MAYBE Time: 0.517667 TRS: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, 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(), Z) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Z)) -> mark 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), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(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), from# mark X -> from# X, from# ok X -> from# X, s# mark X -> s# X, s# ok X -> s# X, active# cons(X1, X2) -> cons#(active X1, X2), active# cons(X1, X2) -> active# X1, active# from X -> cons#(X, from s X), active# from X -> from# s X, active# from X -> from# active X, active# from X -> s# X, active# from X -> active# X, active# s X -> s# active X, active# s X -> active# 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), active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2, active# sel(X1, X2) -> sel#(X1, active X2), active# sel(X1, X2) -> sel#(active X1, X2), active# sel(s X, cons(Y, Z)) -> sel#(X, Z), first#(X1, mark X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2), first#(ok X1, ok X2) -> first#(X1, X2), sel#(X1, mark X2) -> sel#(X1, X2), sel#(mark X1, X2) -> sel#(X1, X2), sel#(ok X1, ok X2) -> sel#(X1, 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, 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# sel(X1, X2) -> sel#(proper X1, proper X2), proper# sel(X1, X2) -> proper# X1, proper# sel(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), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, 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(), Z) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Z)) -> mark 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), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} EDG: { (active# from X -> from# active X, from# ok X -> from# X) (active# from X -> from# active X, from# mark X -> from# X) (proper# from X -> from# proper X, from# ok X -> from# X) (proper# from X -> from# proper X, from# mark X -> from# 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# cons(X1, X2) -> cons#(active X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# cons(X1, X2) -> cons#(active X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (active# sel(X1, X2) -> sel#(active X1, X2), sel#(ok X1, ok X2) -> sel#(X1, X2)) (active# sel(X1, X2) -> sel#(active X1, X2), sel#(mark X1, X2) -> sel#(X1, X2)) (active# sel(X1, X2) -> sel#(active X1, X2), sel#(X1, mark X2) -> sel#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (active# first(X1, X2) -> active# X2, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (active# first(X1, X2) -> active# X2, active# sel(X1, X2) -> sel#(active X1, X2)) (active# first(X1, X2) -> active# X2, active# sel(X1, X2) -> sel#(X1, active X2)) (active# first(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X2) (active# first(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X1) (active# first(X1, X2) -> active# X2, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (active# first(X1, X2) -> active# X2, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (active# first(X1, X2) -> active# X2, active# first(X1, X2) -> first#(active X1, X2)) (active# first(X1, X2) -> active# X2, active# first(X1, X2) -> first#(X1, active X2)) (active# first(X1, X2) -> active# X2, active# first(X1, X2) -> active# X2) (active# first(X1, X2) -> active# X2, active# first(X1, X2) -> active# X1) (active# first(X1, X2) -> active# X2, active# s X -> active# X) (active# first(X1, X2) -> active# X2, active# s X -> s# active X) (active# first(X1, X2) -> active# X2, active# from X -> active# X) (active# first(X1, X2) -> active# X2, active# from X -> s# X) (active# first(X1, X2) -> active# X2, active# from X -> from# active X) (active# first(X1, X2) -> active# X2, active# from X -> from# s X) (active# first(X1, X2) -> active# X2, active# from X -> cons#(X, from s X)) (active# first(X1, X2) -> active# X2, active# cons(X1, X2) -> active# X1) (active# first(X1, X2) -> active# X2, active# cons(X1, X2) -> cons#(active X1, X2)) (first#(X1, mark X2) -> first#(X1, X2), first#(ok X1, ok 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#(X1, mark X2) -> first#(X1, X2)) (first#(ok X1, ok X2) -> first#(X1, X2), first#(ok X1, ok 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#(X1, mark X2) -> first#(X1, X2)) (sel#(mark X1, X2) -> sel#(X1, X2), sel#(ok X1, ok X2) -> sel#(X1, X2)) (sel#(mark X1, X2) -> sel#(X1, X2), sel#(mark X1, X2) -> sel#(X1, X2)) (sel#(mark X1, X2) -> sel#(X1, X2), sel#(X1, mark X2) -> sel#(X1, X2)) (proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# first(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# first(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# from X -> from# proper X) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X2) (proper# sel(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X2, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X2, proper# first(X1, X2) -> proper# X2) (proper# sel(X1, X2) -> proper# X2, proper# first(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X2, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# sel(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# sel(X1, X2) -> proper# X2, proper# from X -> proper# X) (proper# sel(X1, X2) -> proper# X2, proper# from X -> from# proper X) (proper# sel(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# sel(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# sel(s X, cons(Y, Z)) -> sel#(X, Z), sel#(ok X1, ok X2) -> sel#(X1, X2)) (active# sel(s X, cons(Y, Z)) -> sel#(X, Z), sel#(mark X1, X2) -> sel#(X1, X2)) (active# sel(s X, cons(Y, Z)) -> sel#(X, Z), sel#(X1, mark X2) -> sel#(X1, X2)) (active# sel(X1, X2) -> sel#(X1, active