MAYBE Time: 1.399852 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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# head X -> active# X, active# head X -> head# active X, active# 2nd X -> active# X, active# 2nd X -> 2nd# active X, active# 2nd cons(X, XS) -> head# XS, active# take(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2, active# take(X1, X2) -> take#(X1, active X2), active# take(X1, X2) -> take#(active X1, X2), active# take(s N, cons(X, XS)) -> cons#(X, take(N, XS)), active# take(s N, cons(X, XS)) -> take#(N, XS), 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 N, cons(X, XS)) -> sel#(N, XS), head# mark X -> head# X, head# ok X -> head# X, 2nd# mark X -> 2nd# X, 2nd# ok X -> 2nd# X, take#(X1, mark X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(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# head X -> head# proper X, proper# head X -> proper# X, proper# 2nd X -> 2nd# proper X, proper# 2nd X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2), proper# take(X1, X2) -> proper# X1, proper# take(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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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} UR: { 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(proper X1, proper X2), proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), a(x, y) -> x, a(x, y) -> y} EDG: { (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# take(X1, X2) -> take#(proper X1, proper X2), take#(ok X1, ok X2) -> take#(X1, X2)) (proper# take(X1, X2) -> take#(proper X1, proper X2), take#(mark X1, X2) -> take#(X1, X2)) (proper# take(X1, X2) -> take#(proper X1, proper X2), take#(X1, mark X2) -> take#(X1, X2)) (active# cons(X1, X2) -> active# X1, active# sel(s N, cons(X, XS)) -> sel#(N, XS)) (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# take(s N, cons(X, XS)) -> take#(N, XS)) (active# cons(X1, X2) -> active# X1, active# take(s N, cons(X, XS)) -> cons#(X, take(N, XS))) (active# cons(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2)) (active# cons(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2)) (active# cons(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2) (active# cons(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# 2nd cons(X, XS) -> head# XS) (active# cons(X1, X2) -> active# X1, active# 2nd X -> 2nd# active X) (active# cons(X1, X2) -> active# X1, active# 2nd X -> active# X) (active# cons(X1, X2) -> active# X1, active# head X -> head# active X) (active# cons(X1, X2) -> active# X1, active# head X -> active# X) (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 N, cons(X, XS)) -> sel#(N, XS)) (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# take(s N, cons(X, XS)) -> take#(N, XS)) (active# sel(X1, X2) -> active# X1, active# take(s N, cons(X, XS)) -> cons#(X, take(N, XS))) (active# sel(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2)) (active# sel(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2)) (active# sel(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2) (active# sel(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X1, active# 2nd cons(X, XS) -> head# XS) (active# sel(X1, X2) -> active# X1, active# 2nd X -> 2nd# active X) (active# sel(X1, X2) -> active# X1, active# 2nd X -> active# X) (active# sel(X1, X2) -> active# X1, active# head X -> head# active X) (active# sel(X1, X2) -> active# X1, active# head X -> active# X) (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# take(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# 2nd X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# 2nd X -> 2nd# proper X) (proper# take(X1, X2) -> proper# X1, proper# head X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# head X -> head# proper X) (proper# take(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# take(X1, X2) -> proper# X1, proper# from X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# from X -> from# proper X) (proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# take(s N, cons(X, XS)) -> cons#(X, take(N, XS)), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# take(s N, cons(X, XS)) -> cons#(X, take(N, XS)), cons#(mark X1, X2) -> cons#(X1, X2)) (active# sel(s N, cons(X, XS)) -> sel#(N, XS), sel#(ok X1, ok X2) -> sel#(X1, X2)) (active# sel(s N, cons(X, XS)) -> sel#(N, XS), sel#(mark X1, X2) -> sel#(X1, X2)) (active# sel(s N, cons(X, XS)) -> sel#(N, XS), sel#(X1, mark X2) -> sel#(X1, X2)) (from# ok X -> from# X, from# ok X -> from# X) (from# ok X -> from# X, from# mark X -> from# X) (s# ok X -> s# X, s# ok X -> s# X) (s# ok X -> s# X, s# mark X -> s# X) (active# from X -> active# X, active# sel(s N, cons(X, XS)) -> sel#(N, XS)) (active# from X -> active# X, active# sel(X1, X2) -> sel#(active X1, X2)) (active# from X -> active# X, active# sel(X1, X2) -> sel#(X1, active X2)) (active# from X -> active# X, active# sel(X1, X2) -> active# X2) (active# from X -> active# X, active# sel(X1, X2) -> active# X1) (active# from X -> active# X, active# take(s N, cons(X, XS)) -> take#(N, XS)) (active# from X -> active# X, active# take(s N, cons(X, XS)) -> cons#(X, take(N, XS))) (active# from X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (active# from X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (active# from X -> active# X, active# take(X1, X2) -> active# X2) (active# from X -> active# X, active# take(X1, X2) -> active# X1) (active# from X -> active# X, active# 2nd cons(X, XS) -> head# XS) (active# from X -> active# X, active# 2nd X -> 2nd# active X) (active# from X -> active# X, active# 2nd X -> active# X) (active# from X -> active# X, active# head X -> head# active X) (active# from X -> active# X, active# head X -> active# X) (active# from X -> active# X, active# s X -> active# X) (active# from X -> active# X, active# s X -> s# active X) (active# from X -> active# X, active# from X -> active# X) (active# from X -> active# X, active# from X -> s# X) (active# from X -> active# X, active# from X -> from# active X) (active# from X -> active# X, active# from X -> from# s X) (active# from X -> active# X, active# from X -> cons#(X, from s X)) (active# from X -> active# X, active# cons(X1, X2) -> active# X1) (active# from X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# head X -> active# X, active# sel(s N, cons(X, XS)) -> sel#(N, XS)) (active# head X -> active# X, active# sel(X1, X2) -> sel#(active X1, X2)) (active# head X -> active# X, active# sel(X1, X2) -> sel#(X1, active X2)) (active# head X -> active# X, active# sel(X1, X2) -> active# X2) (active# head X -> active# X, active# sel(X1, X2) -> active# X1) (active# head X -> active# X, active# take(s N, cons(X, XS)) -> take#(N, XS)) (active# head X -> active# X, active# take(s N, cons(X, XS)) -> cons#(X, take(N, XS))) (active# head X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (active# head X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (active# head X -> active# X, active# take(X1, X2) -> active# X2) (active# head X -> active# X, active# take(X1, X2) -> active# X1) (active# head X -> active# X, active# 2nd cons(X, XS) -> head# XS) (active# head X -> active# X, active# 2nd X -> 2nd# active X) (active# head X -> active# X, active# 2nd X -> active# X) (active# head X -> active# X, active# head X -> head# active X) (active# head X -> active# X, active# head X -> active# X) (active# head X -> active# X, active# s X -> active# X) (active# head X -> active# X, active# s X -> s# active X) (active# head X -> active# X, active# from X -> active# X) (active# head X -> active# X, active# from X -> s# X) (active# head X -> active# X, active# from X -> from# active X) (active# head X -> active# X, active# from X -> from# s X) (active# head X -> active# X, active# from X -> cons#(X, from s X)) (active# head X -> active# X, active# cons(X1, X2) -> active# X1) (active# head X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (head# mark X -> head# X, head# ok X -> head# X) (head# mark X -> head# X, head# mark X -> head# X) (2nd# mark X -> 2nd# X, 2nd# ok X -> 2nd# X) (2nd# mark X -> 2nd# X, 2nd# mark X -> 2nd# X) (proper# from X -> proper# X, proper# sel(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# sel(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# from X -> proper# X, proper# take(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# take(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# from X -> proper# X, proper# 2nd X -> proper# X) (proper# from X -> proper# X, proper# 2nd X -> 2nd# proper X) (proper# from X -> proper# X, proper# head X -> proper# X) (proper# from X -> proper# X, proper# head X -> head# proper X) (proper# from X -> proper# X, 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proper# head X -> proper# X) (proper# head X -> proper# X, proper# head X -> head# proper X) (proper# head X -> proper# X, proper# s X -> proper# X) (proper# head X -> proper# X, proper# s X -> s# proper X) (proper# head X -> proper# X, proper# from X -> proper# X) (proper# head X -> proper# X, proper# from X -> from# proper X) (proper# head X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# head X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# head X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (top# mark X -> proper# X, proper# sel(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# sel(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (top# mark X -> proper# X, proper# take(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# take(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2)) (top# mark X -> proper# X, proper# 2nd X -> 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cons#(active X1, X2)) (active# 2nd X -> active# X, active# cons(X1, X2) -> active# X1) (active# 2nd X -> active# X, active# from X -> cons#(X, from s X)) (active# 2nd X -> active# X, active# from X -> from# s X) (active# 2nd X -> active# X, active# from X -> from# active X) (active# 2nd X -> active# X, active# from X -> s# X) (active# 2nd X -> active# X, active# from X -> active# X) (active# 2nd X -> active# X, active# s X -> s# active X) (active# 2nd X -> active# X, active# s X -> active# X) (active# 2nd X -> active# X, active# head X -> active# X) (active# 2nd X -> active# X, active# head X -> head# active X) (active# 2nd X -> active# X, active# 2nd X -> active# X) (active# 2nd X -> active# X, active# 2nd X -> 2nd# active X) (active# 2nd X -> active# X, active# 2nd cons(X, XS) -> head# XS) (active# 2nd X -> active# X, active# take(X1, X2) -> active# X1) (active# 2nd X -> active# X, active# take(X1, X2) -> active# X2) (active# 2nd X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (active# 2nd X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (active# 2nd X -> active# X, active# take(s N, cons(X, XS)) -> cons#(X, take(N, XS))) (active# 2nd X -> active# X, active# take(s N, cons(X, XS)) -> take#(N, XS)) (active# 2nd X -> active# X, active# sel(X1, X2) -> active# X1) (active# 2nd X -> active# X, active# sel(X1, X2) -> active# X2) (active# 2nd X -> active# X, active# sel(X1, X2) -> sel#(X1, active X2)) (active# 2nd X -> active# X, active# sel(X1, X2) -> sel#(active X1, X2)) (active# 2nd X -> active# X, active# sel(s N, cons(X, XS)) -> sel#(N, XS)) (active# s X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# s X -> active# X, active# cons(X1, X2) -> active# X1) (active# s X -> active# X, active# from X -> cons#(X, from s X)) (active# s X -> active# X, active# from X -> from# s X) (active# s X -> active# X, active# from X -> from# active X) (active# s X -> active# X, active# from X -> s# X) (active# s X -> active# X, active# from X -> active# X) (active# s X -> active# X, active# s X -> s# active X) (active# s X -> active# X, active# s X -> active# X) (active# s X -> active# X, active# head X -> active# X) (active# s X -> active# X, active# head X -> head# active X) (active# s X -> active# X, active# 2nd X -> active# X) (active# s X -> active# X, active# 2nd X -> 2nd# active X) (active# s X -> active# X, active# 2nd cons(X, XS) -> head# XS) (active# s X -> active# X, active# take(X1, X2) -> active# X1) (active# s X -> active# X, active# take(X1, X2) -> active# X2) (active# s X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (active# s X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (active# s X -> active# X, active# take(s N, cons(X, XS)) -> cons#(X, take(N, XS))) (active# s X -> active# X, active# take(s N, cons(X, XS)) -> take#(N, XS)) (active# s X -> active# X, active# sel(X1, X2) -> active# X1) (active# s X -> active# X, active# sel(X1, X2) -> active# X2) (active# s X -> active# X, active# sel(X1, X2) -> sel#(X1, active X2)) (active# s X -> active# X, active# sel(X1, X2) -> sel#(active X1, X2)) (active# s X -> active# X, active# sel(s N, cons(X, XS)) -> sel#(N, XS)) (active# from X -> s# X, s# mark X -> s# X) (active# from X -> s# X, s# ok X -> s# X) (s# mark X -> s# X, s# mark X -> s# X) (s# mark X -> s# X, s# ok X -> s# X) (from# mark X -> from# X, from# mark X -> from# X) (from# mark X -> from# X, from# ok X -> from# X) (active# take(s N, cons(X, XS)) -> take#(N, XS), take#(X1, mark X2) -> take#(X1, X2)) (active# take(s N, cons(X, XS)) -> take#(N, XS), take#(mark X1, X2) -> take#(X1, X2)) (active# take(s N, cons(X, XS)) -> take#(N, XS), take#(ok X1, ok X2) -> take#(X1, 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# head X -> head# proper X) (proper# sel(X1, X2) -> proper# X1, proper# head X -> proper# X) (proper# sel(X1, X2) -> proper# X1, proper# 2nd X -> 2nd# proper X) (proper# sel(X1, X2) -> proper# X1, proper# 2nd X -> proper# X) (proper# sel(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X1, proper# take(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# head X -> head# proper X) (proper# cons(X1, X2) -> proper# X1, proper# head X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# 2nd X -> 2nd# proper X) (proper# cons(X1, X2) -> proper# X1, proper# 2nd X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# take(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# take(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# take(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# take(X1, X2) -> active# X1, active# from X -> cons#(X, from s X)) (active# take(X1, X2) -> active# X1, active# from X -> from# s X) (active# take(X1, X2) -> active# X1, active# from X -> from# active X) (active# take(X1, X2) -> active# X1, active# from X -> s# X) (active# take(X1, X2) -> active# X1, active# from X -> active# X) (active# take(X1, X2) -> active# X1, active# s X -> s# active X) (active# take(X1, X2) -> active# X1, active# s X -> active# X) (active# take(X1, X2) -> active# X1, active# head X -> active# X) (active# take(X1, X2) -> active# X1, active# head X -> head# active X) (active# take(X1, X2) -> active# X1, active# 2nd X -> active# X) (active# take(X1, X2) -> active# X1, active# 2nd X -> 2nd# active X) (active# take(X1, X2) -> active# X1, active# 2nd cons(X, XS) -> head# XS) (active# take(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1) (active# take(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2) (active# take(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2)) (active# take(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2)) (active# take(X1, X2) -> active# X1, active# take(s N, cons(X, XS)) -> cons#(X, take(N, XS))) (active# take(X1, X2) -> active# X1, active# take(s N, cons(X, XS)) -> take#(N, XS)) (active# take(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X1) (active# take(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2) (active# take(X1, X2) -> active# X1, active# sel(X1, X2) -> sel#(X1, active X2)) (active# take(X1, X2) -> active# X1, active# sel(X1, X2) -> sel#(active X1, X2)) (active# take(X1, X2) -> active# X1, active# sel(s N, cons(X, XS)) -> sel#(N, XS)) (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# take(X1, X2) -> take#(X1, active X2), take#(X1, mark X2) -> take#(X1, X2)) (active# take(X1, X2) -> take#(X1, active X2), take#(mark X1, X2) -> take#(X1, X2)) (active# take(X1, X2) -> take#(X1, active X2), take#(ok X1, ok X2) -> take#(X1, X2)) } STATUS: arrows: 0.860302 SCCS (10): Scc: {top# mark X -> top# proper X, top# ok X -> top# active X} Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# s X -> proper# X, proper# head X -> proper# X, proper# 2nd X -> proper# X, proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2} Scc: {active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# head X -> active# X, active# 2nd X -> active# X, active# take(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2} Scc: {2nd# mark X -> 2nd# X, 2nd# ok X -> 2nd# X} Scc: {head# mark X -> head# X, head# ok X -> head# X} Scc: {s# mark X -> s# X, s# ok X -> s# X} Scc: {from# mark X -> from# X, from# ok X -> from# X} Scc: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, 