MAYBE Time: 0.140490 TRS: { active and(X1, X2) -> and(active X1, X2), active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(X1, X2, X3) -> if(active X1, X2, X3), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(X1, X2) -> add(active X1, X2), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), if(mark X1, X2, X3) -> mark if(X1, X2, X3), if(ok X1, ok X2, ok X3) -> ok if(X1, X2, X3), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), s ok X -> ok s 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), cons(ok X1, ok X2) -> ok cons(X1, X2), from ok X -> ok from X, proper and(X1, X2) -> and(proper X1, proper X2), proper true() -> ok true(), proper false() -> ok false(), proper if(X1, X2, X3) -> if(proper X1, proper X2, proper X3), proper add(X1, X2) -> add(proper X1, proper X2), proper 0() -> ok 0(), proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, top mark X -> top proper X, top ok X -> top active X} DP: DP: { active# and(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2), active# if(X1, X2, X3) -> active# X1, active# if(X1, X2, X3) -> if#(active X1, X2, X3), active# add(X1, X2) -> active# X1, active# add(X1, X2) -> add#(active X1, X2), active# add(s X, Y) -> add#(X, Y), active# add(s X, Y) -> s# add(X, Y), 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)) -> first#(X, Z), active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z)), active# from X -> s# X, active# from X -> cons#(X, from s X), active# from X -> from# s X, and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2), if#(mark X1, X2, X3) -> if#(X1, X2, X3), if#(ok X1, ok X2, ok X3) -> if#(X1, X2, X3), add#(mark X1, X2) -> add#(X1, X2), add#(ok X1, ok X2) -> add#(X1, X2), s# ok X -> s# X, first#(X1, mark X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2), first#(ok X1, ok X2) -> first#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2), from# ok X -> from# X, proper# and(X1, X2) -> and#(proper X1, proper X2), proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2, proper# if(X1, X2, X3) -> if#(proper X1, proper X2, proper X3), proper# if(X1, X2, X3) -> proper# X1, proper# if(X1, X2, X3) -> proper# X2, proper# if(X1, X2, X3) -> proper# X3, proper# add(X1, X2) -> add#(proper X1, proper X2), proper# add(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X2, proper# s X -> s# proper X, proper# s X -> proper# X, proper# first(X1, X2) -> first#(proper X1, proper X2), proper# first(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2), proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> from# proper X, proper# from 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: { active and(X1, X2) -> and(active X1, X2), active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(X1, X2, X3) -> if(active X1, X2, X3), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(X1, X2) -> add(active X1, X2), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), if(mark X1, X2, X3) -> mark if(X1, X2, X3), if(ok X1, ok X2, ok X3) -> ok if(X1, X2, X3), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), s ok X -> ok s 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), cons(ok X1, ok X2) -> ok cons(X1, X2), from ok X -> ok from X, proper and(X1, X2) -> and(proper X1, proper X2), proper true() -> ok true(), proper false() -> ok false(), proper if(X1, X2, X3) -> if(proper X1, proper X2, proper X3), proper add(X1, X2) -> add(proper X1, proper X2), proper 0() -> ok 0(), proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, top mark X -> top proper X, top ok X -> top active X} EDG: { (from# ok X -> from# X, from# ok X -> from# X) (proper# from X -> proper# X, proper# from X -> proper# X) (proper# from X -> proper# X, proper# from X -> from# proper X) (proper# from X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# from X -> proper# X, proper# first(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# first(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# from X -> proper# X, proper# s X -> proper# X) (proper# from X -> proper# X, proper# s X -> s# proper X) (proper# from X -> proper# X, proper# add(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# add(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# add(X1, X2) -> add#(proper X1, proper X2)) (proper# from X -> proper# X, proper# if(X1, X2, X3) -> proper# X3) (proper# from X -> proper# X, proper# if(X1, X2, X3) -> proper# X2) (proper# from X -> proper# X, proper# if(X1, X2, X3) -> proper# X1) (proper# from X -> proper# X, proper# if(X1, X2, X3) -> if#(proper X1, proper X2, proper X3)) (proper# from X -> proper# X, proper# and(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# and(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2)) (top# ok X -> active# X, active# from X -> from# s X) (top# ok