X2), sel#(ok X1, ok X2) -> sel#(X1, X2)) (active# sel(X1, X2) -> sel#(X1, active X2), sel#(mark X1, X2) -> sel#(X1, X2)) (active# sel(X1, X2) -> sel#(X1, active X2), sel#(X1, mark X2) -> sel#(X1, X2)) (proper# first(X1, X2) -> first#(proper X1, proper X2), first#(ok X1, ok X2) -> first#(X1, X2)) (proper# first(X1, X2) -> first#(proper X1, proper X2), first#(mark X1, X2) -> first#(X1, X2)) (proper# first(X1, X2) -> first#(proper X1, proper X2), first#(X1, mark X2) -> first#(X1, X2)) (from# mark X -> from# X, from# ok X -> from# X) (from# mark X -> from# X, from# mark X -> from# X) (s# mark X -> s# X, s# ok X -> s# X) (s# mark X -> s# X, s# mark X -> s# X) (active# from X -> s# X, s# ok X -> s# X) (active# from X -> s# X, s# mark X -> s# X) (active# s X -> active# X, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (active# s X -> active# X, active# sel(X1, X2) -> sel#(active X1, X2)) (active# s X -> active# X, active# sel(X1, X2) -> sel#(X1, active X2)) (active# s X -> active# X, active# sel(X1, X2) -> active# X2) (active# s X -> active# X, active# sel(X1, X2) -> active# X1) (active# s X -> active# X, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (active# s X -> active# X, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (active# s X -> active# X, active# first(X1, X2) -> first#(active X1, X2)) (active# s X -> active# X, active# first(X1, X2) -> first#(X1, active X2)) (active# s X -> active# X, active# first(X1, X2) -> active# X2) (active# s X -> active# X, active# first(X1, X2) -> active# X1) (active# s X -> active# X, active# s X -> active# X) (active# s X -> active# X, active# s X -> s# active X) (active# s X -> active# X, active# from X -> active# X) (active# s X -> active# X, active# from X -> s# X) (active# s X -> active# X, active# from X -> from# active X) (active# s X -> active# X, active# from X -> from# s X) (active# s X -> active# X, active# from X -> cons#(X, from s X)) (active# s X -> active# X, active# cons(X1, X2) -> active# X1) (active# s X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (proper# s X -> proper# X, proper# sel(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# sel(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# s X -> proper# X, proper# first(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# first(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# s X -> proper# X, proper# s X -> proper# X) (proper# s X -> proper# X, proper# s X -> s# proper X) (proper# s X -> proper# X, proper# from X -> proper# X) (proper# s X -> proper# X, proper# from X -> from# proper X) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (top# ok X -> active# X, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (top# ok X -> active# X, active# sel(X1, X2) -> sel#(active X1, X2)) (top# ok X -> active# X, active# sel(X1, X2) -> sel#(X1, active X2)) (top# ok X -> active# X, active# sel(X1, X2) -> active# X2) (top# ok X -> active# X, active# sel(X1, X2) -> active# X1) (top# ok X -> active# X, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (top# ok X -> active# X, active# first(s X, cons(Y, Z)) -> cons#(Y, 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# s X -> active# X) (top# ok X -> active# X, active# s X -> s# active X) (top# ok X -> active# X, active# from X -> active# X) (top# ok X -> active# X, active# from X -> s# X) (top# ok X -> active# X, active# from X -> from# active X) (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# cons(X1, X2) -> active# X1) (top# ok X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# cons(X1, X2) -> active# X1, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (active# cons(X1, X2) -> active# X1, active# sel(X1, X2) -> sel#(active X1, X2)) (active# cons(X1, X2) -> active# X1, active# sel(X1, X2) -> sel#(X1, active X2)) (active# cons(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2) (active# cons(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (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(X1, X2) -> first#(active X1, 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) -> active# X2) (active# cons(X1, X2) -> active# X1, active# first(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# s X -> active# X) (active# cons(X1, X2) -> active# X1, active# s X -> s# active X) (active# cons(X1, X2) -> active# X1, active# from X -> active# X) (active# cons(X1, X2) -> active# X1, active# from X -> s# X) (active# cons(X1, X2) -> active# X1, active# from X -> from# active X) (active# cons(X1, X2) -> active# X1, active# from X -> from# s X) (active# cons(X1, X2) -> active# X1, active# from X -> cons#(X, from s X)) (active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# sel(X1, X2) -> active# X1, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> sel#(active X1, X2)) (active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> sel#(X1, active X2)) (active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2) (active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X1, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (active# sel(X1, X2) -> active# X1, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (active# sel(X1, X2) -> active# X1, active# first(X1, X2) -> first#(active X1, X2)) (active# sel(X1, X2) -> active# X1, active# first(X1, X2) -> first#(X1, active X2)) (active# sel(X1, X2) -> active# X1, active# first(X1, X2) -> active# X2) (active# sel(X1, X2) -> active# X1, active# first(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X1, active# s X -> active# X) (active# sel(X1, X2) -> active# X1, active# s X -> s# active X) (active# sel(X1, X2) -> active# X1, active# from X -> active# X) (active# sel(X1, X2) -> active# X1, active# from X -> s# X) (active# sel(X1, X2) -> active# X1, active# from X -> from# active X) (active# sel(X1, X2) -> active# X1, active# from X -> from# s X) (active# sel(X1, X2) -> active# X1, active# from X -> cons#(X, from s X)) (active# sel(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (proper# first(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2) (proper# first(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X1) (proper# first(X1, X2) -> proper# X1, proper# sel(X1, X2) -> sel#(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# s X -> proper# X) (proper# first(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# first(X1, X2) -> proper# X1, proper# from X -> proper# X) (proper# first(X1, X2) -> proper# X1, proper# from X -> from# 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)) (proper# sel(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# sel(X1, X2) -> proper# X1, proper# from X -> from# proper X) (proper# sel(X1, X2) -> proper# X1, proper# from X -> proper# X) (proper# sel(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# sel(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# sel(X1, X2) -> proper# X1, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X2) (proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# from X -> from# proper X) (proper# cons(X1, X2) -> proper# X1, proper# from X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# cons(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# sel(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# from X -> cons#(X, from s X)) (active# first(X1, X2) -> active# X1, active# from X -> from# s X) (active# first(X1, X2) -> active# X1, active# from X -> from# active X) (active# first(X1, X2) -> active# X1, active# from X -> s# X) (active# first(X1, X2) -> active# X1, active# from X -> active# X) (active# first(X1, X2) -> active# X1, active# s X -> s# active X) (active# first(X1, X2) -> active# X1, active# s X -> active# 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# first(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X1) (active# first(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2) (active# first(X1, X2) -> active# X1, active# sel(X1, X2) -> sel#(X1, active X2)) (active# first(X1, X2) -> active# X1, active# sel(X1, X2) -> sel#(active X1, X2)) (active# first(X1, X2) -> active# X1, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z)), cons#(mark X1, X2) -> cons#(X1, X2)) (active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z)), cons#(ok X1, ok X2) -> cons#(X1, X2)) (top# mark X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# from X -> from# proper X) (top# mark X -> proper# X, proper# from X -> proper# X) (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# sel(X1, X2) -> sel#(proper X1, proper X2)) (top# mark X -> proper# X, proper# sel(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# sel(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# from X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# from X -> from# proper X) (proper# from X -> proper# X, proper# from X -> proper# X) (proper# from X -> proper# X, proper# s X -> s# proper X) (proper# from X -> proper# X, proper# s X -> proper# X) (proper# from X -> proper# X, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# from X -> proper# X, proper# first(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# first(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# from X -> proper# X, proper# sel(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# sel(X1, X2) -> proper# X2) (active# from X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# from X -> active# X, active# cons(X1, X2) -> active# X1) (active# from X -> active# X, active# from X -> cons#(X, from s X)) (active# from X -> active# X, active# from X -> from# s X) (active# from X -> active# X, active# from X -> from# active X) (active# from X -> active# X, active# from X -> s# X) (active# from X -> active# X, active# from X -> active# X) (active# from X -> active# X, active# s X -> s# active X) (active# from X -> active# X, active# s X -> active# X) (active# from X -> active# X, active# first(X1, X2) -> active# X1) (active# from X -> active# X, active# first(X1, X2) -> active# X2) (active# from X -> active# X, active# first(X1, X2) -> first#(X1, active X2)) (active# from X -> active# X, active# first(X1, X2) -> first#(active X1, X2)) (active# from X -> active# X, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (active# from X -> active# X, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (active# from X -> active# X, active# sel(X1, X2) -> active# X1) (active# from X -> active# X, active# sel(X1, X2) -> active# X2) (active# from X -> active# X, active# sel(X1, X2) -> sel#(X1, active X2)) (active# from X -> active# X, active# sel(X1, X2) -> sel#(active X1, X2)) (active# from X -> active# X, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (s# ok X -> s# X, s# mark X -> s# X) (s# ok X -> s# X, s# ok X -> s# X) (from# ok X -> from# X, from# mark X -> from# X) (from# ok X -> from# X, from# ok X -> from# X) (proper# sel(X1, X2) -> sel#(proper X1, proper X2), sel#(X1, mark X2) -> sel#(X1, X2)) (proper# sel(X1, X2) -> sel#(proper X1, proper X2), sel#(mark X1, X2) -> sel#(X1, X2)) (proper# sel(X1, X2) -> sel#(proper X1, proper X2), sel#(ok X1, ok X2) -> sel#(X1, X2)) (proper# cons(X1, X2) -> cons#(proper X1, proper X2), cons#(mark X1, X2) -> cons#(X1, X2)) (proper# cons(X1, X2) -> cons#(proper X1, proper X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# first(X1, X2) -> first#(X1, active X2), first#(X1, mark X2) -> first#(X1, X2)) (active# first(X1, X2) -> first#(X1, active X2), first#(mark