MAYBE Time: 0.054087 TRS: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), recip mark X -> mark recip X, recip ok X -> ok recip X, sqr mark X -> mark sqr X, sqr ok X -> ok sqr X, terms mark X -> mark terms X, terms ok X -> ok terms X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active recip X -> recip active X, active sqr X -> sqr active X, active sqr s X -> mark s add(sqr X, dbl X), active sqr 0() -> mark 0(), active terms N -> mark cons(recip sqr N, terms s N), active terms X -> terms active X, active add(X1, X2) -> add(X1, active X2), active add(X1, X2) -> add(active X1, X2), active add(s X, Y) -> mark s add(X, Y), active add(0(), X) -> mark X, active dbl X -> dbl active X, active dbl s X -> mark s s dbl X, active dbl 0() -> mark 0(), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active first(0(), X) -> mark nil(), add(X1, mark X2) -> mark add(X1, X2), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, first(X1, mark X2) -> mark first(X1, X2), first(mark X1, X2) -> mark first(X1, X2), first(ok X1, ok X2) -> ok first(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper recip X -> recip proper X, proper sqr X -> sqr proper X, proper terms X -> terms 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 nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), 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), recip# mark X -> recip# X, recip# ok X -> recip# X, sqr# mark X -> sqr# X, sqr# ok X -> sqr# X, terms# mark X -> terms# X, terms# ok X -> terms# X, s# ok X -> s# X, active# cons(X1, X2) -> cons#(active X1, X2), active# cons(X1, X2) -> active# X1, active# recip X -> recip# active X, active# recip X -> active# X, active# sqr X -> sqr# active X, active# sqr X -> active# X, active# sqr s X -> sqr# X, active# sqr s X -> s# add(sqr X, dbl X), active# sqr s X -> add#(sqr X, dbl X), active# sqr s X -> dbl# X, active# terms N -> cons#(recip sqr N, terms s N), active# terms N -> recip# sqr N, active# terms N -> sqr# N, active# terms N -> terms# s N, active# terms N -> s# N, active# terms X -> terms# active X, active# terms X -> active# X, active# add(X1, X2) -> active# X1, active# add(X1, X2) -> active# X2, active# add(X1, X2) -> add#(X1, active X2), active# add(X1, X2) -> add#(active X1, X2), active# add(s X, Y) -> s# add(X, Y), active# add(s X, Y) -> add#(X, Y), active# dbl X -> active# X, active# dbl X -> dbl# active X, active# dbl s X -> s# s dbl X, active# dbl s X -> s# dbl X, active# dbl s X -> dbl# X, active# first(X1, X2) -> active# X1, active# first(X1, X2) -> active# X2, active# first(X1, X2) -> first#(X1, active X2), active# first(X1, X2) -> first#(active X1, X2), active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z)), active# first(s X, cons(Y, Z)) -> first#(X, Z), add#(X1, mark X2) -> add#(X1, X2), add#(mark X1, X2) -> add#(X1, X2), add#(ok X1, ok X2) -> add#(X1, X2), dbl# mark X -> dbl# X, dbl# ok X -> dbl# X, first#(X1, mark X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2), first#(ok X1, ok X2) -> first#(X1, X2), proper# cons(X1, X2) -> cons#(proper X1, proper X2), proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# recip X -> recip# proper X, proper# recip X -> proper# X, proper# sqr X -> sqr# proper X, proper# sqr X -> proper# X, proper# terms X -> terms# proper X, proper# terms X -> proper# X, proper# s X -> s# proper X, proper# s X -> proper# X, proper# add(X1, X2) -> add#(proper X1, proper X2), proper# add(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X2, proper# dbl X -> dbl# proper X, proper# dbl X -> proper# X, proper# first(X1, X2) -> first#(proper X1, proper X2), proper# first(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X2, 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), recip mark X -> mark recip X, recip ok X -> ok recip X, sqr mark X -> mark sqr X, sqr ok X -> ok sqr X, terms mark X -> mark terms X, terms ok X -> ok terms X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active recip X -> recip active X, active sqr X -> sqr active X, active sqr s X -> mark s add(sqr X, dbl X), active sqr 0() -> mark 0(), active terms N -> mark cons(recip sqr N, terms s N), active terms X -> terms active X, active add(X1, X2) -> add(X1, active X2), active add(X1, X2) -> add(active X1, X2), active add(s X, Y) -> mark s add(X, Y), active add(0(), X) -> mark X, active dbl X -> dbl active X, active dbl s X -> mark s s dbl X, active dbl 0() -> mark 0(), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active first(0(), X) -> mark nil(), add(X1, mark X2) -> mark add(X1, X2), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, first(X1, mark X2) -> mark first(X1, X2), first(mark X1, X2) -> mark first(X1, X2), first(ok X1, ok X2) -> ok first(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper recip X -> recip proper X, proper sqr X -> sqr proper X, proper terms X -> terms 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 nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} EDG: { (active# add(X1, X2) -> add#(active X1, X2), add#(ok X1, ok X2) -> add#(X1, X2)) (active# add(X1, X2) -> add#(active X1, X2), add#(mark X1, X2) -> add#(X1, X2)) (active# add(X1, X2) -> add#(active X1, X2), add#(X1, mark X2) -> add#(X1, X2)) (active# dbl s X -> s# s dbl X, s# ok X -> s# X) (active# recip X -> recip# active X, recip# ok X -> recip# X) (active# recip X -> recip# active X, recip# mark X -> recip# X) (active# terms X -> terms# active X, terms# ok X -> terms# X) (active# terms X -> terms# active X, terms# mark X -> terms# X) (active# dbl s X -> s# dbl X, s# ok X -> s# X) (proper# sqr X -> sqr# proper X, sqr# ok X -> sqr# X) (proper# sqr X -> sqr# proper X, sqr# mark X -> sqr# X) (proper# s X -> s# proper X, s# ok X -> s# 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# terms N -> recip# sqr N, recip# ok X -> recip# X) (active# terms N -> recip# sqr N, recip# mark X -> recip# 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)) (add#(X1, mark X2) -> add#(X1, X2), add#(ok X1, ok X2) -> add#(X1, X2)) (add#(X1, mark X2) -> add#(X1, X2), add#(mark X1, X2) -> add#(X1, X2)) (add#(X1, mark X2) -> add#(X1, X2), add#(X1, mark X2) -> add#(X1, X2)) (add#(ok X1, ok X2) -> add#(X1, X2), add#(ok X1, ok X2) -> add#(X1, X2)) (add#(ok X1, ok X2) -> add#(X1, X2), add#(mark X1, X2) -> add#(X1, X2)) (add#(ok X1, ok