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: { take#(X1, mark X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)} SCC (2): Strict: {top# mark X -> top# proper X, top# ok X -> top# active X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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 (10): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# s X -> proper# X, proper# head X -> proper# X, proper# 2nd X -> proper# X, proper# take(X1, X2) -> proper# X1, proper# take(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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = x0 + x1, [sel](x0, x1) = x0 + x1 + 1, [mark](x0) = 1, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [head](x0) = x0, [2nd](x0) = x0, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 0, [proper#](x0) = x0 Strict: proper# sel(X1, X2) -> proper# X2 1 + 1X1 + 1X2 >= 0 + 1X2 proper# sel(X1, X2) -> proper# X1 1 + 1X1 + 1X2 >= 0 + 1X1 proper# take(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# take(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 proper# 2nd X -> proper# X 0 + 1X >= 0 + 1X proper# head X -> proper# X 0 + 1X >= 0 + 1X proper# s X -> proper# X 0 + 1X >= 0 + 1X proper# from X -> proper# X 0 + 1X >= 0 + 1X proper# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 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) 2 + 1X1 + 1X2 >= 3 + 1X1 + 1X2 proper 0() -> ok 0() 1 >= 1 proper take(X1, X2) -> take(proper X1, proper X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 proper nil() -> ok nil() 2 >= 2 proper 2nd X -> 2nd proper X 1 + 1X >= 1 + 1X proper head X -> head proper X 1 + 1X >= 1 + 1X 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 + 1X2 >= 2 + 1X1 + 1X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 1X1 + 0X2 >= 1 + 0X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 1 + 1X1 + 0X2 >= 1 + 0X1 + 0X2 2nd ok X -> ok 2nd X 1 + 1X >= 1 + 1X 2nd mark X -> mark 2nd X 1 + 0X >= 1 + 0X head ok X -> ok head X 1 + 1X >= 1 + 1X head mark X -> mark head X 1 + 0X >= 1 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 1 + 0X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 1 + 0XS + 0N active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active take(0(), XS) -> mark nil() 0 + 0XS >= 1 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 1 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 1 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 0 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 1 + 0X active head X -> head active X 0 + 0X >= 0 + 0X 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 >= 1 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 1 + 0X >= 1 + 0X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 1 + 0X >= 1 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# s X -> proper# X, proper# head X -> proper# X, proper# 2nd X -> proper# X, proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2} 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# head X -> proper# X, proper# 2nd X -> proper# X, proper# take(X1, X2) -> proper# X1, proper# take(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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = x0 + x1 + 1, [sel](x0, x1) = x0 + x1, [mark](x0) = 0, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [head](x0) = x0, [2nd](x0) = x0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 1, [proper#](x0) = x0 Strict: proper# take(X1, X2) -> proper# X2 1 + 1X1 + 1X2 >= 0 + 1X2 proper# take(X1, X2) -> proper# X1 1 + 1X1 + 1X2 >= 0 + 1X1 proper# 2nd X -> proper# X 0 + 1X >= 0 + 1X proper# head X -> proper# X 0 + 1X >= 0 + 1X proper# s X -> proper# X 0 + 1X >= 0 + 1X proper# from X -> proper# X 0 + 1X >= 0 + 1X proper# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 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 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper 2nd X -> 2nd proper X 0 + 0X >= 0 + 0X proper head X -> head proper X 0 + 0X >= 0 + 0X 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) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 1 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 2nd ok X -> ok 2nd X 1 + 1X >= 1 + 1X 2nd mark X -> mark 2nd X 0 + 0X >= 0 + 0X head ok X -> ok head X 1 + 1X >= 1 + 1X head mark X -> mark head X 0 + 0X >= 0 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 0 + 0X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 0 + 0XS + 0N 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 take(0(), XS) -> mark nil() 0 + 0XS >= 0 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 0 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 0 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 0 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 0 + 0X active head X -> head active X 0 + 0X >= 0 + 0X 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 + 1X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# s X -> proper# X, proper# head X -> proper# X, proper# 2nd X -> proper# X} SCC (6): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# s X -> proper# X, proper# head X -> proper# X, proper# 2nd X -> proper# 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = 0, [sel](x0, x1) = x0 + 1, [mark](x0) = 0, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [head](x0) = x0, [2nd](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 1, [proper#](x0) = x0 Strict: proper# 2nd X -> proper# X 1 + 1X >= 0 + 1X proper# head X -> proper# X 0 + 1X >= 0 + 1X proper# s X -> proper# X 0 + 1X >= 0 + 1X proper# from X -> proper# X 0 + 1X >= 0 + 1X proper# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 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 take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper 2nd X -> 2nd proper X 0 + 0X >= 1 + 0X proper head X -> head proper X 0 + 0X >= 0 + 0X 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) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 take(mark X1, X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 2nd ok X -> ok 2nd X 2 + 1X >= 2 + 1X 2nd mark X -> mark 2nd X 1 + 0X >= 0 + 0X head ok X -> ok head X 1 + 1X >= 1 + 1X head mark X -> mark head X 0 + 0X >= 0 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 0 + 0X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 0 + 0XS + 0N active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active take(0(), XS) -> mark nil() 0 + 0XS >= 0 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 0 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 0 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 1 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 0 + 0X active head X -> head active X 0 + 0X >= 0 + 0X 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 + 1X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# s X -> proper# X, proper# head X -> proper# X} SCC (5): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# s X -> proper# X, proper# head X -> proper# 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = 0, [sel](x0, x1) = 1, [mark](x0) = 0, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [head](x0) = x0 + 1, [2nd](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 1, [proper#](x0) = x0 Strict: proper# head X -> proper# X 1 + 1X >= 0 + 1X proper# s X -> proper# X 0 + 1X >= 0 + 1X proper# from X -> proper# X 0 + 1X >= 0 + 1X proper# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 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 take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper 2nd X -> 2nd proper X 0 + 0X >= 0 + 0X proper head X -> head proper X 0 + 0X >= 1 + 0X 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) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 take(mark X1, X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 2nd ok X -> ok 2nd X 0 + 0X >= 1 + 0X 2nd mark X -> mark 2nd X 0 + 0X >= 0 + 0X head ok X -> ok head X 2 + 1X >= 2 + 1X head mark X -> mark head X 1 + 0X >= 0 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 0 + 0X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 0 + 0XS + 0N active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active take(0(), XS) -> mark nil() 0 + 0XS >= 0 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 0 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 0 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 0 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 0 + 0X active