X1, X2) -> first#(X1, X2)) (active# first(X1, X2) -> first#(X1, active X2), first#(ok X1, ok X2) -> first#(X1, X2)) (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)) (proper# first(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# first(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# first(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# first(X1, X2) -> proper# X2, proper# from X -> from# proper X) (proper# first(X1, X2) -> proper# X2, proper# from X -> proper# X) (proper# first(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# first(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# first(X1, X2) -> proper# X2, proper# first(X1, X2) -> first#(proper X1, proper X2)) (proper# first(X1, X2) -> proper# X2, proper# first(X1, X2) -> proper# X1) (proper# first(X1, X2) -> proper# X2, proper# first(X1, X2) -> proper# X2) (proper# first(X1, X2) -> proper# X2, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# first(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1) (proper# first(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X2) (sel#(ok X1, ok X2) -> sel#(X1, X2), sel#(X1, mark X2) -> sel#(X1, X2)) (sel#(ok X1, ok X2) -> sel#(X1, X2), sel#(mark X1, X2) -> sel#(X1, X2)) (sel#(ok X1, ok X2) -> sel#(X1, X2), sel#(ok X1, ok X2) -> sel#(X1, X2)) (sel#(X1, mark X2) -> sel#(X1, X2), sel#(X1, mark X2) -> sel#(X1, X2)) (sel#(X1, mark X2) -> sel#(X1, X2), sel#(mark X1, X2) -> sel#(X1, X2)) (sel#(X1, mark X2) -> sel#(X1, X2), sel#(ok X1, ok X2) -> sel#(X1, X2)) (first#(mark X1, X2) -> first#(X1, X2), first#(X1, mark 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#(ok X1, ok X2) -> first#(X1, X2)) (active# sel(X1, X2) -> active# X2, active# cons(X1, X2) -> cons#(active X1, X2)) (active# sel(X1, X2) -> active# X2, active# cons(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X2, active# from X -> cons#(X, from s X)) (active# sel(X1, X2) -> active# X2, active# from X -> from# s X) (active# sel(X1, X2) -> active# X2, active# from X -> from# active X) (active# sel(X1, X2) -> active# X2, active# from X -> s# X) (active# sel(X1, X2) -> active# X2, active# from X -> active# X) (active# sel(X1, X2) -> active# X2, active# s X -> s# active X) (active# sel(X1, X2) -> active# X2, active# s X -> active# X) (active# sel(X1, X2) -> active# X2, active# first(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X2, active# first(X1, X2) -> active# X2) (active# sel(X1, X2) -> active# X2, active# first(X1, X2) -> first#(X1, active X2)) (active# sel(X1, X2) -> active# X2, active# first(X1, X2) -> first#(active X1, X2)) (active# sel(X1, X2) -> active# X2, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (active# sel(X1, X2) -> active# X2, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (active# sel(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X2) (active# sel(X1, X2) -> active# X2, active# sel(X1, X2) -> sel#(X1, active X2)) (active# sel(X1, X2) -> active# X2, active# sel(X1, X2) -> sel#(active X1, X2)) (active# sel(X1, X2) -> active# X2, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (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# from X -> cons#(X, from s X), cons#(mark X1, X2) -> cons#(X1, X2)) (active# from X -> cons#(X, from s X), cons#(ok X1, ok X2) -> cons#(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)) (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# s X -> s# proper X, s# mark X -> s# X) (proper# s X -> s# proper X, s# ok X -> s# X) (active# s X -> s# active X, s# mark X -> s# X) (active# s X -> s# active X, s# ok X -> s# X) (active# from X -> from# s X, from# mark X -> from# X) (active# from X -> from# s X, from# ok X -> from# X) } STATUS: arrows: 0.850479 SCCS (8): Scc: {top# mark X -> top# proper X, top# ok X -> top# active X} Scc: { active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# first(X1, X2) -> active# X1, active# first(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2} Scc: { proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# s X -> proper# X, proper# first(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2} Scc: { sel#(X1, mark X2) -> sel#(X1, X2), sel#(mark X1, X2) -> sel#(X1, X2), sel#(ok X1, ok X2) -> sel#(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: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)} Scc: {s# mark X -> s# X, s# ok X -> s# X} Scc: {from# mark X -> from# X, from# ok X -> from# X} 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), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, 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(), Z) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Z)) -> mark 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), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} Fail SCC (7): Strict: { active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# first(X1, X2) -> active# X1, active# first(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, 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(), Z) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Z)) -> mark 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), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [first](x0, x1) = x0 + x1 + 1, [sel](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 1, [active#](x0) = x0 + 1 Strict: active# sel(X1, X2) -> active# X2 2 + 1X1 + 1X2 >= 1 + 1X2 active# sel(X1, X2) -> active# X1 2 + 1X1 + 1X2 >= 1 + 1X1 active# first(X1, X2) -> active# X2 2 + 1X1 + 1X2 >= 1 + 1X2 active# first(X1, X2) -> active# X1 2 + 1X1 + 1X2 >= 1 + 1X1 active# s X -> active# X 2 + 1X >= 1 + 1X active# from X -> active# X 2 + 1X >= 1 + 1X active# cons(X1, X2) -> active# X1 2 + 1X1 + 0X2 >= 1 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper first(X1, X2) -> first(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper s X -> s proper X 0 + 0X >= 1 + 0X proper from X -> from proper X 0 + 0X >= 1 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 first(ok X1, ok X2) -> ok first(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 first(mark X1, X2) -> mark first(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 first(X1, mark X2) -> mark first(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel(0(), cons(X, Z)) -> mark X 4 + 1X + 0Z >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 4 + 1X + 0Z + 1Y >= 2 + 1X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active first(0(), Z) -> mark nil() 3 + 1Z >= 2 active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 4 + 1X + 0Z + 1Y >= 2 + 0X + 0Z + 1Y active first(X1, X2) -> first(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active first(X1, X2) -> first(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s X -> s active X 2 + 1X >= 2 + 1X active from X -> from active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X from ok X -> ok from X 2 + 1X >= 2 + 1X from mark X -> mark from X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed SCC (8): Strict: { proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# s X -> proper# X, proper# first(X1, X2) -> proper# X1, proper# first(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, 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(), Z) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Z)) -> mark 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), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1 + 1, [first](x0, x1) = x0 + x1 + 1, [sel](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 0, [proper#](x0) = x0 + 1 Strict: proper# sel(X1, X2) -> proper# X2 2 + 1X1 + 1X2 >= 1 + 1X2 proper# sel(X1, X2) -> proper# X1 2 + 1X1 + 1X2 >= 1 + 1X1 proper# first(X1, X2) -> proper# X2 2 + 1X1 + 1X2 >= 1 + 1X2 proper# first(X1, X2) -> proper# X1 2 + 1X1 + 1X2 >= 1 + 1X1 proper# s X -> proper# X 2 + 1X >= 1 + 1X proper# from X -> proper# X 2 + 1X >= 1 + 1X proper# cons(X1, X2) -> proper# X2 2 + 1X1 + 1X2 >= 1 + 1X2 proper# cons(X1, X2) -> proper# X1 2 + 1X1 + 1X2 >= 1 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper first(X1, X2) -> first(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper s X -> s proper X 0 + 0X >= 1 + 0X proper from X -> from proper X 0 + 0X >= 1 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 first(ok X1, ok X2) -> ok first(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 first(mark X1, X2) -> mark first(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 first(X1, mark X2) -> mark first(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel(0(), cons(X, Z)) -> mark X 3 + 1X + 1Z >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 4 + 1X + 1Z + 1Y >= 2 + 1X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active first(0(), Z) -> mark nil() 2 + 1Z >= 2 active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 4 + 1X + 1Z + 1Y >= 3 + 1X + 1Z + 1Y active first(X1, X2) -> first(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active first(X1, X2) -> first(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s X -> s active X 2 + 1X >= 2 + 1X active from X -> from active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 4 + 2X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X from ok X -> ok from X 2 + 1X >= 2 + 1X from mark X -> mark from X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 Qed SCC (3): Strict: { sel#(X1, mark X2) -> sel#(X1, X2), sel#(mark X1, X2) -> sel#(X1, X2), sel#(ok X1, ok X2) -> sel#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, 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(), Z) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Z)) -> mark 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), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = 0, [first](x0, x1) = 0, [sel](x0, x1) = x0 + x1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = 0, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 0, [sel#](x0, x1) = x0 + 1 Strict: sel#(ok X1, ok X2) -> sel#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel#(mark X1, X2) -> sel#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel#(X1, mark X2) -> sel#(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper first(X1, X2) -> first(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper s X -> s proper X 0 + 0X >= 0 + 0X proper from X -> from proper X 0 + 0X >= 1 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 first(ok X1, ok X2) -> ok first(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(mark X1, X2) -> mark first(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(X1, mark X2) -> mark first(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(0(), cons(X, Z)) -> mark X 0 + 0X + 0Z >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Z + 0Y >= 1 + 1X + 1Z active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 active first(0(), Z) -> mark nil() 0 + 0Z >= 2 active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 0 + 0X + 0Z + 0Y >= 1 + 0X + 0Z + 0Y active first(X1, X2) -> first(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active first(X1, X2) -> first(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 0 + 0X active from X -> from active X 0 + 0X >= 1 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 1 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 1 + 0X from ok X -> ok from X 2 + 1X >= 2 + 1X from mark X -> mark from X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: {sel#(X1, mark X2) -> sel#(X1, X2)} SCC (1): Strict: {sel#(X1, mark