X2) -> add#(X1, X2), add#(X1, mark X2) -> add#(X1, X2)) (first#(mark X1, X2) -> first#(X1, X2), first#(ok X1, ok X2) -> first#(X1, X2)) (first#(mark X1, X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2)) (first#(mark X1, X2) -> first#(X1, X2), first#(X1, mark X2) -> first#(X1, X2)) (active# terms N -> cons#(recip sqr N, terms s N), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# terms N -> cons#(recip sqr N, terms s N), cons#(mark X1, X2) -> cons#(X1, X2)) (active# add(X1, X2) -> active# X1, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (active# add(X1, X2) -> active# X1, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (active# add(X1, X2) -> active# X1, active# first(X1, X2) -> first#(active X1, X2)) (active# add(X1, X2) -> active# X1, active# first(X1, X2) -> first#(X1, active X2)) (active# add(X1, X2) -> active# X1, active# first(X1, X2) -> active# X2) (active# add(X1, X2) -> active# X1, active# first(X1, X2) -> active# X1) (active# add(X1, X2) -> active# X1, active# dbl s X -> dbl# X) (active# add(X1, X2) -> active# X1, active# dbl s X -> s# dbl X) (active# add(X1, X2) -> active# X1, active# dbl s X -> s# s dbl X) (active# add(X1, X2) -> active# X1, active# dbl X -> dbl# active X) (active# add(X1, X2) -> active# X1, active# dbl X -> active# X) (active# add(X1, X2) -> active# X1, active# add(s X, Y) -> add#(X, Y)) (active# add(X1, X2) -> active# X1, active# add(s X, Y) -> s# add(X, Y)) (active# add(X1, X2) -> active# X1, active# add(X1, X2) -> add#(active X1, X2)) (active# add(X1, X2) -> active# X1, active# add(X1, X2) -> add#(X1, active X2)) (active# add(X1, X2) -> active# X1, active# add(X1, X2) -> active# X2) (active# add(X1, X2) -> active# X1, active# add(X1, X2) -> active# X1) (active# add(X1, X2) -> active# X1, active# terms X -> active# X) (active# add(X1, X2) -> active# X1, active# terms X -> terms# active X) (active# add(X1, X2) -> active# X1, active# terms N -> s# N) (active# add(X1, X2) -> active# X1, active# terms N -> terms# s N) (active# add(X1, X2) -> active# X1, active# terms N -> sqr# N) (active# add(X1, X2) -> active# X1, active# terms N -> recip# sqr N) (active# add(X1, X2) -> active# X1, active# terms N -> cons#(recip sqr N, terms s N)) (active# add(X1, X2) -> active# X1, active# sqr s X -> dbl# X) (active# add(X1, X2) -> active# X1, active# sqr s X -> add#(sqr X, dbl X)) (active# add(X1, X2) -> active# X1, active# sqr s X -> s# add(sqr X, dbl X)) (active# add(X1, X2) -> active# X1, active# sqr s X -> sqr# X) (active# add(X1, X2) -> active# X1, active# sqr X -> active# X) (active# add(X1, X2) -> active# X1, active# sqr X -> sqr# active X) (active# add(X1, X2) -> active# X1, active# recip X -> active# X) (active# add(X1, X2) -> active# X1, active# recip X -> recip# active X) (active# add(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# add(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (proper# cons(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X1, proper# dbl X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# dbl X -> dbl# proper X) (proper# cons(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# add(X1, X2) -> add#(proper X1, proper X2)) (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# terms X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# terms X -> terms# proper X) (proper# cons(X1, X2) -> proper# X1, proper# sqr X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# sqr X -> sqr# proper X) (proper# cons(X1, X2) -> proper# X1, proper# recip X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# recip X -> recip# proper X) (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)) (proper# first(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X2) (proper# first(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X1) (proper# first(X1, X2) -> proper# X1, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# first(X1, X2) -> proper# X1, proper# dbl X -> proper# X) (proper# first(X1, X2) -> proper# X1, proper# dbl X -> dbl# proper X) (proper# first(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X2) (proper# first(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X1) (proper# first(X1, X2) -> proper# X1, proper# add(X1, X2) -> add#(proper X1, proper X2)) (proper# first(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# first(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# first(X1, X2) -> proper# X1, proper# terms X -> proper# X) (proper# first(X1, X2) -> proper# X1, proper# terms X -> terms# proper X) (proper# first(X1, X2) -> proper# X1, proper# sqr X -> proper# X) (proper# first(X1, X2) -> proper# X1, proper# sqr X -> sqr# proper X) (proper# first(X1, X2) -> proper# X1, proper# recip X -> proper# X) (proper# first(X1, X2) -> proper# X1, proper# recip X -> recip# proper X) (proper# first(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# first(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# first(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (recip# ok X -> recip# X, recip# ok X -> recip# X) (recip# ok X -> recip# X, recip# mark X -> recip# X) (sqr# ok X -> sqr# X, sqr# ok X -> sqr# X) (sqr# ok X -> sqr# X, sqr# mark X -> sqr# X) (terms# ok X -> terms# X, terms# ok X -> terms# X) (terms# ok X -> terms# X, terms# mark X -> terms# X) (active# recip X -> active# X, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (active# recip X -> active# X, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (active# recip X -> active# X, active# first(X1, X2) -> first#(active X1, X2)) (active# recip X -> active# X, active# first(X1, X2) -> first#(X1, active X2)) (active# recip X -> active# X, active# first(X1, X2) -> active# X2) (active# recip X -> active# X, active# first(X1, X2) -> active# X1) (active# recip X -> active# X, active# dbl s X -> dbl# X) (active# recip X -> active# X, active# dbl s X -> s# dbl X) (active# recip X -> active# X, active# dbl s X -> s# s dbl X) (active# recip X -> active# X, active# dbl X -> dbl# active X) (active# recip X -> active# X, active# dbl X -> active# X) (active# recip X -> active# X, active# add(s X, Y) -> add#(X, Y)) (active# recip X -> active# X, active# add(s X, Y) -> s# add(X, Y)) (active# recip X -> active# X, active# add(X1, X2) -> add#(active X1, X2)) (active# recip X -> active# X, active# add(X1, X2) -> add#(X1, active X2)) (active# recip