1, X2, X3) -> filter(X1, X2, active X3), active filter(X1, X2, X3) -> filter(X1, active X2, X3), active filter(X1, X2, X3) -> filter(active X1, X2, X3), active filter(cons(X, Y), 0(), M) -> mark cons(0(), filter(Y, M, M)), active filter(cons(X, Y), s N, M) -> mark cons(X, filter(Y, N, M)), active s X -> s active X, active sieve X -> sieve active X, active sieve cons(0(), Y) -> mark cons(0(), sieve Y), active sieve cons(s N, Y) -> mark cons(s N, sieve filter(Y, N, N)), active nats X -> nats active X, active nats N -> mark cons(N, nats s N), active zprimes() -> mark sieve nats s s 0(), s mark X -> mark s X, s ok X -> ok s X, sieve mark X -> mark sieve X, sieve ok X -> ok sieve X, nats mark X -> mark nats X, nats ok X -> ok nats X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper filter(X1, X2, X3) -> filter(proper X1, proper X2, proper X3), proper s X -> s proper X, proper sieve X -> sieve proper X, proper nats X -> nats proper X, proper zprimes() -> ok zprimes(), top mark X -> top proper X, top ok X -> top active X} Open SCC (8): Strict: { proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X1, proper# filter(X1, X2, X3) -> proper# X2, proper# filter(X1, X2, X3) -> proper# X3, proper# s X -> proper# X, proper# sieve X -> proper# X, proper# nats X -> proper# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), filter(X1, X2, mark X3) -> mark filter(X1, X2, X3), filter(X1, mark X2, X3) -> mark filter(X1, X2, X3), filter(mark X1, X2, X3) -> mark filter(X1, X2, X3), filter(ok X1, ok X2, ok X3) -> ok filter(X1, X2, X3), active cons(X1, X2) -> cons(active X1, X2), active filter(X1, X2, X3) -> filter(X1, X2, active X3), active filter(X1, X2, X3) -> filter(X1, active X2, X3), active filter(X1, X2, X3) -> filter(active X1, X2, X3), active filter(cons(X, Y), 0(), M) -> mark cons(0(), filter(Y, M, M)), active filter(cons(X, Y), s N, M) -> mark cons(X, filter(Y, N, M)), active s X -> s active X, active sieve X -> sieve active X, active sieve cons(0(), Y) -> mark cons(0(), sieve Y), active sieve cons(s N, Y) -> mark cons(s N, sieve filter(Y, N, N)), active nats X -> nats active X, active nats N -> mark cons(N, nats s N), active zprimes() -> mark sieve nats s s 0(), s mark X -> mark s X, s ok X -> ok s X, sieve mark X -> mark sieve X, sieve ok X -> ok sieve X, nats mark X -> mark nats X, nats ok X -> ok nats X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper filter(X1, X2, X3) -> filter(proper X1, proper X2, proper X3), proper s X -> s proper X, proper sieve X -> sieve proper X, proper nats X -> nats proper X, proper zprimes() -> ok zprimes(), top mark X -> top proper X, top ok X -> top active X} Open SCC (7): Strict: { active# cons(X1, X2) -> active# X1, active# filter(X1, X2, X3) -> active# X1, active# filter(X1, X2, X3) -> active# X2, active# filter(X1, X2, X3) -> active# X3, active# s X -> active# X, active# sieve X -> active# X, active# nats X -> active# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), filter(X1, X2, mark X3) -> mark filter(X1, X2, X3), filter(X1, mark X2, X3) -> mark filter(X1, X2, X3), filter(mark X1, X2, X3) -> mark filter(X1, X2, X3), filter(ok X1, ok X2, ok X3) -> ok filter(X1, X2, X3), active cons(X1, X2) -> cons(active X1, X2), active filter(X1, X2, X3) -> filter(X1, X2, active X3), active filter(X1, X2, X3) -> filter(X1, active X2, X3), active filter(X1, X2, X3) -> filter(active X1, X2, X3), active filter(cons(X, Y), 0(), M) -> mark cons(0(), filter(Y, M, M)), active filter(cons(X, Y), s N, M) -> mark cons(X, filter(Y, N, M)), active s X -> s active X, active sieve X -> sieve active X, active sieve cons(0(), Y) -> mark cons(0(), sieve Y), active sieve cons(s N, Y) -> mark cons(s N, sieve filter(Y, N, N)), active nats X -> nats active X, active nats N -> mark cons(N, nats s N), active