X2) -> sel#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, 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(), Z) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Z)) -> mark 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), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = x0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [nil] = 1, [0] = 0, [sel#](x0, x1) = x0 Strict: sel#(X1, mark X2) -> sel#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 1 + 1X proper sel(X1, X2) -> sel(proper X1, proper X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 proper 0() -> ok 0() 0 >= 1 proper first(X1, X2) -> first(proper X1, proper X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 proper nil() -> ok nil() 1 >= 2 proper s X -> s proper X 1 + 1X >= 1 + 1X proper from X -> from proper X 1 + 1X >= 1 + 1X proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(ok X1, ok X2) -> ok first(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(mark X1, X2) -> mark first(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(X1, mark X2) -> mark first(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active sel(0(), cons(X, Z)) -> mark X 3 + 1X + 0Z >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 0Z + 1Y >= 2 + 0X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active first(0(), Z) -> mark nil() 2 + 1Z >= 2 active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 3 + 0X + 0Z + 1Y >= 2 + 0X + 0Z + 1Y active first(X1, X2) -> first(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active first(X1, X2) -> first(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active s X -> s active X 2 + 1X >= 2 + 1X active from X -> from active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X from ok X -> ok from X 2 + 1X >= 2 + 1X from mark X -> mark from X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed 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), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, 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(), Z) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Z)) -> mark 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), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = 0, [first](x0, x1) = 0, [sel](x0, x1) = x0 + x1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = 0, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 0, [first#](x0, x1) = x0 + 1 Strict: first#(ok X1, ok X2) -> first#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first#(mark X1, X2) -> first#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first#(X1, mark X2) -> first#(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper first(X1, X2) -> first(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper s X -> s proper X 0 + 0X >= 0 + 0X proper from X -> from proper X 0 + 0X >= 1 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 first(ok X1, ok X2) -> ok first(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(mark X1, X2) -> mark first(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(X1, mark X2) -> mark first(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(0(), cons(X, Z)) -> mark X 0 + 0X + 0Z >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Z + 0Y >= 1 + 1X + 1Z active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 active first(0(), Z) -> mark nil() 0 + 0Z >= 2 active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 0 + 0X + 0Z + 0Y >= 1 + 0X + 0Z + 0Y active first(X1, X2) -> first(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active first(X1, X2) -> first(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 0 + 0X active from X -> from active X 0 + 0X >= 1 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 1 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 1 + 0X from ok X -> ok from X 2 + 1X >= 2 + 1X from mark X -> mark from X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: {first#(X1, mark X2) -> first#(X1, X2)} SCC (1): Strict: {first#(X1, mark X2) -> first#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, 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(), Z) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Z)) -> mark 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), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = x0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [nil] = 1, [0] = 0, [first#](x0, x1) = x0 Strict: first#(X1, mark X2) -> first#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 1 + 1X proper sel(X1, X2) -> sel(proper X1, proper X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 proper 0() -> ok 0() 0 >= 1 proper first(X1, X2) -> first(proper X1, proper X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 proper nil() -> ok nil() 1 >= 2 proper s X -> s proper X 1 + 1X >= 1 + 1X proper from X -> from proper X 1 + 1X >= 1 + 1X proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(ok X1, ok X2) -> ok first(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(mark X1, X2) -> mark first(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(X1, mark X2) -> mark first(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active sel(0(), cons(X, Z)) -> mark X 3 + 1X + 0Z >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 0Z + 1Y >= 2 + 0X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active first(0(), Z) -> mark nil() 2 + 1Z >= 2 active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 3 + 0X + 0Z + 1Y >= 2 + 0X + 0Z + 1Y active first(X1, X2) -> first(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active first(X1, X2) -> first(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active s X -> s active X 2 + 1X >= 2 + 1X active from X -> from active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X