head X -> head active X 0 + 0X >= 1 + 0X 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 + 1X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# s X -> proper# X} SCC (4): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# s X -> proper# 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = 0, [sel](x0, x1) = x0 + x1, [mark](x0) = 0, [from](x0) = x0, [s](x0) = x0 + 1, [active](x0) = 0, [head](x0) = 0, [2nd](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 0, [proper#](x0) = x0 Strict: proper# s X -> proper# X 1 + 1X >= 0 + 1X proper# from X -> proper# X 0 + 1X >= 0 + 1X proper# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 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 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper 2nd X -> 2nd proper X 0 + 0X >= 0 + 0X proper head X -> head proper X 0 + 0X >= 0 + 0X proper s X -> s proper X 0 + 0X >= 1 + 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) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 take(mark X1, X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 2nd ok X -> ok 2nd X 0 + 0X >= 1 + 0X 2nd mark X -> mark 2nd X 0 + 0X >= 0 + 0X head ok X -> ok head X 0 + 0X >= 1 + 0X head mark X -> mark head X 0 + 0X >= 0 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 0 + 0X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 0 + 0XS + 0N 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 take(0(), XS) -> mark nil() 0 + 0XS >= 0 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 0 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 0 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 0 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 0 + 0X active head X -> head active X 0 + 0X >= 0 + 0X active s X -> s active X 0 + 0X >= 1 + 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 + 1X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 1 + 0X >= 0 + 0X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X} SCC (3): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = 0, [sel](x0, x1) = 0, [mark](x0) = 0, [from](x0) = x0 + 1, [s](x0) = 0, [active](x0) = 0, [head](x0) = 0, [2nd](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 1, [proper#](x0) = x0 Strict: proper# from X -> proper# X 1 + 1X >= 0 + 1X proper# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 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 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper 2nd X -> 2nd proper X 0 + 0X >= 0 + 0X proper head X -> head proper X 0 + 0X >= 0 + 0X 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) 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 take(ok X1, ok X2) -> ok take(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 take(mark X1, X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 2nd ok X -> ok 2nd X 0 + 0X >= 1 + 0X 2nd mark X -> mark 2nd X 0 + 0X >= 0 + 0X head ok X -> ok head X 0 + 0X >= 1 + 0X head mark X -> mark head X 0 + 0X >= 0 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 0 + 0X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 0 + 0XS + 0N 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 take(0(), XS) -> mark nil() 0 + 0XS >= 0 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 0 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 0 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 0 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 0 + 0X active head X -> head active X 0 + 0X >= 0 + 0X 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 >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 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 2 + 1X >= 2 + 1X from mark X -> mark from X 1 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2} SCC (2): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = 0, [active](x0) = x0 + 1, [head](x0) = x0 + 1, [2nd](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = 0, [top](x0) = 0, [nil] = 1, [0] = 0, [proper#](x0) = x0 + 1 Strict: 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 >= 0 proper take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 0 proper 2nd X -> 2nd proper X 0 + 0X >= 1 + 0X proper head X -> head proper X 0 + 0X >= 1 + 0X 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 >= 1 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(X1, mark X2) -> mark take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 2nd ok X -> ok 2nd X 1 + 0X >= 0 + 0X 2nd mark X -> mark 2nd X 2 + 1X >= 2 + 1X head ok X -> ok head X 1 + 0X >= 0 + 0X head mark X -> mark head X 2 + 1X >= 2 + 1X active sel(0(), cons(X, XS)) -> mark X 2 + 0X + 0XS >= 1 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 2 + 0X + 0XS + 0N >= 2 + 0XS + 0N active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active take(0(), XS) -> mark nil() 2 + 1XS >= 2 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 3 + 1X + 1XS + 0N >= 3 + 1X + 1XS + 0N active take(X1, X2) -> take(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active 2nd cons(X, XS) -> mark head XS 3 + 1X + 1XS >= 2 + 1XS active 2nd X -> 2nd active X 2 + 1X >= 2 + 1X active head cons(X, XS) -> mark X 3 + 1X + 1XS >= 1 + 1X active head X -> head active X 2 + 1X >= 2 + 1X active s X -> s active X 1 + 0X >= 0 + 0X active from X -> from active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 3 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 s ok X -> ok s X 0 + 0X >= 0 + 0X s mark X -> mark s X 0 + 0X >= 1 + 0X from ok X -> ok from X 1 + 0X >= 0 + 0X from mark X -> mark from X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 Qed SCC (9): Strict: {active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# head X -> active# X, active# 2nd X -> active# X, active# take(X1, X2) -> active# X1, active# take(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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = x0 + x1, [sel](x0, x1) = x0 + x1 + 1, [mark](x0) = 1, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [head](x0) = x0, [2nd](x0) = x0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 0, [active#](x0) = x0 Strict: active# sel(X1, X2) -> active# X2 1 + 1X1 + 1X2 >= 0 + 1X2 active# sel(X1, X2) -> active# X1 1 + 1X1 + 1X2 >= 0 + 1X1 active# take(X1, X2) -> active# X2 0 + 1X1 + 1X2 >= 0 + 1X2 active# take(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 active# 2nd X -> active# X 0 + 1X >= 0 + 1X active# head X -> active# X 0 + 1X >= 0 + 1X active# s X -> active# X 0 + 1X >= 0 + 1X active# from X -> active# X 0 + 1X >= 0 + 1X active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 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 take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper 2nd X -> 2nd proper X 0 + 0X >= 0 + 0X proper head X -> head proper X 0 + 0X >= 0 + 0X 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) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 1X1 + 0X2 >= 1 + 0X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 1 + 1X1 + 0X2 >= 1 + 0X1 + 0X2 2nd ok X -> ok 2nd X 1 + 1X >= 1 + 1X 2nd mark X -> mark 2nd X 1 + 0X >= 1 + 0X head ok X -> ok head X 1 + 1X >= 1 + 1X head mark X -> mark head X 1 + 0X >= 1 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 1 + 0X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 1 + 0XS + 0N active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active take(0(), XS) -> mark nil() 0 + 0XS >= 1 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 1 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 1 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 0 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 1 + 0X active head X -> head active X 0 + 0X >= 0 + 0X 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 >= 1 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 1 + 0X >= 1 + 0X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 1 + 0X >= 1 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# head X -> active# X, active# 2nd X -> active# X, active# take(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2} SCC (7): Strict: {active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# head X -> active# X, active# 2nd X -> active# X, active# take(X1, X2) -> active# X1, active# take(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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = x0 + x1 + 1, [sel](x0, x1) = x0 + x1, [mark](x0) = 0, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [head](x0) = x0, [2nd](x0) = x0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 