X -> active# X, active# add(X1, X2) -> active# X2) (active# recip X -> active# X, active# add(X1, X2) -> active# X1) (active# recip X -> active# X, active# terms X -> active# X) (active# recip X -> active# X, active# terms X -> terms# active X) (active# recip X -> active# X, active# terms N -> s# N) (active# recip X -> active# X, active# terms N -> terms# s N) (active# recip X -> active# X, active# terms N -> sqr# N) (active# recip X -> active# X, active# terms N -> recip# sqr N) (active# recip X -> active# X, active# terms N -> cons#(recip sqr N, terms s N)) (active# recip X -> active# X, active# sqr s X -> dbl# X) (active# recip X -> active# X, active# sqr s X -> add#(sqr X, dbl X)) (active# recip X -> active# X, active# sqr s X -> s# add(sqr X, dbl X)) (active# recip X -> active# X, active# sqr s X -> sqr# X) (active# recip X -> active# X, active# sqr X -> active# X) (active# recip X -> active# X, active# sqr X -> sqr# active X) (active# recip X -> active# X, active# recip X -> active# X) (active# recip X -> active# X, active# recip X -> recip# active X) (active# recip X -> active# X, active# cons(X1, X2) -> active# X1) (active# recip X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# sqr s X -> sqr# X, sqr# ok X -> sqr# X) (active# sqr s X -> sqr# X, sqr# mark X -> sqr# X) (active# terms X -> active# X, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (active# terms X -> active# X, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (active# terms X -> active# X, active# first(X1, X2) -> first#(active X1, X2)) (active# terms X -> active# X, active# first(X1, X2) -> first#(X1, active X2)) (active# terms X -> active# X, active# first(X1, X2) -> active# X2) (active# terms X -> active# X, active# first(X1, X2) -> active# X1) (active# terms X -> active# X, active# dbl s X -> dbl# X) (active# terms X -> active# X, active# dbl s X -> s# dbl X) (active# terms X -> active# X, active# dbl s X -> s# s dbl X) (active# terms X -> active# X, active# dbl X -> dbl# active X) (active# terms X -> active# X, active# dbl X -> active# X) (active# terms X -> active# X, active# add(s X, Y) -> add#(X, Y)) (active# terms X -> active# X, active# add(s X, Y) -> s# add(X, Y)) (active# terms X -> active# X, active# add(X1, X2) -> add#(active X1, X2)) (active# terms X -> active# X, active# add(X1, X2) -> add#(X1, active X2)) (active# terms X -> active# X, active# add(X1, X2) -> active# X2) (active# terms X -> active# X, active# add(X1, X2) -> active# X1) (active# terms X -> active# X, active# terms X -> active# X) (active# terms X -> active# X, active# terms X -> terms# active X) (active# terms X -> active# X, active# terms N -> s# N) (active# terms X -> active# X, active# terms N -> terms# s N) (active# terms X -> active# X, active# terms N -> sqr# N) (active# terms X -> active# X, active# terms N -> recip# sqr N) (active# terms X -> active# X, active# terms N -> cons#(recip sqr N, terms s N)) (active# terms X -> active# X, active# sqr s X -> dbl# X) (active# terms X -> active# X, active# sqr s X -> add#(sqr X, dbl X)) (active# terms X -> active# X, active# sqr s X -> s# add(sqr X, dbl X)) (active# terms X -> active# X, active# sqr s X -> sqr# X) (active# terms X -> active# X, active# sqr X -> active# X) (active# terms X -> active# X, active# sqr X -> sqr# active X) (active# terms X -> active# X, active# recip X -> active# X) (active# terms X -> active# X, active# recip X -> recip# active X) (active# terms X -> active# X, active# cons(X1, X2) -> active# X1) (active# terms X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# dbl s X -> dbl# X, dbl# ok X -> dbl# X) (active# dbl s X -> dbl# X, dbl# mark X -> dbl# X) (dbl# ok X -> dbl# X, dbl# ok X -> dbl# X) (dbl# ok X -> dbl# X, dbl# mark X -> dbl# X) (proper# sqr X -> proper# X, proper# first(X1, X2) -> proper# X2) (proper# sqr X -> proper# X, proper# first(X1, X2) -> proper# X1) (proper# sqr X -> proper# X, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# sqr X -> proper# X, proper# dbl X -> proper# X) (proper# sqr X -> proper# X, proper# dbl X -> dbl# proper X) (proper# sqr X -> proper# X, proper# add(X1, X2) -> proper# X2) (proper# sqr X -> proper# X, proper# add(X1, X2) -> proper# X1) (proper# sqr X -> proper# X, proper# add(X1, X2) -> add#(proper X1, proper X2)) (proper# sqr X -> proper# X, proper# s X -> proper# X) (proper# sqr X -> 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-> active# X, active# first(X1, X2) -> active# X2) (top# ok X -> active# X, active# first(X1, X2) -> first#(X1, active X2)) (top# ok X -> active# X, active# first(X1, X2) -> first#(active X1, X2)) (top# ok X -> active# X, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (top# ok X -> active# X, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (proper# dbl X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# dbl X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# dbl X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# dbl X -> proper# X, proper# recip X -> recip# proper X) (proper# dbl X -> proper# X, proper# recip X -> proper# X) (proper# dbl X -> proper# X, proper# sqr X -> sqr# proper X) (proper# dbl X -> proper# X, proper# sqr X -> proper# X) (proper# dbl X -> proper# X, proper# terms X -> terms# proper X) (proper# dbl X -> proper# X, proper# terms X -> proper# X) (proper# dbl X -> proper# X, proper# s X -> s# proper X) (proper# dbl X -> proper# X, proper# s X -> proper# X) (proper# dbl X -> proper# X, proper# add(X1, X2) -> add#(proper X1, proper X2)) (proper# dbl X -> proper# X, proper# add(X1, X2) -> proper# X1) (proper# dbl X -> proper# X, proper# add(X1, X2) -> proper# X2) (proper# dbl X -> proper# X, proper# dbl X -> dbl# proper X) (proper# dbl X -> proper# X, proper# dbl X -> proper# X) (proper# dbl X -> proper# X, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# dbl X -> proper# X, proper# first(X1, X2) -> proper# X1) (proper# dbl X -> proper# X, proper# first(X1, X2) -> proper# X2) (proper# terms X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# terms X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# terms X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# terms X -> proper# X, proper# recip X -> recip# proper X) (proper# terms X -> proper# X, proper# recip X -> proper# X) (proper# terms X -> proper# X, proper# sqr