X -> active# X, active# from X -> cons#(X, from s X)) (top# ok X -> active# X, active# from X -> s# X) (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)) (top# ok X -> active# X, active# first(X1, X2) -> first#(active X1, X2)) (top# ok X -> active# X, active# first(X1, X2) -> first#(X1, active X2)) (top# ok X -> active# X, active# first(X1, X2) -> active# X2) (top# ok X -> active# X, active# first(X1, X2) -> active# X1) (top# ok X -> active# X, active# add(s X, Y) -> s# add(X, Y)) (top# ok X -> active# X, active# add(s X, Y) -> add#(X, Y)) (top# ok X -> active# X, active# add(X1, X2) -> add#(active X1, X2)) (top# ok X -> active# X, active# add(X1, X2) -> active# X1) (top# ok X -> active# X, active# if(X1, X2, X3) -> if#(active X1, X2, X3)) (top# ok X -> active# X, active# if(X1, X2, X3) -> active# X1) (top# ok X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (top# ok X -> active# X, active# and(X1, X2) -> active# X1) (active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z)), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# and(X1, X2) -> active# X1, active# from X -> from# s X) (active# and(X1, X2) -> active# X1, active# from X -> cons#(X, from s X)) (active# and(X1, X2) -> active# X1, active# from X -> s# X) (active# and(X1, X2) -> active# X1, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (active# and(X1, X2) -> active# X1, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (active# and(X1, X2) -> active# X1, active# first(X1, X2) -> first#(active X1, X2)) (active# and(X1, X2) -> active# X1, active# first(X1, X2) -> first#(X1, active X2)) (active# and(X1, X2) -> active# X1, active# first(X1, X2) -> active# X2) (active# and(X1, X2) -> active# X1, active# first(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# add(s X, Y) -> s# add(X, Y)) (active# and(X1, X2) -> active# X1, active# add(s X, Y) -> add#(X, Y)) (active# and(X1, X2) -> active# X1, active# add(X1, X2) -> add#(active X1, X2)) (active# and(X1, X2) -> active# X1, active# add(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# if(X1, X2, X3) -> if#(active X1, X2, X3)) (active# and(X1, X2) -> active# X1, active# if(X1, X2, X3) -> active# X1) (active# and(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# and(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (active# add(X1, X2) -> active# X1, active# from X -> from# s X) (active# add(X1, X2) -> active# X1, active# from X -> cons#(X, from s X)) (active# add(X1, X2) -> active# X1, active# from X -> s# X) (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(s X, cons(Y, Z)) -> 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# add(s X, Y) -> s# add(X, Y)) (active# add(X1, X2) -> active# X1, active# add(s X, Y) -> 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) -> active# X1) (active# add(X1, X2) -> active# X1, active# if(X1, X2, X3) -> if#(active X1, X2, X3)) (active# add(X1, X2) -> active# X1, active# if(X1, X2, X3) -> active# X1) (active# add(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# add(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (proper# and(X1, X2) -> proper# X1, proper# from X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# from X -> from# proper X) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# and(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# add(X1, X2) -> add#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# if(X1, X2, X3) -> proper# X3) (proper# and(X1, X2) -> proper# X1, proper# if(X1, X2, X3) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# if(X1, X2, X3) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# if(X1, X2, X3) -> if#(proper X1, proper X2, proper X3)) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# add(X1, X2) -> proper# X1, proper# from X -> proper# X) (proper# add(X1, X2) -> proper# X1, proper# from X -> from# proper X) (proper# add(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# add(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# add(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# add(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X2) (proper# add(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X1) (proper# add(X1, X2) -> proper# X1, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# add(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# add(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# add(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X2) (proper# add(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X1) (proper# add(X1, X2) -> proper# X1, proper# add(X1, X2) -> add#(proper X1, proper X2)) (proper# add(X1, X2) -> proper# X1, proper# if(X1, X2, X3) -> proper# X3) (proper# add(X1, X2) -> proper# X1, proper# if(X1, X2, X3) -> proper# X2) (proper# add(X1, X2) -> proper# X1, proper# if(X1, X2, X3) -> proper# X1) (proper# add(X1, X2) -> proper# X1, proper# if(X1, X2, X3) -> if#(proper