1, [active#](x0) = x0 Strict: active# take(X1, X2) -> active# X2 1 + 1X1 + 1X2 >= 0 + 1X2 active# take(X1, X2) -> active# X1 1 + 1X1 + 1X2 >= 0 + 1X1 active# 2nd X -> active# X 0 + 1X >= 0 + 1X active# head X -> active# X 0 + 1X >= 0 + 1X active# s X -> active# X 0 + 1X >= 0 + 1X active# from X -> active# X 0 + 1X >= 0 + 1X active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 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 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper 2nd X -> 2nd proper X 0 + 0X >= 0 + 0X proper head X -> head proper X 0 + 0X >= 0 + 0X 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) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 1 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 2nd ok X -> ok 2nd X 1 + 1X >= 1 + 1X 2nd mark X -> mark 2nd X 0 + 0X >= 0 + 0X head ok X -> ok head X 1 + 1X >= 1 + 1X head mark X -> mark head X 0 + 0X >= 0 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 0 + 0X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 0 + 0XS + 0N 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 take(0(), XS) -> mark nil() 0 + 0XS >= 0 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 0 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 0 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 0 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 0 + 0X active head X -> head active X 0 + 0X >= 0 + 0X 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 + 1X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# head X -> active# X, active# 2nd X -> active# X} SCC (5): Strict: {active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# head X -> active# X, active# 2nd X -> 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = 0, [sel](x0, x1) = x0 + 1, [mark](x0) = 0, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [head](x0) = x0, [2nd](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 1, [active#](x0) = x0 Strict: active# 2nd X -> active# X 1 + 1X >= 0 + 1X active# head X -> active# X 0 + 1X >= 0 + 1X active# s X -> active# X 0 + 1X >= 0 + 1X active# from X -> active# X 0 + 1X >= 0 + 1X active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 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 take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper 2nd X -> 2nd proper X 0 + 0X >= 1 + 0X proper head X -> head proper X 0 + 0X >= 0 + 0X 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) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 take(mark X1, X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 2nd ok X -> ok 2nd X 2 + 1X >= 2 + 1X 2nd mark X -> mark 2nd X 1 + 0X >= 0 + 0X head ok X -> ok head X 1 + 1X >= 1 + 1X head mark X -> mark head X 0 + 0X >= 0 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 0 + 0X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 0 + 0XS + 0N active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active take(0(), XS) -> mark nil() 0 + 0XS >= 0 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 0 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 0 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 1 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 0 + 0X active head X -> head active X 0 + 0X >= 0 + 0X 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 + 1X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# head X -> active# X} SCC (4): Strict: {active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# head X -> 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = 0, [sel](x0, x1) = 1, [mark](x0) = 0, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [head](x0) = x0 + 1, [2nd](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 1, [active#](x0) = x0 Strict: active# head X -> active# X 1 + 1X >= 0 + 1X active# s X -> active# X 0 + 1X >= 0 + 1X active# from X -> active# X 0 + 1X >= 0 + 1X active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 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 take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper 2nd X -> 2nd proper X 0 + 0X >= 0 + 0X proper head X -> head proper X 0 + 0X >= 1 + 0X 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) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 take(mark X1, X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 2nd ok X -> ok 2nd X 0 + 0X >= 1 + 0X 2nd mark X -> mark 2nd X 0 + 0X >= 0 + 0X head ok X -> ok head X 2 + 1X >= 2 + 1X head mark X -> mark head X 1 + 0X >= 0 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 0 + 0X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 0 + 0XS + 0N active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active take(0(), XS) -> mark nil() 0 + 0XS >= 0 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 0 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 0 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 0 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 0 + 0X active head X -> head active X 0 + 0X >= 1 + 0X 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 + 1X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X} SCC (3): Strict: {active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = 0, [sel](x0, x1) = x0 + x1, [mark](x0) = 0, [from](x0) = x0, [s](x0) = x0 + 1, [active](x0) = 0, [head](x0) = 0, [2nd](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 0, [active#](x0) = x0 Strict: active# s X -> active# X 1 + 1X >= 0 + 1X active# from X -> active# X 0 + 1X >= 0 + 1X active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 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 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper 2nd X -> 2nd proper X 0 + 0X >= 0 + 0X proper head X -> head proper X 0 + 0X >= 0 + 0X proper s X -> s proper X 0 + 0X >= 1 + 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) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 take(mark X1, X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 2nd ok X -> ok 2nd X 0 + 0X >= 1 + 0X 2nd mark X -> mark 2nd X 0 + 0X >= 0 + 0X head ok X -> ok head X 0 + 0X >= 1 + 0X head mark X -> mark head X 0 + 0X >= 0 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 0 + 0X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 0 + 0XS + 0N 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 take(0(), XS) -> mark nil() 0 + 0XS >= 0 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 0 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 0 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 0 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 0 + 0X active head X -> head active X 0 + 0X >= 0 + 0X active s X -> s active X 0 + 0X >= 1 + 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 + 1X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 1 + 0X >= 0 + 0X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1, active# from X -> active# X} SCC (2): Strict: {active# cons(X1, X2) -> active# X1, active# from X -> 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = 0, [sel](x0, x1) = 0, [mark](x0) = 0, [from](x0) = x0 + 1, [s](x0) = 0, [active](x0) = 0, [head](x0) = 0, [2nd](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 1, [active#](x0) = x0 Strict: active# from X -> active# X 1 + 1X >= 0 + 1X active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 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 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper 2nd X -> 2nd proper X 0 + 0X >= 0 + 0X proper head X -> head proper X 0 + 0X >= 0 + 0X 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) 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 take(ok X1, ok X2) -> ok take(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 take(mark X1, X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 2nd ok X -> ok 2nd X 0 + 0X >= 1 + 0X 2nd mark X -> mark 2nd X 0 + 0X >= 0 + 0X head ok X -> ok head X 0 + 0X >= 1 + 0X head mark X -> mark head X 0 + 0X >= 0 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 0 + 0X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 0 + 0XS + 0N 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 take(0(), XS) -> mark nil() 0 + 0XS >= 0 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 0 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 0 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 0 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 0 + 0X active head X -> head active X 0 + 0X >= 0 + 0X 