X -> sqr# proper X) (proper# terms X -> proper# X, proper# sqr X -> proper# X) (proper# terms X -> proper# X, proper# terms X -> terms# proper X) (proper# terms X -> proper# X, proper# terms X -> proper# X) (proper# terms X -> proper# X, proper# s X -> s# proper X) (proper# terms X -> proper# X, proper# s X -> proper# X) (proper# terms X -> proper# X, proper# add(X1, X2) -> add#(proper X1, proper X2)) (proper# terms X -> proper# X, proper# add(X1, X2) -> proper# X1) (proper# terms X -> proper# X, proper# add(X1, X2) -> proper# X2) (proper# terms X -> proper# X, proper# dbl X -> dbl# proper X) (proper# terms X -> proper# X, proper# dbl X -> proper# X) (proper# terms X -> proper# X, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# terms X -> proper# X, proper# first(X1, X2) -> proper# X1) (proper# terms X -> proper# X, proper# first(X1, X2) -> proper# X2) (proper# recip X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# recip X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# recip X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# recip X -> proper# X, proper# recip X -> recip# proper X) (proper# recip X -> proper# X, proper# recip X -> proper# X) (proper# recip X -> proper# X, proper# sqr X -> sqr# proper X) (proper# recip X -> proper# X, proper# sqr X -> proper# X) (proper# recip X -> proper# X, proper# terms X -> terms# proper X) (proper# recip X -> proper# X, proper# terms X -> proper# X) (proper# recip X -> proper# X, proper# s X -> s# proper X) (proper# recip X -> proper# X, proper# s X -> proper# X) (proper# recip X -> proper# X, proper# add(X1, X2) -> add#(proper X1, proper X2)) (proper# recip X -> proper# X, proper# add(X1, X2) -> proper# X1) (proper# recip X -> proper# X, proper# add(X1, X2) -> proper# X2) (proper# recip X -> proper# X, proper# dbl X -> dbl# proper X) (proper# recip X -> proper# X, proper# dbl X -> proper# X) (proper# recip X -> proper# X, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# recip X -> proper# X, proper# first(X1, X2) -> proper# X1) (proper# recip X -> proper# X, proper# first(X1, X2) -> proper# X2) (dbl# mark X -> dbl# X, dbl# mark X -> dbl# X) (dbl# mark X -> dbl# X, dbl# ok X -> dbl# X) (active# dbl X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# dbl X -> active# X, active# cons(X1, X2) -> active# X1) (active# dbl X -> active# X, active# recip X -> recip# active X) (active# dbl X -> active# X, active# recip X -> active# X) (active# dbl X -> active# X, active# sqr X -> sqr# active X) (active# dbl X -> active# X, active# sqr X -> active# X) (active# dbl X -> active# X, active# sqr s X -> sqr# X) (active# dbl X -> active# X, active# sqr s X -> s# add(sqr X, dbl X)) (active# dbl X -> active# X, active# sqr s X -> add#(sqr X, dbl X)) (active# dbl X -> active# X, active# sqr s X -> dbl# X) (active# dbl X -> active# X, active# terms N -> cons#(recip sqr N, terms s N)) (active# dbl X -> active# X, active# terms N -> recip# sqr N) (active# dbl X -> active# X, active# terms N -> sqr# N) (active# dbl X -> active# X, active# terms N -> terms# s N) (active# dbl X -> active# X, active# terms N -> s# N) (active# dbl X -> active# X, active# terms X -> terms# active X) (active# dbl X -> active# X, active# terms X -> active# X) (active# dbl X -> active# X, active# add(X1, X2) -> active# X1) (active# dbl X -> active# X, active# add(X1, X2) -> active# X2) (active# dbl X -> active# X, active# add(X1, X2) -> add#(X1, active X2)) (active# dbl X -> active# X, active# add(X1, X2) -> add#(active X1, X2)) (active# dbl X -> active# X, active# add(s X, Y) -> s# add(X, Y)) (active# dbl X -> active# X, active# add(s X, Y) -> add#(X, Y)) (active# dbl X -> active# X, active# dbl X -> active# X) (active# dbl X -> active# X, active# dbl X -> dbl# active X) (active# dbl X -> active# X, active# dbl s X -> s# s dbl X) (active# dbl X -> active# X, active# dbl s X -> s# dbl X) (active# dbl X -> active# X, active# dbl s X -> dbl# X) (active# dbl X -> active# X, active# first(X1, X2) -> active# X1) (active# dbl X -> active# X, active# first(X1, X2) -> active# X2) (active# dbl X -> active# X, active# first(X1, X2) -> first#(X1, active X2)) (active# dbl X -> active# X, active# first(X1, X2) -> first#(active X1, X2)) (active# dbl X -> active# X, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (active# dbl X -> active# X, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (active# sqr s X -> dbl# X, dbl# mark X -> dbl# X) (active# sqr s X -> dbl# X, dbl# ok X -> dbl# X) (active# sqr X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# sqr X -> active# X, active# cons(X1, X2) -> active# X1) (active# sqr X -> active# X, active# recip X -> recip# active X) (active# sqr X -> active# X, active# recip X -> active# X) (active# sqr X -> active# X, active# sqr X -> sqr# active X) (active# sqr X -> active# X, active# sqr X -> active# X) (active# sqr X -> active# X, active# sqr s X -> sqr# X) (active# sqr X -> active# X, active# sqr s X -> s# add(sqr X, dbl X)) (active# sqr X -> active# X, active# sqr s X -> add#(sqr X, dbl X)) (active# sqr X -> active# X, active# sqr s X -> dbl# X) (active# sqr X -> active# X, active# terms N -> cons#(recip sqr N, terms s N)) (active# sqr X -> active# X, active# terms N -> recip# sqr N) (active# sqr X -> active# X, active# terms N -> sqr# N) (active# sqr X -> active# X, active# terms N -> terms# s N) (active# sqr X -> active# X, active# terms N -> s# N) (active# sqr X -> active# X, active# terms X -> terms# active X) (active# sqr X -> active# X, active# terms X -> active# X) (active# sqr X -> active# X, active# add(X1, X2) -> active# X1) (active# sqr X -> active# X, active# add(X1, X2) -> active# X2) (active# sqr X -> active# X, active# add(X1, X2) -> add#(X1, active X2)) (active# sqr X -> active# X, active# add(X1, X2) -> add#(active X1, X2)) (active# sqr X -> active# X, active# add(s X, Y) -> s# add(X, Y)) (active# sqr X -> active# X, active# add(s X, Y) -> add#(X, Y)) (active# sqr X -> active# X, active# dbl X -> active# X) (active# sqr X -> active# X, active# dbl X -> dbl# active X) (active# sqr X -> active# X, active# dbl s X -> s# s dbl X) (active# sqr X -> active# X, active# dbl s X -> s# dbl X) (active# sqr X -> active# X, active# dbl s X -> dbl# X) (active# sqr X -> active# X, active# first(X1, X2) -> active# X1) (active# sqr