X1, proper X2, proper X3)) (proper# add(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# add(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# add(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X1, proper# from X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# from X -> from# 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# 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# s X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# s X -> s# 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# if(X1, X2, X3) -> proper# X3) (proper# cons(X1, X2) -> proper# X1, proper# if(X1, X2, X3) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# if(X1, X2, X3) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# if(X1, X2, X3) -> if#(proper X1, proper X2, proper X3)) (proper# cons(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (active# first(X1, X2) -> first#(X1, active X2), first#(ok X1, ok X2) -> first#(X1, X2)) (active# first(X1, X2) -> first#(X1, active X2), first#(X1, mark X2) -> first#(X1, X2)) (proper# add(X1, X2) -> add#(proper X1, proper X2), add#(ok X1, ok X2) -> add#(X1, X2)) (proper# add(X1, X2) -> add#(proper X1, proper X2), add#(mark X1, X2) -> add#(X1, X2)) (proper# cons(X1, X2) -> cons#(proper X1, proper X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (proper# and(X1, X2) -> proper# X2, proper# from X -> proper# X) (proper# and(X1, X2) -> proper# X2, proper# from X -> from# proper X) (proper# and(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X2, proper# first(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# first(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X2, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# 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first(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# first(X1, X2) -> proper# X1, proper# from X -> from# proper X) (proper# first(X1, X2) -> proper# X1, proper# from X -> proper# X) (proper# if(X1, X2, X3) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# if(X1, X2, X3) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# if(X1, X2, X3) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# if(X1, X2, X3) -> proper# X1, proper# if(X1, X2, X3) -> if#(proper X1, proper X2, proper X3)) (proper# if(X1, X2, X3) -> proper# X1, proper# if(X1, X2, X3) -> proper# X1) (proper# if(X1, X2, X3) -> proper# X1, proper# if(X1, X2, X3) -> proper# X2) (proper# if(X1, X2, X3) -> proper# X1, proper# if(X1, X2, X3) -> proper# X3) (proper# if(X1, X2, X3) -> proper# X1, proper# add(X1, X2) -> add#(proper X1, proper X2)) (proper# if(X1, X2, X3) -> proper# X1, proper# add(X1, X2) -> proper# X1) (proper# if(X1, X2, X3) -> proper# X1, proper# add(X1, X2) -> proper# X2) (proper# if(X1, X2, X3) -> proper# X1, proper# s X -> s# proper X) (proper# if(X1, X2, X3) -> proper# X1, proper# s X -> proper# X) (proper# if(X1, X2, X3) -> proper# X1, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# if(X1, X2, X3) -> proper# X1, proper# first(X1, X2) -> proper# X1) (proper# if(X1, X2, X3) -> proper# X1, proper# first(X1, X2) -> proper# X2) (proper# if(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# if(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# if(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# if(X1, X2, X3) -> proper# X1, proper# from X -> from# proper X) (proper# if(X1, X2, X3) -> proper# X1, proper# from X -> proper# X) (active# first(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (active# first(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# first(X1, X2) -> active# X1, active# if(X1, X2, X3) -> active# X1) (active# first(X1, X2) -> active# X1, active# if(X1, X2, X3) -> if#(active X1, X2, X3)) (active# first(X1, X2) -> active# X1, active# add(X1, X2) -> active# X1) (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) -> add#(X, Y)) (active# first(X1, X2) -> active# X1, active# add(s X, Y) -> s# add(X, Y)) (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)) -> first#(X, Z)) (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# from X -> s# X) (active# first(X1, X2) -> active# X1, active# from X -> cons#(X, from s X)) (active# first(X1, X2) -> active# X1, active# from X -> from# s X) (active# if(X1, X2, X3) -> active# X1, active# and(X1, X2) -> active# X1) (active# if(X1, X2, X3) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# if(X1, X2, X3) -> active# X1, active# if(X1, X2, X3) -> active# X1) (active# if(X1, X2, X3) -> active# X1, active# if(X1, X2, X3) -> if#(active X1, X2, X3)) (active# if(X1, X2, X3) -> active# X1, active# add(X1, X2) -> active# X1) (active# if(X1, X2, X3) -> active# X1, active# add(X1, X2) -> add#(active