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 >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 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 2 + 1X >= 2 + 1X from mark X -> mark from X 1 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1} SCC (1): Strict: {active# cons(X1, X2) -> active# X1} 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](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, [head](x0) = x0 + 1, [2nd](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [nil] = 1, [0] = 0, [active#](x0) = x0 Strict: active# cons(X1, X2) -> active# X1 1 + 1X1 + 0X2 >= 0 + 1X1 Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper sel(X1, X2) -> sel(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper 0() -> ok 0() 1 >= 1 proper take(X1, X2) -> take(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 proper nil() -> ok nil() 2 >= 2 proper 2nd X -> 2nd proper X 2 + 1X >= 2 + 1X proper head X -> head proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper from X -> from proper X 2 + 1X >= 2 + 1X proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(X1, mark X2) -> mark take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 2nd ok X -> ok 2nd X 2 + 1X >= 2 + 1X 2nd mark X -> mark 2nd X 2 + 1X >= 2 + 1X head ok X -> ok head X 2 + 1X >= 2 + 1X head mark X -> mark head X 2 + 1X >= 2 + 1X active sel(0(), cons(X, XS)) -> mark X 2 + 0X + 0XS >= 1 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 3 + 0X + 0XS + 1N >= 2 + 0XS + 1N active sel(X1, X2) -> sel(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active take(0(), XS) -> mark nil() 2 + 1XS >= 2 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 3 + 1X + 0XS + 0N >= 2 + 1X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active 2nd cons(X, XS) -> mark head XS 3 + 1X + 0XS >= 2 + 1XS active 2nd X -> 2nd active X 2 + 1X >= 2 + 1X active head cons(X, XS) -> mark X 3 + 1X + 0XS >= 1 + 1X active head X -> head active X 2 + 1X >= 2 + 1X 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: {2nd# mark X -> 2nd# X, 2nd# ok X -> 2nd# 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = 0, [sel](x0, x1) = 0, [mark](x0) = x0, [from](x0) = 0, [s](x0) = 0, [active](x0) = 0, [head](x0) = 0, [2nd](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 0, [0] = 1, [2nd#](x0) = x0 Strict: 2nd# ok X -> 2nd# X 1 + 1X >= 0 + 1X 2nd# mark X -> 2nd# 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 take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper 2nd X -> 2nd proper X 0 + 0X >= 0 + 0X proper head X -> head proper X 0 + 0X >= 0 + 0X 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 take(ok X1, ok X2) -> ok take(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 take(mark X1, X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 2nd ok X -> ok 2nd X 0 + 0X >= 1 + 0X 2nd mark X -> mark 2nd X 0 + 0X >= 0 + 0X head ok X -> ok head X 0 + 0X >= 1 + 0X head mark X -> mark head X 0 + 0X >= 0 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 0 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 0 + 0XS + 0N 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 take(0(), XS) -> mark nil() 0 + 0XS >= 0 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 0 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 0 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 0 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 0 + 1X active head X -> head active X 0 + 0X >= 0 + 0X 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: {2nd# mark X -> 2nd# X} SCC (1): Strict: {2nd# mark X -> 2nd# 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](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, [head](x0) = x0 + 1, [2nd](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [nil] = 1, [0] = 0, [2nd#](x0) = x0 Strict: 2nd# mark X -> 2nd# X 1 + 1X >= 0 + 1X Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper sel(X1, X2) -> sel(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper 0() -> ok 0() 1 >= 1 proper take(X1, X2) -> take(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 proper nil() -> ok nil() 2 >= 2 proper 2nd X -> 2nd proper X 2 + 1X >= 2 + 1X proper head X -> head proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper from X -> from proper X 2 + 1X >= 2 + 1X proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(X1, mark X2) -> mark take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 2nd ok X -> ok 2nd X 2 + 1X >= 2 + 1X 2nd mark X -> mark 2nd X 2 + 1X >= 2 + 1X head ok X -> ok head X 2 + 1X >= 2 + 1X head mark X -> mark head X 2 + 1X >= 2 + 1X active sel(0(), cons(X, XS)) -> mark X 2 + 0X + 0XS >= 1 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 3 + 0X + 0XS + 1N >= 2 + 0XS + 1N active sel(X1, X2) -> sel(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active take(0(), XS) -> mark nil() 2 + 1XS >= 2 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 3 + 1X + 0XS + 0N >= 2 + 1X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active 2nd cons(X, XS) -> mark head XS 3 + 1X + 0XS >= 2 + 1XS active 2nd X -> 2nd active X 2 + 1X >= 2 + 1X active head cons(X, XS) -> mark X 3 + 1X + 0XS >= 1 + 1X active head X -> head active X 2 + 1X >= 2 + 1X 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: {head# mark X -> head# X, head# ok X -> head# 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = 0, [sel](x0, x1) = 0, [mark](x0) = x0, [from](x0) = 0, [s](x0) = 0, [active](x0) = 0, [head](x0) = 0, [2nd](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 0, [0] = 1, [head#](x0) = x0 Strict: head# ok X -> head# X 1 + 1X >= 0 + 1X head# mark X -> head# 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 take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper 2nd X -> 2nd proper X 0 + 0X >= 0 + 0X proper head X -> head proper X 0 + 0X >= 0 + 0X 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 take(ok X1, ok X2) -> ok take(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 take(mark X1, X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 2nd ok X -> ok 2nd X 0 + 0X >= 1 + 0X 2nd mark X -> mark 2nd X 0 + 0X >= 0 + 0X head ok X -> ok head X 0 + 0X >= 1 + 0X head mark X -> mark head X 0 + 0X >= 0 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 0 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 0 + 0XS + 0N 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 take(0(), XS) -> mark nil() 0 + 0XS >= 0 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 0 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 0 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 0 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 0 + 1X active head X -> head active X 0 + 0X >= 0 + 0X 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: {head# mark X -> head# X} SCC (1): Strict: {head# mark X -> head# 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](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, [head](x0) = x0 + 1, [2nd](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [nil] = 1, [0] = 0, [head#](x0) = x0 Strict: head# mark X -> head# X 1 + 1X >= 0 + 1X Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper sel(X1, X2) -> sel(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper 0() -> ok 0() 1 >= 1 proper take(X1, X2) -> take(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 proper nil() -> ok nil() 2 >= 2 proper 2nd X -> 2nd proper X 2 + 1X >= 2 + 1X proper head X -> head proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper from X -> from proper X 2 + 1X >= 2 + 1X proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(X1, mark X2) -> mark take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 2nd ok X -> ok 2nd X 2 + 1X >= 2 + 1X 2nd mark X -> mark 2nd X 2 + 1X >= 2 + 1X head ok X -> ok head X 2 + 1X >= 2 + 1X head mark X -> mark head X 2 + 1X >= 2 + 1X active sel(0(), cons(X, XS)) -> mark X 2 + 0X + 0XS >= 1 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 3 + 0X + 0XS + 1N >= 2 + 0XS + 1N active sel(X1, X2) -> sel(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active take(0(), XS) -> mark nil() 2 + 1XS >= 2 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 3 + 1X + 0XS + 0N >= 2 + 1X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active 2nd cons(X, XS) -> mark head XS 3 + 1X + 0XS >= 2 + 1XS active 2nd X -> 2nd active X 2 + 1X >= 2 + 1X active head cons(X, XS) -> mark X 3 + 1X + 0XS >= 1 + 1X active head X -> head active X 2 + 1X >= 2 + 1X 