X -> active# X, active# first(X1, X2) -> active# X2) (active# sqr X -> active# X, active# first(X1, X2) -> first#(X1, active X2)) (active# sqr X -> active# X, active# first(X1, X2) -> first#(active X1, X2)) (active# sqr X -> active# X, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (active# sqr X -> active# X, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (s# ok X -> s# X, s# ok X -> s# X) (terms# mark X -> terms# X, terms# mark X -> terms# X) (terms# mark X -> terms# X, terms# ok X -> terms# X) (sqr# mark X -> sqr# X, sqr# mark X -> sqr# X) (sqr# mark X -> sqr# X, sqr# ok X -> sqr# X) (recip# mark X -> recip# X, recip# mark X -> recip# X) (recip# mark X -> recip# X, recip# ok X -> recip# X) (proper# add(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# add(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# add(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# add(X1, X2) -> proper# X1, proper# recip X -> recip# proper X) (proper# add(X1, X2) -> proper# X1, proper# recip X -> proper# X) (proper# add(X1, X2) -> proper# X1, proper# sqr X -> sqr# proper X) (proper# add(X1, X2) -> proper# X1, proper# sqr X -> proper# X) (proper# add(X1, X2) -> proper# X1, proper# terms X -> terms# proper X) (proper# add(X1, X2) -> proper# X1, proper# terms X -> proper# X) (proper# add(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# add(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# add(X1, X2) -> proper# X1, proper# add(X1, X2) -> add#(proper X1, proper X2)) (proper# add(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X1) (proper# add(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X2) (proper# add(X1, X2) -> proper# X1, proper# dbl X -> dbl# proper X) (proper# add(X1, X2) -> proper# X1, proper# dbl X -> proper# X) (proper# add(X1, X2) -> proper# X1, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# add(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X1) (proper# add(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X2) (active# first(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# first(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# first(X1, X2) -> active# X1, active# recip X -> recip# active X) (active# first(X1, X2) -> active# X1, active# recip X -> active# X) (active# first(X1, X2) -> active# X1, active# sqr X -> sqr# active X) (active# first(X1, X2) -> active# X1, active# sqr X -> active# X) (active# first(X1, X2) -> active# X1, active# sqr s X -> sqr# X) (active# first(X1, X2) -> active# X1, active# sqr s X -> s# add(sqr X, dbl X)) (active# first(X1, X2) -> active# X1, active# sqr s X -> add#(sqr X, dbl X)) (active# first(X1, X2) -> active# X1, active# sqr s X -> dbl# X) (active# first(X1, X2) -> active# X1, active# terms N -> cons#(recip sqr N, terms s N)) (active# first(X1, X2) -> active# X1, active# terms N -> recip# sqr N) (active# first(X1, X2) -> active# X1, active# terms N -> sqr# N) (active# first(X1, X2) -> active# X1, active# terms N -> terms# s N) (active# first(X1, X2) -> active# X1, active# terms N -> s# N) (active# first(X1, X2) -> active# X1, active# terms X -> terms# active X) (active# first(X1, X2) -> active# X1, active# terms X -> active# X) (active# first(X1, X2) -> active# X1, active# add(X1, X2) -> active# X1) (active# first(X1, X2) -> active# X1, active# add(X1, X2) -> active# X2) (active# first(X1, X2) -> active# X1, active# add(X1, X2) -> add#(X1, active X2)) (active# first(X1, X2) -> active# X1, active# add(X1, X2) -> add#(active X1, X2)) (active# first(X1, X2) -> active# X1, active# add(s X, Y) -> s# add(X, Y)) (active# first(X1, X2) -> active# X1, active# add(s X, Y) -> add#(X, Y)) (active# first(X1, X2) -> active# X1, active# dbl X -> active# X) (active# first(X1, X2) -> active# X1, active# dbl X -> dbl# active X) (active# first(X1, X2) -> active# X1, active# dbl s X -> s# s dbl X) (active# first(X1, X2) -> active# X1, active# dbl s X -> s# dbl X) (active# first(X1, X2) -> active# X1, active# dbl s X -> dbl# X) (active# first(X1, X2) -> active# X1, active# first(X1, X2) -> active# X1) (active# first(X1, X2) -> active# X1, active# first(X1, X2) -> active# X2) (active# first(X1, X2) -> active# X1, active# first(X1, X2) -> first#(X1, active X2)) (active# first(X1, X2) -> active# X1, active# first(X1, X2) -> first#(active X1, X2)) (active# first(X1, X2) -> active# X1, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (active# first(X1, X2) -> active# X1, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# recip X -> recip# active X) (active# cons(X1, X2) -> active# X1, active# recip X -> active# X) (active# cons(X1, X2) -> active# X1, active# sqr X -> sqr# active X) (active# cons(X1, X2) -> active# X1, active# sqr X -> active# X) (active# cons(X1, X2) -> active# X1, active# sqr s X -> sqr# X) (active# cons(X1, X2) -> active# X1, active# sqr s X -> s# add(sqr X, dbl X)) (active# cons(X1, X2) -> active# X1, active# sqr s X -> add#(sqr X, dbl X)) (active# cons(X1, X2) -> active# X1, active# sqr s X -> dbl# X) (active# cons(X1, X2) -> active# X1, active# terms N -> cons#(recip sqr N, terms s N)) (active# cons(X1, X2) -> active# X1, active# terms N -> recip# sqr N) (active# cons(X1, X2) -> active# X1, active# terms N -> sqr# N) (active# cons(X1, X2) -> active# X1, active# terms N -> terms# s N) (active# cons(X1, X2) -> active# X1, active# terms N -> s# N) (active# cons(X1, X2) -> active# X1, active# terms X -> terms# active X) (active# cons(X1, X2) -> active# X1, active# terms X -> active# X) (active# cons(X1, X2) -> active# X1, active# add(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# add(X1, X2) -> active# X2) (active# cons(X1, X2) -> active# X1, active# add(X1, X2) -> add#(X1, active X2)) (active# cons(X1, X2) -> active# X1, active# add(X1, X2) -> add#(active X1, X2)) (active# cons(X1, X2) -> active# X1, active# add(s X, Y) -> s# add(X, Y)) (active# cons(X1, X2) -> active# X1, active# add(s X, Y) -> add#(X, Y)) (active# cons(X1, X2) -> active# X1, active# dbl X -> active# X) (active# cons(X1, X2) -> active# X1, active# dbl X -> dbl# active X) (active# cons(X1, X2) -> active# X1, active# dbl s X -> s# s dbl X) (active# cons(X1, X2) -> active# X1, active# dbl s X -> s# dbl X) (active# cons(X1, X2) -> active# X1, active# dbl s X -> dbl# X) (active# cons(X1, X2) -> active# X1, active# first(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# first(X1, X2) -> active# X2) (active# cons(X1, X2) -> active# X1, active# first(X1, X2) -> first#(X1, active X2)) (active# cons(X1, X2) -> active# X1, active# first(X1, X2) -> first#(active X1, X2)) (active# cons(X1, X2) -> active# X1, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (active# cons(X1, X2) -> active# X1, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (first#(ok X1, ok X2) -> first#(X1, X2), first#(X1, mark X2) -> first#(X1, X2)) (first#(ok X1, ok X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2)) (first#(ok X1, ok X2) -> first#(X1, X2), first#(ok X1, ok X2) -> first#(X1, X2)) (first#(X1, mark X2) -> first#(X1, X2), first#(X1, mark X2) -> first#(X1, X2)) (first#(X1, mark X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2)) (first#(X1, mark X2) -> first#(X1, X2), first#(ok X1, ok X2) -> first#(X1, X2)) (add#(mark X1, X2) -> add#(X1, X2), add#(X1, mark X2) -> add#(X1, X2)) (add#(mark X1, X2) -> add#(X1, X2), add#(mark X1, X2) -> add#(X1, X2)) (add#(mark X1, X2) -> add#(X1, X2), add#(ok X1, ok X2) -> add#(X1, X2)) (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# terms N -> terms# s N, terms# mark X -> terms# X) (active# terms N -> terms# s N, terms# ok X -> terms# 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# dbl X -> dbl# proper X, dbl# mark X -> dbl# X) (proper# dbl X -> dbl# proper X, dbl# ok X -> dbl# X) (proper# terms X -> terms# proper X, terms# mark X -> terms# X) (proper# terms X -> terms# proper X, terms# ok X -> terms# X) (proper# recip X -> recip# proper X, recip# mark X -> recip# X) (proper# recip X -> recip# proper X, recip# ok X -> recip# X) (active# dbl X -> dbl# active X, dbl# mark X -> dbl# X) (active# dbl X -> dbl# active X, dbl# ok X -> dbl# X) (active# sqr X -> sqr# active X, sqr# mark X -> sqr# X) (active# sqr X -> sqr# active X, sqr# ok X -> sqr# X) (active# first(s X, cons(Y, Z)) -> first#(X, Z), first#(X1, mark X2) -> first#(X1, X2)) (active# first(s X, cons(Y, Z)) -> first#(X, Z), first#(mark X1, X2) -> first#(X1, X2)) (active# first(s X, cons(Y, Z)) -> first#(X, Z), first#(ok X1, ok X2) -> first#(X1, X2)) (active# first(X1, X2) -> first#(active X1, X2), first#(X1, mark X2) -> first#(X1, X2)) (active# first(X1, X2) -> first#(active X1, X2), first#(mark X1, X2) -> first#(X1, X2)) (active# first(X1, X2) -> first#(active X1, X2), first#(ok X1, ok X2) -> first#(X1, 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)) } STATUS: arrows: 0.875091 SCCS (11): Scc: {top# mark X -> top# proper X, top# ok X -> top# active X} Scc: { active# cons(X1, X2) -> active# X1, active# recip X -> active# X, active# sqr X -> active# X, active# terms X -> active# X, active# add(X1, X2) -> active# X1, active# add(X1, X2) -> active# X2, active# dbl X -> active# X, active# first(X1, X2) -> active# X1, active# first(X1, X2) -> active# X2} Scc: { proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# recip X -> proper# X, proper# sqr X -> proper# X, proper# terms X -> proper# X, proper# s X -> proper# X, proper# add(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X2, proper# dbl X -> proper# X, proper# first(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X2} Scc: {dbl# mark X -> dbl# X, dbl# ok X -> dbl# X} Scc: {terms# mark X -> terms# X, terms# ok X -> terms# X} Scc: {sqr# mark X -> sqr# X, sqr# ok X -> sqr# X} Scc: {recip# mark X -> recip# X, recip# ok X -> recip# X} Scc: {s# ok X -> s# X} Scc: { first#(X1, mark X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2), first#(ok X1, ok X2) -> first#(X1, X2)} Scc: { add#(X1, mark X2) -> add#(X1, X2), add#(mark X1, X2) -> add#(X1, X2), add#(ok X1, ok X2) -> add#(X1, X2)} 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), recip mark X -> mark recip X, recip ok X -> ok recip X, sqr mark X -> mark sqr X, sqr ok X -> ok sqr X, terms mark X -> mark terms X, terms ok X -> ok terms X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active recip X -> recip active X, active sqr X -> sqr active X, active sqr s X -> mark s add(sqr X, dbl X), active sqr 0() -> mark 0(), active terms N -> mark cons(recip sqr N, terms s N), active terms X -> terms active X, active add(X1, X2) -> add(X1, active X2), active add(X1, X2) -> add(active X1, X2), active add(s X, Y) -> mark s add(X, Y), active add(0(), X) -> mark X, active dbl X -> dbl active X, active dbl s X -> mark s s dbl X, active dbl 0() -> mark 0(), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active first(0(), X) -> mark nil(), add(X1, mark X2) -> mark add(X1, X2), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, first(X1, mark X2) -> mark first(X1, X2), first(mark X1, X2) -> mark first(X1, X2), first(ok X1, ok X2) -> ok first(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper recip X -> recip proper X, proper sqr X -> sqr proper X, proper terms X -> terms 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 nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} Open SCC (9): Strict: { active# cons(X1, X2) -> active# X1, active# recip X -> active# X, active# sqr X -> active# X, active# terms X -> active# X, active# add(X1, X2) -> active# X1, active# add(X1, X2) -> active# X2, active# dbl X -> active# X, active# first(X1, X2) -> active# X1, active# first(X1, X2) -> active# X2} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), recip mark X -> mark recip X, recip ok X -> ok recip X, sqr mark X -> mark sqr X, sqr ok X -> ok sqr X, terms mark X -> mark terms X, terms ok X -> ok terms X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active recip X -> recip active X, active sqr X -> sqr active X, active sqr s X -> mark s add(sqr X, dbl X), active sqr 0() -> mark 0(), active terms N -> mark cons(recip sqr N, terms s N), active terms X -> terms active X, active add(X1, X2) -> add(X1, active X2), active add(X1, X2) -> add(active X1, X2), active add(s X, Y) -> mark s add(X, Y), active add(0(), X) -> mark X, active dbl X -> dbl active X, active dbl s X -> mark s s dbl X, active dbl 0() -> mark 0(), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active first(0(), X) -> mark nil(), add(X1, mark X2) -> mark add(X1, X2), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, first(X1, mark X2) -> mark first(X1, X2), first(mark X1, X2) -> mark first(X1, X2), first(ok