X1, X2)) (active# if(X1, X2, X3) -> active# X1, active# add(s X, Y) -> add#(X, Y)) (active# if(X1, X2, X3) -> active# X1, active# add(s X, Y) -> s# add(X, Y)) (active# if(X1, X2, X3) -> active# X1, active# first(X1, X2) -> active# X1) (active# if(X1, X2, X3) -> active# X1, active# first(X1, X2) -> active# X2) (active# if(X1, X2, X3) -> active# X1, active# first(X1, X2) -> first#(X1, active X2)) (active# if(X1, X2, X3) -> active# X1, active# first(X1, X2) -> first#(active X1, X2)) (active# if(X1, X2, X3) -> active# X1, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (active# if(X1, X2, X3) -> active# X1, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (active# if(X1, X2, X3) -> active# X1, active# from X -> s# X) (active# if(X1, X2, X3) -> active# X1, active# from X -> cons#(X, from s X)) (active# if(X1, X2, X3) -> active# X1, active# from X -> from# s X) (proper# if(X1, X2, X3) -> if#(proper X1, proper X2, proper X3), if#(mark X1, X2, X3) -> if#(X1, X2, X3)) (proper# if(X1, X2, X3) -> if#(proper X1, proper X2, proper X3), if#(ok X1, ok X2, ok X3) -> if#(X1, X2, X3)) (top# mark X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2)) (top# mark X -> proper# X, proper# and(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# and(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# if(X1, X2, X3) -> if#(proper X1, proper X2, proper X3)) (top# mark X -> proper# X, proper# if(X1, X2, X3) -> proper# X1) (top# mark X -> proper# X, proper# if(X1, X2, X3) -> proper# X2) (top# mark X -> proper# X, proper# if(X1, X2, X3) -> proper# X3) (top# mark X -> proper# X, proper# add(X1, X2) -> add#(proper X1, proper X2)) (top# mark X -> proper# X, proper# add(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# add(X1, X2) -> proper# X2) (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# first(X1, X2) -> first#(proper X1, proper X2)) (top# mark X -> proper# X, proper# first(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# first(X1, X2) -> proper# 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# from X -> from# proper X) (top# mark X -> proper# X, proper# from X -> proper# X) (proper# s X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# s X -> proper# X, proper# and(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# and(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# if(X1, X2, X3) -> if#(proper X1, proper X2, proper X3)) (proper# s X -> proper# X, proper# if(X1, X2, X3) -> proper# X1) (proper# s X -> proper# X, proper# if(X1, X2, X3) -> proper# X2) (proper# s X -> proper# X, proper# if(X1, X2, X3) -> proper# X3) (proper# s X -> proper# X, proper# add(X1, X2) -> add#(proper X1, proper X2)) (proper# s X -> proper# X, proper# add(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# add(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# s X -> s# proper X) (proper# s X -> proper# X, proper# s X -> proper# X) (proper# s X -> proper# X, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# s X -> proper# X, proper# first(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# first(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# from X -> from# proper X) (proper# s X -> proper# X, proper# from X -> proper# X) (s# ok X -> s# X, s# ok X -> s# X) (active# add(s X, Y) -> add#(X, Y), add#(mark X1, X2) -> add#(X1, X2)) } STATUS: arrows: 0.842649 SCCS (10): Scc: {top# mark X -> top# proper X, top# ok X -> top# active X} Scc: { active# and(X1, X2) -> active# X1, active# if(X1, X2, X3) -> active# X1, active# add(X1, X2) -> active# X1, active# first(X1, X2) -> active# X1, active# first(X1, X2) -> active# X2} Scc: { proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2, proper# if(X1, X2, X3) -> proper# X1, proper# if(X1, X2, X3) -> proper# X2, proper# if(X1, X2, X3) -> proper# X3, proper# add(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X2, proper# s X -> proper# X, proper# first(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X} Scc: {cons#(ok X1, ok X2) -> cons#(X1, X2)} Scc: { first#(X1, mark X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2), first#(ok X1, ok X2) -> first#(X1, X2)} Scc: { if#(mark X1, X2, X3) -> if#(X1, X2, X3), if#(ok X1, ok X2, ok X3) -> if#(X1, X2, X3)} Scc: { and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)} Scc: {from# ok X -> from# X} Scc: {s# ok X -> s# X} Scc: { add#(mark X1, X2) -> add#(X1, X2), add#(ok X1, ok X2) -> add#(X1, X2)} SCC (2): Strict: {top# mark X -> top# proper X, top# ok X -> top# active X} Weak: { active and(X1, X2) -> and(active X1, X2), active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(X1, X2, X3) -> if(active X1, X2, X3), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(X1, X2) -> add(active X1, X2), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), if(mark