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = 0, [sel](x0, x1) = 0, [mark](x0) = x0, [from](x0) = 0, [s](x0) = 0, [active](x0) = 0, [head](x0) = 0, [2nd](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 take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper 2nd X -> 2nd proper X 0 + 0X >= 0 + 0X proper head X -> head proper X 0 + 0X >= 0 + 0X 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 take(ok X1, ok X2) -> ok take(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 take(mark X1, X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 2nd ok X -> ok 2nd X 0 + 0X >= 1 + 0X 2nd mark X -> mark 2nd X 0 + 0X >= 0 + 0X head ok X -> ok head X 0 + 0X >= 1 + 0X head mark X -> mark head X 0 + 0X >= 0 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 0 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 0 + 0XS + 0N 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 take(0(), XS) -> mark nil() 0 + 0XS >= 0 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 0 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 0 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 0 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 0 + 1X active head X -> head active X 0 + 0X >= 0 + 0X 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](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, [head](x0) = x0 + 1, [2nd](x0) = x0 + 1, [proper](x0) = x0 + 1, [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 >= 2 + 1X proper sel(X1, X2) -> sel(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper 0() -> ok 0() 1 >= 1 proper take(X1, X2) -> take(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 proper nil() -> ok nil() 2 >= 2 proper 2nd X -> 2nd proper X 2 + 1X >= 2 + 1X proper head X -> head proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper from X -> from proper X 2 + 1X >= 2 + 1X proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(X1, mark X2) -> mark take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 2nd ok X -> ok 2nd X 2 + 1X >= 2 + 1X 2nd mark X -> mark 2nd X 2 + 1X >= 2 + 1X head ok X -> ok head X 2 + 1X >= 2 + 1X head mark X -> mark head X 2 + 1X >= 2 + 1X active sel(0(), cons(X, XS)) -> mark X 2 + 0X + 0XS >= 1 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 3 + 0X + 0XS + 1N >= 2 + 0XS + 1N active sel(X1, X2) -> sel(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active take(0(), XS) -> mark nil() 2 + 1XS >= 2 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 3 + 1X + 0XS + 0N >= 2 + 1X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active 2nd cons(X, XS) -> mark head XS 3 + 1X + 0XS >= 2 + 1XS active 2nd X -> 2nd active X 2 + 1X >= 2 + 1X active head cons(X, XS) -> mark X 3 + 1X + 0XS >= 1 + 1X active head X -> head active X 2 + 1X >= 2 + 1X 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = 0, [sel](x0, x1) = 0, [mark](x0) = x0, [from](x0) = 0, [s](x0) = 0, [active](x0) = 0, [head](x0) = 0, [2nd](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 take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper 2nd X -> 2nd proper X 0 + 0X >= 0 + 0X proper head X -> head proper X 0 + 0X >= 0 + 0X 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 take(ok X1, ok X2) -> ok take(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 take(mark X1, X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> mark take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 2nd ok X -> ok 2nd X 0 + 0X >= 1 + 0X 2nd mark X -> mark 2nd X 0 + 0X >= 0 + 0X head ok X -> ok head X 0 + 0X >= 1 + 0X head mark X -> mark head X 0 + 0X >= 0 + 0X active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 0 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 0 + 0XS + 0N 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 take(0(), XS) -> mark nil() 0 + 0XS >= 0 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 0 + 0X + 0XS + 0N >= 0 + 0X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active take(X1, X2) -> take(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active 2nd cons(X, XS) -> mark head XS 0 + 0X + 0XS >= 0 + 0XS active 2nd X -> 2nd active X 0 + 0X >= 0 + 0X active head cons(X, XS) -> mark X 0 + 0X + 0XS >= 0 + 1X active head X -> head active X 0 + 0X >= 0 + 0X 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](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, [head](x0) = x0 + 1, [2nd](x0) = x0 + 1, [proper](x0) = x0 + 1, [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 >= 2 + 1X proper sel(X1, X2) -> sel(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper 0() -> ok 0() 1 >= 1 proper take(X1, X2) -> take(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 proper nil() -> ok nil() 2 >= 2 proper 2nd X -> 2nd proper X 2 + 1X >= 2 + 1X proper head X -> head proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper from X -> from proper X 2 + 1X >= 2 + 1X proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(X1, mark X2) -> mark take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 2nd ok X -> ok 2nd X 2 + 1X >= 2 + 1X 2nd mark X -> mark 2nd X 2 + 1X >= 2 + 1X head ok X -> ok head X 2 + 1X >= 2 + 1X head mark X -> mark head X 2 + 1X >= 2 + 1X active sel(0(), cons(X, XS)) -> mark X 2 + 0X + 0XS >= 1 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 3 + 0X + 0XS + 1N >= 2 + 0XS + 1N active sel(X1, X2) -> sel(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active take(0(), XS) -> mark nil() 2 + 1XS >= 2 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 3 + 1X + 0XS + 0N >= 2 + 1X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active 2nd cons(X, XS) -> mark head XS 3 + 1X + 0XS >= 2 + 1XS active 2nd X -> 2nd active X 2 + 1X >= 2 + 1X active head cons(X, XS) -> mark X 3 + 1X + 0XS >= 1 + 1X active head X -> head active X 2 + 1X >= 2 + 1X 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + x1, [mark](x0) = x0 + 1, [from](x0) = 0, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [head](x0) = x0 + 1, [2nd](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 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper 2nd X -> 2nd proper X 0 + 0X >= 1 + 0X proper head X -> head proper X 0 + 0X >= 1 + 0X proper s X -> s proper X 0 + 0X >= 1 + 0X proper from X -> from proper X 0 + 0X >= 0 + 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 + 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 take(ok X1, ok X2) -> ok take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(X1, mark X2) -> mark take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 2nd ok X -> ok 2nd X 2 + 1X >= 2 + 1X 2nd mark X -> mark 2nd X 2 + 1X >= 2 + 1X head ok X -> ok head X 2 + 1X >= 2 + 1X head mark X -> mark head X 2 + 1X >= 2 + 1X active sel(0(), cons(X, XS)) -> mark X 2 + 1X + 0XS >= 1 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 3 + 1X + 0XS + 1N >= 1 + 1XS + 1N active sel(X1, X2) -> sel(active X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active take(0(), XS) -> mark nil() 2 + 1XS >= 2 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 3 + 1X + 0XS + 0N >= 2 + 1X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active 2nd cons(X, XS) -> mark head XS 3 + 1X + 0XS >= 2 + 1XS active 2nd X -> 2nd active X 2 + 1X >= 2 + 1X active head cons(X, XS) -> mark X 3 + 1X + 0XS >= 1 + 1X active head X -> head active X 2 + 1X >= 2 + 1X active s X -> s active X 2 + 1X >= 2 + 1X active from X -> from active X 1 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 1 + 0X >= 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 0 + 0X >= 1 + 0X from mark X -> mark from X 0 + 0X >= 1 + 0X 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](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, [head](x0) = x0 + 1, [2nd](x0) = x0 + 1, [proper](x0) = x0 + 1, [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 >= 2 + 1X proper sel(X1, X2) -> sel(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper 0() -> ok 0() 1 >= 1 proper take(X1, X2) -> take(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 proper nil() -> ok nil() 2 >= 2 proper 2nd X -> 2nd proper X 2 + 1X >= 2 + 1X proper head X -> head proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper from X -> from proper X 2 + 1X >= 2 + 1X proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(X1, mark X2) -> mark take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 2nd ok X -> ok 2nd X 2 + 1X >= 2 + 1X 2nd mark X -> mark 2nd X 2 + 1X >= 2 + 1X head ok X -> ok head