zprimes() -> mark sieve nats s s 0(), s mark X -> mark s X, s ok X -> ok s X, sieve mark X -> mark sieve X, sieve ok X -> ok sieve X, nats mark X -> mark nats X, nats ok X -> ok nats X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper filter(X1, X2, X3) -> filter(proper X1, proper X2, proper X3), proper s X -> s proper X, proper sieve X -> sieve proper X, proper nats X -> nats proper X, proper zprimes() -> ok zprimes(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: {nats# mark X -> nats# X, nats# ok X -> nats# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), filter(X1, X2, mark X3) -> mark filter(X1, X2, X3), filter(X1, mark X2, X3) -> mark filter(X1, X2, X3), filter(mark X1, X2, X3) -> mark filter(X1, X2, X3), filter(ok X1, ok X2, ok X3) -> ok filter(X1, X2, X3), active cons(X1, X2) -> cons(active X1, X2), active filter(X1, X2, X3) -> filter(X1, X2, active X3), active filter(X1, X2, X3) -> filter(X1, active X2, X3), active filter(X1, X2, X3) -> filter(active X1, X2, X3), active filter(cons(X, Y), 0(), M) -> mark cons(0(), filter(Y, M, M)), active filter(cons(X, Y), s N, M) -> mark cons(X, filter(Y, N, M)), active s X -> s active X, active sieve X -> sieve active X, active sieve cons(0(), Y) -> mark cons(0(), sieve Y), active sieve cons(s N, Y) -> mark cons(s N, sieve filter(Y, N, N)), active nats X -> nats active X, active nats N -> mark cons(N, nats s N), active zprimes() -> mark sieve nats s s 0(), s mark X -> mark s X, s ok X -> ok s X, sieve mark X -> mark sieve X, sieve ok X -> ok sieve X, nats mark X -> mark nats X, nats ok X -> ok nats X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper filter(X1, X2, X3) -> filter(proper X1, proper X2, proper X3), proper s X -> s proper X, proper sieve X -> sieve proper X, proper nats X -> nats proper X, proper zprimes() -> ok zprimes(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: {s# mark X -> s# X, s# ok X -> s# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), filter(X1, X2, mark X3) -> mark filter(X1, X2, X3), filter(X1, mark X2, X3) -> mark filter(X1, X2, X3), filter(mark X1, X2, X3) -> mark filter(X1, X2, X3), filter(ok X1, ok X2, ok X3) -> ok filter(X1, X2, X3), active cons(X1, X2) -> cons(active X1, X2), active filter(X1, X2, X3) -> filter(X1, X2, active X3), active filter(X1, X2, X3) -> filter(X1, active X2, X3), active filter(X1, X2, X3) -> filter(active X1, X2, X3), active filter(cons(X, Y), 0(), M) -> mark cons(0(), filter(Y, M, M)), active filter(cons(X, Y), s N, M) -> mark cons(X, filter(Y, N, M)), active s X -> s active X, active sieve X -> sieve active X, active sieve cons(0(), Y) -> mark cons(0(), sieve Y), active sieve cons(s N, Y) -> mark cons(s N, sieve filter(Y, N, N)), active nats X -> nats active X, active nats N -> mark cons(N, nats s N), active zprimes() -> mark sieve nats s s 0(), s mark X -> mark s X, s ok X -> ok s X, sieve mark X -> mark sieve X, sieve ok X -> ok sieve X, nats mark X -> mark nats X, nats ok X -> ok nats X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper filter(X1, X2, X3) -> filter(proper X1, proper X2, proper X3), proper s X -> s proper X, proper sieve X -> sieve proper X, proper nats X -> nats proper X, proper zprimes() -> ok zprimes(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: {sieve# mark X -> sieve# X, sieve# ok X -> sieve# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), filter(X1, X2, mark X3) -> mark filter(X1, X2, X3), filter(X1, mark X2, X3) -> mark filter(X1, X2, X3), filter(mark X1, X2, X3) -> mark filter(X1, X2, X3), filter(ok X1, ok X2, ok X3) -> ok filter(X1, X2, X3), active cons(X1, X2) -> cons(active X1, X2), active filter(X1, X2, X3) -> filter(X1, X2, active X3), active filter(X1, X2, X3) -> filter(X1, active X2, X3), active filter(X1, X2, X3) -> filter(active X1, X2, X3), active filter(cons(X, Y), 0(), M) -> mark cons(0(), filter(Y, M, M)), active filter(cons(X, Y), s N, M) -> mark cons(X, filter(Y, N, M)), active s X -> s active X, active sieve X -> sieve active X, active sieve cons(0(), Y) -> mark cons(0(), sieve Y), active sieve cons(s N, Y) -> mark cons(s N, sieve filter(Y, N, N)), active nats X -> nats active X, active nats N -> mark cons(N, nats s N), active zprimes() -> mark sieve nats s s 0(), s mark X -> mark s X, s ok X -> ok s X, sieve mark X -> mark sieve X, sieve ok X -> ok sieve X, nats mark X -> mark nats X, nats ok X -> ok nats X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper filter(X1, X2, X3) -> filter(proper X1, proper X2, proper X3), proper s X -> s proper X, proper sieve X -> sieve proper X, proper nats X -> nats proper X, proper zprimes() -> ok zprimes(), top mark X -> top proper X, top ok X -> top active X} Open SCC (4): Strict: { filter#(X1, X2, mark X3) -> filter#(X1, X2, X3), filter#(X1, mark X2, X3) -> filter#(X1, X2, X3), filter#(mark X1, X2, X3) -> filter#(X1, X2, X3), filter#(ok X1, ok X2, ok X3) -> filter#(X1, X2, X3)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), filter(X1, X2, mark X3) -> mark filter(X1, X2, X3), filter(X1, mark X2, X3) -> mark filter(X1, X2, X3), filter(mark X1, X2, X3) -> mark filter(X1, X2, X3), filter(ok X1, ok X2, ok X3) -> ok filter(X1, X2, X3), active cons(X1, X2) -> cons(active X1, X2), active filter(X1, X2, X3) -> filter(X1, X2, active X3), active filter(X1, X2, X3) -> filter(X1, active X2, X3), active filter(X1, X2, X3) -> filter(active X1, X2, X3), active filter(cons(X, Y), 0(), M) -> mark cons(0(), filter(Y, M, M)), active filter(cons(X, Y), s N, M) -> mark cons(X, filter(Y, N, M)), active s X -> s active X, active sieve X -> sieve active X, active sieve cons(0(), Y) -> mark cons(0(), sieve Y), active sieve cons(s N, Y) -> mark cons(s N, sieve filter(Y, N, N)), active nats X -> nats active X, active nats N -> mark cons(N, nats s N), active zprimes() -> mark sieve nats s s 0(), s mark X -> mark s X, s ok X -> ok s X, sieve mark X -> mark sieve X, sieve ok X -> ok sieve X, nats mark X -> mark nats X, nats ok X -> ok nats X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper filter(X1, X2, X3) -> filter(proper X1, proper X2, proper X3), proper s X -> s proper X, proper sieve X -> sieve proper X, proper nats X -> nats proper X, proper zprimes() -> ok zprimes(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), filter(X1, X2, mark X3) -> mark filter(X1, X2, X3), filter(X1, mark X2, X3) -> mark filter(X1, X2, X3), filter(mark X1, X2, X3) -> mark filter(X1, X2, X3), filter(ok X1, ok X2, ok X3) -> ok filter(X1, X2, X3), active cons(X1, X2) -> cons(active X1, X2), active filter(X1, X2, X3) -> filter(X1, X2, active X3), active filter(X1, X2, X3) -> filter(X1, active X2, X3), active filter(X1, X2, X3) -> filter(active X1, X2, X3), active filter(cons(X, Y), 0(), M) -> mark cons(0(), filter(Y, M, M)), active filter(cons(X, Y), s N, M) -> mark cons(X, filter(Y, N, M)), active s X -> s active X, active sieve X -> sieve active X, active sieve cons(0(), Y) -> mark cons(0(), sieve Y), active sieve cons(s N, Y) -> mark cons(s N, sieve filter(Y, N, N)), active nats X -> nats active X, active nats N -> mark cons(N, nats s N), active zprimes() -> mark sieve nats s s 0(), s mark X -> mark s X, s ok X -> ok s X, sieve mark X -> mark sieve X, sieve ok X -> ok sieve X, nats mark X -> mark nats X, nats ok X -> ok nats X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper filter(X1, X2, X3) -> filter(proper X1, proper X2, proper X3), proper s X -> s proper X, proper sieve X -> sieve proper X, proper nats X -> nats proper X, proper zprimes() -> ok zprimes(), top mark X -> top proper X, top ok X -> top active X} Open