X1, X2, X3) -> mark if(X1, X2, X3), if(ok X1, ok X2, ok X3) -> ok if(X1, X2, X3), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), s ok X -> ok s 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), cons(ok X1, ok X2) -> ok cons(X1, X2), from ok X -> ok from X, proper and(X1, X2) -> and(proper X1, proper X2), proper true() -> ok true(), proper false() -> ok false(), proper if(X1, X2, X3) -> if(proper X1, proper X2, proper X3), proper add(X1, X2) -> add(proper X1, proper X2), proper 0() -> ok 0(), proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (5): Strict: { active# and(X1, X2) -> active# X1, active# if(X1, X2, X3) -> active# X1, active# add(X1, X2) -> active# X1, active# first(X1, X2) -> active# X1, active# first(X1, X2) -> active# X2} Weak: { active and(X1, X2) -> and(active X1, X2), active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(X1, X2, X3) -> if(active X1, X2, X3), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(X1, X2) -> add(active X1, X2), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), if(mark X1, X2, X3) -> mark if(X1, X2, X3), if(ok X1, ok X2, ok X3) -> ok if(X1, X2, X3), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), s ok X -> ok s 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), cons(ok X1, ok X2) -> ok cons(X1, X2), from ok X -> ok from X, proper and(X1, X2) -> and(proper X1, proper X2), proper true() -> ok true(), proper false() -> ok false(), proper if(X1, X2, X3) -> if(proper X1, proper X2, proper X3), proper add(X1, X2) -> add(proper X1, proper X2), proper 0() -> ok 0(), proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (13): Strict: { proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2, proper# if(X1, X2, X3) -> proper# X1, proper# if(X1, X2, X3) -> proper# X2, proper# if(X1, X2, X3) -> proper# X3, proper# add(X1, X2) -> proper# X1, proper# add(X1, X2) -> proper# X2, proper# s X -> proper# X, proper# first(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X} Weak: { active and(X1, X2) -> and(active X1, X2), active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(X1, X2, X3) -> if(active X1, X2, X3), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(X1, X2) -> add(active X1, X2), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), if(mark X1, X2, X3) -> mark if(X1, X2, X3), if(ok X1, ok X2, ok X3) -> ok if(X1, X2, X3), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), s ok X -> ok s 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), cons(ok X1, ok X2) -> ok cons(X1, X2), from ok X -> ok from X, proper and(X1, X2) -> and(proper X1, proper X2), proper true() -> ok true(), proper false() -> ok false(), proper if(X1, X2, X3) -> if(proper X1, proper X2, proper X3), proper add(X1, X2) -> add(proper X1, proper X2), proper 0() -> ok 0(), proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (1): Strict: {cons#(ok X1, ok X2) -> cons#(X1, X2)} Weak: { active and(X1, X2) -> and(active X1, X2), active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(X1, X2, X3) -> if(active X1, X2, X3), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(X1, X2) -> add(active X1, X2), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), if(mark X1, X2, X3) -> mark if(X1, X2, X3), if(ok X1, ok X2, ok X3) -> ok if(X1, X2, X3), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), s ok X -> ok s 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), cons(ok X1, ok X2) -> ok cons(X1, X2), from ok X -> ok from X, proper and(X1, X2) -> and(proper X1, proper X2), proper true() -> ok true(), proper false() -> ok false(), proper if(X1, X2, X3) -> if(proper X1, proper X2, proper X3), proper add(X1, X2) -> add(proper X1, proper X2), proper 0() -> ok 0(), proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, 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: { active and(X1, X2) -> and(active X1, X2), active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(X1, X2, X3) -> if(active X1, X2, X3), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(X1, X2) -> add(active X1, X2), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), if(mark X1, X2, X3) -> mark if(X1, X2, X3), if(ok X1, ok X2, ok X3) -> ok if(X1, X2, X3), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), s ok X -> ok s 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), cons(ok X1, ok X2) -> ok cons(X1, X2), from ok X -> ok from X, proper and(X1, X2) -> and(proper X1, proper X2), proper true() -> ok true(), proper false() -> ok false(), proper if(X1, X2, X3) -> if(proper X1, proper X2, proper X3), proper add(X1, X2) -> add(proper X1, proper X2), proper 0() -> ok 0(), proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: { if#(mark X1, X2, X3) -> if#(X1, X2, X3), if#(ok X1, ok X2, ok