X1, ok X2) -> ok first(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper recip X -> recip proper X, proper sqr X -> sqr proper X, proper terms X -> terms 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 nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} Open SCC (11): Strict: { proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# recip X -> proper# X, proper# sqr X -> proper# X, proper# terms X -> proper# X, proper# s X -> proper# X, proper# add(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X2, proper# dbl X -> proper# X, proper# first(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X2} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), recip mark X -> mark recip X, recip ok X -> ok recip X, sqr mark X -> mark sqr X, sqr ok X -> ok sqr X, terms mark X -> mark terms X, terms ok X -> ok terms X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active recip X -> recip active X, active sqr X -> sqr active X, active sqr s X -> mark s add(sqr X, dbl X), active sqr 0() -> mark 0(), active terms N -> mark cons(recip sqr N, terms s N), active terms X -> terms active X, active add(X1, X2) -> add(X1, active X2), active add(X1, X2) -> add(active X1, X2), active add(s X, Y) -> mark s add(X, Y), active add(0(), X) -> mark X, active dbl X -> dbl active X, active dbl s X -> mark s s dbl X, active dbl 0() -> mark 0(), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active first(0(), X) -> mark nil(), add(X1, mark X2) -> mark add(X1, X2), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, first(X1, mark X2) -> mark first(X1, X2), first(mark X1, X2) -> mark first(X1, X2), first(ok X1, ok X2) -> ok first(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper recip X -> recip proper X, proper sqr X -> sqr proper X, proper terms X -> terms 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 nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: {dbl# mark X -> dbl# X, dbl# ok X -> dbl# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), recip mark X -> mark recip X, recip ok X -> ok recip X, sqr mark X -> mark sqr X, sqr ok X -> ok sqr X, terms mark X -> mark terms X, terms ok X -> ok terms X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active recip X -> recip active X, active sqr X -> sqr active X, active sqr s X -> mark s add(sqr X, dbl X), active sqr 0() -> mark 0(), active terms N -> mark cons(recip sqr N, terms s N), active terms X -> terms active X, active add(X1, X2) -> add(X1, active X2), active add(X1, X2) -> add(active X1, X2), active add(s X, Y) -> mark s add(X, Y), active add(0(), X) -> mark X, active dbl X -> dbl active X, active dbl s X -> mark s s dbl X, active dbl 0() -> mark 0(), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active first(0(), X) -> mark nil(), add(X1, mark X2) -> mark add(X1, X2), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, first(X1, mark X2) -> mark first(X1, X2), first(mark X1, X2) -> mark first(X1, X2), first(ok X1, ok X2) -> ok first(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper recip X -> recip proper X, proper sqr X -> sqr proper X, proper terms X -> terms 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 nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: {terms# mark X -> terms# X, terms# ok X -> terms# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), recip mark X -> mark recip X, recip ok X -> ok recip X, sqr mark X -> mark sqr X, sqr ok X -> ok sqr X, terms mark X -> mark terms X, terms ok X -> ok terms X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active recip X -> recip active X, active sqr X -> sqr active X, active sqr s X -> mark s add(sqr X, dbl X), active sqr 0() -> mark 0(), active terms N -> mark cons(recip sqr N, terms s N), active terms X -> terms active X, active add(X1, X2) -> add(X1, active X2), active add(X1, X2) -> add(active X1, X2), active add(s X, Y) -> mark s add(X, Y), active add(0(), X) -> mark X, active dbl X -> dbl active X, active dbl s X -> mark s s dbl X, active dbl 0() -> mark 0(), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active first(0(), X) -> mark nil(), add(X1, mark X2) -> mark add(X1, X2), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, first(X1, mark X2) -> mark first(X1, X2), first(mark X1, X2) -> mark first(X1, X2), first(ok X1, ok X2) -> ok first(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper recip X -> recip proper X, proper sqr X -> sqr proper X, proper terms X -> terms 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 nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: {sqr# mark X -> sqr# X, sqr# ok X -> sqr# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), recip mark X -> mark recip X, recip ok X -> ok recip X, sqr mark X -> mark sqr X, sqr ok X -> ok sqr X, terms mark X -> mark terms X, terms ok X -> ok terms X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active recip X -> recip active X, active sqr X -> sqr active X, active sqr s X -> mark s add(sqr X, dbl X), active sqr 0() -> mark 0(), active terms N -> mark cons(recip sqr N, terms s N), active terms X -> terms active X, active add(X1, X2) -> add(X1, active X2), active add(X1, X2) -> add(active X1, X2), active add(s X, Y) -> mark s add(X, Y), active add(0(), X) -> mark X, active dbl X -> dbl active X, active dbl s X -> mark s s dbl X, active dbl 0() -> mark 0(), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active first(0(), X) -> mark nil(), add(X1, mark X2) -> mark add(X1, X2), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, first(X1, mark X2) -> mark first(X1, X2), first(mark X1, X2) -> mark first(X1, X2), first(ok X1, ok X2) -> ok first(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper recip X -> recip proper X, proper sqr X -> sqr proper X, proper terms X -> terms 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 nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: {recip# mark X -> recip# X, recip# ok X -> recip# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), recip mark X -> mark recip X, recip ok X -> ok recip X, sqr mark X -> mark sqr X, sqr ok X -> ok sqr X, terms mark X -> mark terms X, terms ok X -> ok terms X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active recip X -> recip active X, active sqr X -> sqr active X, active sqr s X -> mark s add(sqr X, dbl X), active