X 2 + 1X >= 2 + 1X head mark X -> mark head X 2 + 1X >= 2 + 1X active sel(0(), cons(X, XS)) -> mark X 2 + 0X + 0XS >= 1 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 3 + 0X + 0XS + 1N >= 2 + 0XS + 1N active sel(X1, X2) -> sel(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active take(0(), XS) -> mark nil() 2 + 1XS >= 2 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 3 + 1X + 0XS + 0N >= 2 + 1X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active 2nd cons(X, XS) -> mark head XS 3 + 1X + 0XS >= 2 + 1XS active 2nd X -> 2nd active X 2 + 1X >= 2 + 1X active head cons(X, XS) -> mark X 3 + 1X + 0XS >= 1 + 1X active head X -> head active X 2 + 1X >= 2 + 1X 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: { 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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](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, [head](x0) = x0 + 1, [2nd](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 1, [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 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper 2nd X -> 2nd proper X 0 + 0X >= 1 + 0X proper head X -> head proper X 0 + 0X >= 1 + 0X 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 take(ok X1, ok X2) -> ok take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(X1, mark X2) -> mark take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 2nd ok X -> ok 2nd X 2 + 1X >= 2 + 1X 2nd mark X -> mark 2nd X 2 + 1X >= 2 + 1X head ok X -> ok head X 2 + 1X >= 2 + 1X head mark X -> mark head X 2 + 1X >= 2 + 1X active sel(0(), cons(X, XS)) -> mark X 3 + 1X + 0XS >= 1 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 3 + 1X + 0XS + 0N >= 2 + 1XS + 0N 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 take(0(), XS) -> mark nil() 2 + 1XS >= 2 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 3 + 1X + 0XS + 0N >= 2 + 1X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active 2nd cons(X, XS) -> mark head XS 3 + 1X + 0XS >= 2 + 1XS active 2nd X -> 2nd active X 2 + 1X >= 2 + 1X active head cons(X, XS) -> mark X 3 + 1X + 0XS >= 1 + 1X active head X -> head active X 2 + 1X >= 2 + 1X 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: {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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](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, [head](x0) = x0 + 1, [2nd](x0) = x0 + 1, [proper](x0) = x0 + 1, [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 >= 2 + 1X proper sel(X1, X2) -> sel(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper 0() -> ok 0() 1 >= 1 proper take(X1, X2) -> take(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 proper nil() -> ok nil() 2 >= 2 proper 2nd X -> 2nd proper X 2 + 1X >= 2 + 1X proper head X -> head proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper from X -> from proper X 2 + 1X >= 2 + 1X proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(X1, mark X2) -> mark take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 2nd ok X -> ok 2nd X 2 + 1X >= 2 + 1X 2nd mark X -> mark 2nd X 2 + 1X >= 2 + 1X head ok X -> ok head X 2 + 1X >= 2 + 1X head mark X -> mark head X 2 + 1X >= 2 + 1X active sel(0(), cons(X, XS)) -> mark X 2 + 0X + 0XS >= 1 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 3 + 0X + 0XS + 1N >= 2 + 0XS + 1N active sel(X1, X2) -> sel(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active take(0(), XS) -> mark nil() 2 + 1XS >= 2 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 3 + 1X + 0XS + 0N >= 2 + 1X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active 2nd cons(X, XS) -> mark head XS 3 + 1X + 0XS >= 2 + 1XS active 2nd X -> 2nd active X 2 + 1X >= 2 + 1X active head cons(X, XS) -> mark X 3 + 1X + 0XS >= 1 + 1X active head X -> head active X 2 + 1X >= 2 + 1X 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: { take#(X1, mark X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](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, [head](x0) = x0 + 1, [2nd](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [0] = 1, [take#](x0, x1) = x0 + 1 Strict: take#(ok X1, ok X2) -> take#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 take#(mark X1, X2) -> take#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 take#(X1, mark X2) -> take#(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 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper take(X1, X2) -> take(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper 2nd X -> 2nd proper X 0 + 0X >= 1 + 0X proper head X -> head proper X 0 + 0X >= 1 + 0X 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 take(ok X1, ok X2) -> ok take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(X1, mark X2) -> mark take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 2nd ok X -> ok 2nd X 2 + 1X >= 2 + 1X 2nd mark X -> mark 2nd X 2 + 1X >= 2 + 1X head ok X -> ok head X 2 + 1X >= 2 + 1X head mark X -> mark head X 2 + 1X >= 2 + 1X active sel(0(), cons(X, XS)) -> mark X 3 + 1X + 0XS >= 1 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 3 + 1X + 0XS + 0N >= 2 + 1XS + 0N 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 take(0(), XS) -> mark nil() 2 + 1XS >= 2 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 3 + 1X + 0XS + 0N >= 2 + 1X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active 2nd cons(X, XS) -> mark head XS 3 + 1X + 0XS >= 2 + 1XS active 2nd X -> 2nd active X 2 + 1X >= 2 + 1X active head cons(X, XS) -> mark X 3 + 1X + 0XS >= 1 + 1X active head X -> head active X 2 + 1X >= 2 + 1X 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: {take#(X1, mark X2) -> take#(X1, X2)} SCC (1): Strict: {take#(X1, mark X2) -> take#(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 head X -> head active X, active head cons(X, XS) -> mark X, active 2nd X -> 2nd active X, active 2nd cons(X, XS) -> mark head XS, active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)), active take(0(), XS) -> mark nil(), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(s N, cons(X, XS)) -> mark sel(N, XS), active sel(0(), cons(X, XS)) -> mark X, head mark X -> mark head X, head ok X -> ok head X, 2nd mark X -> mark 2nd X, 2nd ok X -> ok 2nd X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(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 head X -> head proper X, proper 2nd X -> 2nd proper X, proper nil() -> ok nil(), proper take(X1, X2) -> take(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, [take](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, [head](x0) = x0 + 1, [2nd](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [nil] = 1, [0] = 0, [take#](x0, x1) = x0 Strict: take#(X1, mark X2) -> take#(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 >= 2 + 1X proper sel(X1, X2) -> sel(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper 0() -> ok 0() 1 >= 1 proper take(X1, X2) -> take(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 proper nil() -> ok nil() 2 >= 2 proper 2nd X -> 2nd proper X 2 + 1X >= 2 + 1X proper head X -> head proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper from X -> from proper X 2 + 1X >= 2 + 1X proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 take(ok X1, ok X2) -> ok take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(mark X1, X2) -> mark take(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 take(X1, mark X2) -> mark take(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 2nd ok X -> ok 2nd X 2 + 1X >= 2 + 1X 2nd mark X -> mark 2nd X 2 + 1X >= 2 + 1X head ok X -> ok head X 2 + 1X >= 2 + 1X head mark X -> mark head X 2 + 1X >= 2 + 1X active sel(0(), cons(X, XS)) -> mark X 2 + 0X + 0XS >= 1 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 3 + 0X + 0XS + 1N >= 2 + 0XS + 1N active sel(X1, X2) -> sel(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active take(0(), XS) -> mark nil() 2 + 1XS >= 2 active take(s N, cons(X, XS)) -> mark cons(X, take(N, XS)) 3 + 1X + 0XS + 0N >= 2 + 1X + 0XS + 0N active take(X1, X2) -> take(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active take(X1, X2) -> take(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active 2nd cons(X, XS) -> mark head XS 3 + 1X + 0XS >= 2 + 1XS active 2nd X -> 2nd active X 2 + 1X >= 2 + 1X active head cons(X, XS) -> mark X 3 + 1X + 0XS >= 1 + 1X active head X -> head active X 2 + 1X >= 2 + 1X 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