X3) -> if#(X1, X2, X3)} Weak: { active and(X1, X2) -> and(active X1, X2), active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(X1, X2, X3) -> if(active X1, X2, X3), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(X1, X2) -> add(active X1, X2), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), if(mark X1, X2, X3) -> mark if(X1, X2, X3), if(ok X1, ok X2, ok X3) -> ok if(X1, X2, X3), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), s ok X -> ok s 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), cons(ok X1, ok X2) -> ok cons(X1, X2), from ok X -> ok from X, proper and(X1, X2) -> and(proper X1, proper X2), proper true() -> ok true(), proper false() -> ok false(), proper if(X1, X2, X3) -> if(proper X1, proper X2, proper X3), proper add(X1, X2) -> add(proper X1, proper X2), proper 0() -> ok 0(), proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: { and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)} Weak: { active and(X1, X2) -> and(active X1, X2), active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(X1, X2, X3) -> if(active X1, X2, X3), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(X1, X2) -> add(active X1, X2), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), if(mark X1, X2, X3) -> mark if(X1, X2, X3), if(ok X1, ok X2, ok X3) -> ok if(X1, X2, X3), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), s ok X -> ok s 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), cons(ok X1, ok X2) -> ok cons(X1, X2), from ok X -> ok from X, proper and(X1, X2) -> and(proper X1, proper X2), proper true() -> ok true(), proper false() -> ok false(), proper if(X1, X2, X3) -> if(proper X1, proper X2, proper X3), proper add(X1, X2) -> add(proper X1, proper X2), proper 0() -> ok 0(), proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (1): Strict: {from# ok X -> from# X} Weak: { active and(X1, X2) -> and(active X1, X2), active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(X1, X2, X3) -> if(active X1, X2, X3), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(X1, X2) -> add(active X1, X2), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), if(mark X1, X2, X3) -> mark if(X1, X2, X3), if(ok X1, ok X2, ok X3) -> ok if(X1, X2, X3), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), s ok X -> ok s 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), cons(ok X1, ok X2) -> ok cons(X1, X2), from ok X -> ok from X, proper and(X1, X2) -> and(proper X1, proper X2), proper true() -> ok true(), proper false() -> ok false(), proper if(X1, X2, X3) -> if(proper X1, proper X2, proper X3), proper add(X1, X2) -> add(proper X1, proper X2), proper 0() -> ok 0(), proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (1): Strict: {s# ok X -> s# X} Weak: { active and(X1, X2) -> and(active X1, X2), active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(X1, X2, X3) -> if(active X1, X2, X3), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(X1, X2) -> add(active X1, X2), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), if(mark X1, X2, X3) -> mark if(X1, X2, X3), if(ok X1, ok X2, ok X3) -> ok if(X1, X2, X3), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), s ok X -> ok s 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), cons(ok X1, ok X2) -> ok cons(X1, X2), from ok X -> ok from X, proper and(X1, X2) -> and(proper X1, proper X2), proper true() -> ok true(), proper false() -> ok false(), proper if(X1, X2, X3) -> if(proper X1, proper X2, proper X3), proper add(X1, X2) -> add(proper X1, proper X2), proper 0() -> ok 0(), proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: { add#(mark X1, X2) -> add#(X1, X2), add#(ok X1, ok X2) -> add#(X1, X2)} Weak: { active and(X1, X2) -> and(active X1, X2), active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(X1, X2, X3) -> if(active X1, X2, X3), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(X1, X2) -> add(active X1, X2), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active first(X1, X2) -> first(X1, active X2), active first(X1, X2) -> first(active X1, X2), active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), if(mark X1, X2, X3) -> mark if(X1, X2, X3), if(ok X1, ok X2, ok X3) -> ok if(X1, X2, X3), add(mark X1, X2) -> mark add(X1, X2), add(ok X1, ok X2) -> ok add(X1, X2), s ok X -> ok s 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), cons(ok X1, ok X2) -> ok cons(X1, X2), from ok X -> ok from X, proper and(X1, X2) -> and(proper X1, proper X2), proper true() -> ok true(), proper false() -> ok false(), proper if(X1, X2, X3) -> if(proper X1, proper X2, proper X3), proper add(X1, X2) -> add(proper X1, proper X2), proper 0() -> ok 0(), proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, top mark X -> top proper X, top ok X -> top active X} Open