sqr 0() -> mark 0(), active terms N -> mark cons(recip sqr N, terms s N), active terms X -> terms active X, active add(X1, X2) -> add(X1, active X2), active add(X1, X2) -> add(active X1, X2), active add(s X, Y) -> mark s add(X, Y), active add(0(), X) -> mark X, active dbl X -> dbl active X, active dbl s X -> mark s s dbl X, active dbl 0() -> mark 0(), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active first(0(), X) -> mark nil(), add(X1, mark X2) -> mark add(X1, X2), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, first(X1, mark X2) -> mark first(X1, X2), first(mark X1, X2) -> mark first(X1, X2), first(ok X1, ok X2) -> ok first(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper recip X -> recip proper X, proper sqr X -> sqr proper X, proper terms X -> terms 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 nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} Open SCC (1): Strict: {s# ok X -> s# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), recip mark X -> mark recip X, recip ok X -> ok recip X, sqr mark X -> mark sqr X, sqr ok X -> ok sqr X, terms mark X -> mark terms X, terms ok X -> ok terms X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active recip X -> recip active X, active sqr X -> sqr active X, active sqr s X -> mark s add(sqr X, dbl X), active sqr 0() -> mark 0(), active terms N -> mark cons(recip sqr N, terms s N), active terms X -> terms active X, active add(X1, X2) -> add(X1, active X2), active add(X1, X2) -> add(active X1, X2), active add(s X, Y) -> mark s add(X, Y), active add(0(), X) -> mark X, active dbl X -> dbl active X, active dbl s X -> mark s s dbl X, active dbl 0() -> mark 0(), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active first(0(), X) -> mark nil(), add(X1, mark X2) -> mark add(X1, X2), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, first(X1, mark X2) -> mark first(X1, X2), first(mark X1, X2) -> mark first(X1, X2), first(ok X1, ok X2) -> ok first(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper recip X -> recip proper X, proper sqr X -> sqr proper X, proper terms X -> terms 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 nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} Open SCC (3): Strict: { first#(X1, mark X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2), first#(ok X1, ok X2) -> first#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), recip mark X -> mark recip X, recip ok X -> ok recip X, sqr mark X -> mark sqr X, sqr ok X -> ok sqr X, terms mark X -> mark terms X, terms ok X -> ok terms X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active recip X -> recip active X, active sqr X -> sqr active X, active sqr s X -> mark s add(sqr X, dbl X), active sqr 0() -> mark 0(), active terms N -> mark cons(recip sqr N, terms s N), active terms X -> terms active X, active add(X1, X2) -> add(X1, active X2), active add(X1, X2) -> add(active X1, X2), active add(s X, Y) -> mark s add(X, Y), active add(0(), X) -> mark X, active dbl X -> dbl active X, active dbl s X -> mark s s dbl X, active dbl 0() -> mark 0(), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active first(0(), X) -> mark nil(), add(X1, mark X2) -> mark add(X1, X2), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, first(X1, mark X2) -> mark first(X1, X2), first(mark X1, X2) -> mark first(X1, X2), first(ok X1, ok X2) -> ok first(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper recip X -> recip proper X, proper sqr X -> sqr proper X, proper terms X -> terms 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 nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} Open SCC (3): Strict: { add#(X1, mark X2) -> add#(X1, X2), add#(mark X1, X2) -> add#(X1, X2), add#(ok X1, ok X2) -> add#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), recip mark X -> mark recip X, recip ok X -> ok recip X, sqr mark X -> mark sqr X, sqr ok X -> ok sqr X, terms mark X -> mark terms X, terms ok X -> ok terms X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active recip X -> recip active X, active sqr X -> sqr active X, active sqr s X -> mark s add(sqr X, dbl X), active sqr 0() -> mark 0(), active terms N -> mark cons(recip sqr N, terms s N), active terms X -> terms active X, active add(X1, X2) -> add(X1, active X2), active add(X1, X2) -> add(active X1, X2), active add(s X, Y) -> mark s add(X, Y), active add(0(), X) -> mark X, active dbl X -> dbl active X, active dbl s X -> mark s s dbl X, active dbl 0() -> mark 0(), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active first(0(), X) -> mark nil(), add(X1, mark X2) -> mark add(X1, X2), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, first(X1, mark X2) -> mark first(X1, X2), first(mark X1, X2) -> mark first(X1, X2), first(ok X1, ok X2) -> ok first(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper recip X -> recip proper X, proper sqr X -> sqr proper X, proper terms X -> terms 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 nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), 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), recip mark X -> mark recip X, recip ok X -> ok recip X, sqr mark X -> mark sqr X, sqr ok X -> ok sqr X, terms mark X -> mark terms X, terms ok X -> ok terms X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active recip X -> recip active X, active sqr X -> sqr active X, active sqr s X -> mark s add(sqr X, dbl X), active sqr 0() -> mark 0(), active terms N -> mark cons(recip sqr N, terms s N), active terms X -> terms active X, active add(X1, X2) -> add(X1, active X2), active add(X1, X2) -> add(active X1, X2), active add(s X, Y) -> mark s add(X, Y), active add(0(), X) -> mark X, active dbl X -> dbl active X, active dbl s X -> mark s s dbl X, active dbl 0() -> mark 0(), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active first(0(), X) -> mark nil(), add(X1, mark X2) -> mark add(X1, X2), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, first(X1, mark X2) -> mark first(X1, X2), first(mark X1, X2) -> mark first(X1, X2), first(ok X1, ok X2) -> ok first(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper recip X -> recip proper X, proper sqr X -> sqr proper X, proper terms X -> terms 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 nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} Open