from ok X -> ok from X 2 + 1X >= 2 + 1X from mark X -> mark from X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed 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), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, 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(), Z) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Z)) -> mark 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), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 0, [cons#](x0, x1) = x0 Strict: cons#(ok X1, ok X2) -> cons#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons#(mark X1, X2) -> cons#(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper first(X1, X2) -> first(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper s X -> s proper X 0 + 0X >= 1 + 0X proper from X -> from proper X 0 + 0X >= 1 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(ok X1, ok X2) -> ok first(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(mark X1, X2) -> mark first(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(X1, mark X2) -> mark first(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active sel(0(), cons(X, Z)) -> mark X 3 + 1X + 0Z >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 0Z + 1Y >= 2 + 0X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active first(0(), Z) -> mark nil() 2 + 1Z >= 2 active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 3 + 0X + 0Z + 1Y >= 2 + 0X + 0Z + 1Y active first(X1, X2) -> first(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active first(X1, X2) -> first(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active s X -> s active X 2 + 1X >= 2 + 1X active from X -> from active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X from ok X -> ok from X 2 + 1X >= 2 + 1X from mark X -> mark from X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 SCCS (1): Scc: {cons#(mark X1, X2) -> cons#(X1, X2)} SCC (1): Strict: {cons#(mark X1, X2) -> cons#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, 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(), Z) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Z)) -> mark 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), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = x0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [nil] = 1, [0] = 0, [cons#](x0, x1) = x0 Strict: cons#(mark X1, X2) -> cons#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 1 + 1X proper sel(X1, X2) -> sel(proper X1, proper X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 proper 0() -> ok 0() 0 >= 1 proper first(X1, X2) -> first(proper X1, proper X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 proper nil() -> ok nil() 1 >= 2 proper s X -> s proper X 1 + 1X >= 1 + 1X proper from X -> from proper X 1 + 1X >= 1 + 1X proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(ok X1, ok X2) -> ok first(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(mark X1, X2) -> mark first(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(X1, mark X2) -> mark first(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active sel(0(), cons(X, Z)) -> mark X 3 + 1X + 0Z >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 0Z + 1Y >= 2 + 0X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active first(0(), Z) -> mark nil() 2 + 1Z >= 2 active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 3 + 0X + 0Z + 1Y >= 2 + 0X + 0Z + 1Y active first(X1, X2) -> first(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active first(X1, X2) -> first(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active s X -> s active X 2 + 1X >= 2 + 1X active from X -> from active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X from ok X -> ok from X 2 + 1X >= 2 + 1X from mark X -> mark from X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed SCC (2): Strict: {s# mark X -> s# X, s# ok X -> s# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, 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(), Z) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Z)) -> mark 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), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = 0, [first](x0, x1) = 0, [sel](x0, x1) = 0, [mark](x0) = x0, [from](x0) = 0, [s](x0) = 0, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 0, [0] = 1, [s#](x0) = x0 Strict: s# ok X -> s# X 1 + 1X >= 0 + 1X s# mark X -> s# X 0 + 1X >= 0 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper first(X1, X2) -> first(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper s X -> s proper X 0 + 0X >= 0 + 0X proper from X -> from proper X 0 + 0X >= 0 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(ok X1, ok X2) -> ok first(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(mark X1, X2) -> mark first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(X1, mark X2) -> mark first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(0(), cons(X, Z)) -> mark X 0 + 0X + 0Z >= 0 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Z + 0Y >= 0 + 0X + 0Z active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active first(0(), Z) -> mark nil() 0 + 0Z >= 0 active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 0 + 0X + 0Z + 0Y >= 0 + 0X + 0Z + 0Y active first(X1, X2) -> first(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active first(X1, X2) -> first(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 0 + 0X active from X -> from active X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 0 + 0X from ok X -> ok from X 0 + 0X >= 1 + 0X from mark X -> mark from X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {s# mark X -> s# X} SCC (1): Strict: {s# mark X -> s# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, 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(), Z) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Z)) -> mark 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), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = x0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [nil] = 1, [0] = 0, [s#](x0) = x0 Strict: s# mark X -> s# X 1 + 1X >= 0 + 1X Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 1 + 1X proper sel(X1, X2) -> sel(proper X1, proper X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 proper 0() -> ok 0() 0 >= 1 proper first(X1, X2) -> first(proper X1, proper X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 proper nil() -> ok nil() 1 >= 2 proper s X -> s proper X 1 + 1X >= 1 + 1X proper from X -> from proper X 1 + 1X >= 1 + 1X proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(ok X1, ok X2) -> ok first(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(mark X1, X2) -> mark first(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(X1, mark X2) -> mark first(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active sel(0(), cons(X, Z)) -> mark X 3 + 1X + 0Z >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 0Z + 1Y >= 2 + 0X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active first(0(), Z) -> mark nil() 2 + 1Z >= 2 active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 3 + 0X + 0Z + 1Y >= 2 + 0X + 0Z + 1Y active first(X1, X2) -> first(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active first(X1, X2) -> first(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active s X -> s active X 2 + 1X >= 2 + 1X active from X -> from active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X from ok X -> ok from X 2 + 1X >= 2 + 1X from mark X -> mark from X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed SCC (2): Strict: {from# mark X -> from# X, from# ok X -> from# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, 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(), Z) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Z)) -> mark 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), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = 0, [first](x0, x1) = 0, [sel](x0, x1) = 0, [mark](x0) = x0, [from](x0) = 0, [s](x0) = 0, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 0, [0] = 1, [from#](x0) = x0 Strict: from# ok X -> from# X 1 + 1X >= 0 + 1X from# mark X -> from# X 0 + 1X >= 0 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper first(X1, X2) -> first(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper s X -> s proper X 0 + 0X >= 0 + 0X proper from X -> from proper X 0 + 0X >= 0 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(ok X1, ok X2) -> ok first(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(mark X1, X2) -> mark first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(X1, mark X2) -> mark first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(0(), cons(X, Z)) -> mark X 0 + 0X + 0Z >= 0 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Z + 0Y >= 0 + 0X + 0Z active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active first(0(), Z) -> mark nil() 0 + 0Z >= 0 active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 0 + 0X + 0Z + 0Y >= 0 + 0X + 0Z + 0Y active first(X1, X2) -> first(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active first(X1, X2) -> first(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 0 + 0X active from X -> from active X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 0 + 0X from ok X -> ok from X 0 + 0X >= 1 + 0X from mark X -> mark from X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {from# mark X -> from# X} SCC (1): Strict: {from# mark X -> from# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, 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(), Z) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Z)) -> mark 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), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper first(X1, X2) -> first(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = x0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [nil] = 1, [0] = 0, [from#](x0) = x0 Strict: from# mark X -> from# X 1 + 1X >= 0 + 1X Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 1 + 1X proper sel(X1, X2) -> sel(proper X1, proper X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 proper 0() -> ok 0() 0 >= 1 proper first(X1, X2) -> first(proper X1, proper X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 proper nil() -> ok nil() 1 >= 2 proper s X -> s proper X 1 + 1X >= 1 + 1X proper from X -> from proper X 1 + 1X >= 1 + 1X proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(ok X1, ok X2) -> ok first(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(mark X1, X2) -> mark first(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 first(X1, mark X2) -> mark first(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active sel(0(), cons(X, Z)) -> mark X 3 + 1X + 0Z >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 0Z + 1Y >= 2 + 0X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active first(0(), Z) -> mark nil() 2 + 1Z >= 2 active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 3 + 0X + 0Z + 1Y >= 2 + 0X + 0Z + 1Y active first(X1, X2) -> first(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active first(X1, X2) -> first(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active s X -> s active X 2 + 1X >= 2 + 1X active from X -> from active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X from ok X -> ok from X 2 + 1X >= 2 + 1X from mark X -> mark from X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed