MAYBE Time: 0.676892 TRS: { active app(X1, X2) -> app(X1, active X2), active app(X1, X2) -> app(active X1, X2), active app(nil(), YS) -> mark YS, active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)), 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 zWadr(XS, nil()) -> mark nil(), active zWadr(X1, X2) -> zWadr(X1, active X2), active zWadr(X1, X2) -> zWadr(active X1, X2), active zWadr(nil(), YS) -> mark nil(), active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)), active prefix X -> prefix active X, active prefix L -> mark cons(nil(), zWadr(L, prefix L)), app(X1, mark X2) -> mark app(X1, X2), app(mark X1, X2) -> mark app(X1, X2), app(ok X1, ok X2) -> ok app(X1, X2), 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, zWadr(X1, mark X2) -> mark zWadr(X1, X2), zWadr(mark X1, X2) -> mark zWadr(X1, X2), zWadr(ok X1, ok X2) -> ok zWadr(X1, X2), prefix mark X -> mark prefix X, prefix ok X -> ok prefix X, proper app(X1, X2) -> app(proper X1, proper X2), proper nil() -> ok nil(), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper zWadr(X1, X2) -> zWadr(proper X1, proper X2), proper prefix X -> prefix proper X, top mark X -> top proper X, top ok X -> top active X} DP: DP: { active# app(X1, X2) -> active# X1, active# app(X1, X2) -> active# X2, active# app(X1, X2) -> app#(X1, active X2), active# app(X1, X2) -> app#(active X1, X2), active# app(cons(X, XS), YS) -> app#(XS, YS), active# app(cons(X, XS), YS) -> cons#(X, app(XS, YS)), active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2), active# from X -> active# X, active# from X -> cons#(X, from s X), active# from X -> from# active X, active# from X -> from# s X, active# from X -> s# X, active# s X -> active# X, active# s X -> s# active X, active# zWadr(X1, X2) -> active# X1, active# zWadr(X1, X2) -> active# X2, active# zWadr(X1, X2) -> zWadr#(X1, active X2), active# zWadr(X1, X2) -> zWadr#(active X1, X2), active# zWadr(cons(X, XS), cons(Y, YS)) -> app#(Y, cons(X, nil())), active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(X, nil()), active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(app(Y, cons(X, nil())), zWadr(XS, YS)), active# zWadr(cons(X, XS), cons(Y, YS)) -> zWadr#(XS, YS), active# prefix X -> active# X, active# prefix X -> prefix# active X, active# prefix L -> cons#(nil(), zWadr(L, prefix L)), active# prefix L -> zWadr#(L, prefix L), app#(X1, mark X2) -> app#(X1, X2), app#(mark X1, X2) -> app#(X1, X2), app#(ok X1, ok X2) -> app#(X1, X2), 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, zWadr#(X1, mark X2) -> zWadr#(X1, X2), zWadr#(mark X1, X2) -> zWadr#(X1, X2), zWadr#(ok X1, ok X2) -> zWadr#(X1, X2), prefix# mark X -> prefix# X, prefix# ok X -> prefix# X, proper# app(X1, X2) -> app#(proper X1, proper X2), proper# app(X1, X2) -> proper# X1, proper# app(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2), proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> from# proper X, proper# from X -> proper# X, proper# s X -> s# proper X, proper# s X -> proper# X, proper# zWadr(X1, X2) -> zWadr#(proper X1, proper X2), proper# zWadr(X1, X2) -> proper# X1, proper# zWadr(X1, X2) -> proper# X2, proper# prefix X -> prefix# proper X, proper# prefix X -> proper# X, top# mark X -> proper# X, top# mark X -> top# proper X, top# ok X -> active# X, top# ok X -> top# active X} TRS: { active app(X1, X2) -> app(X1, active X2), active app(X1, X2) -> app(active X1, X2), active app(nil(), YS) -> mark YS, active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)), 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 zWadr(XS, nil()) -> mark nil(), active zWadr(X1, X2) -> zWadr(X1, active X2), active zWadr(X1, X2) -> zWadr(active X1, X2), active zWadr(nil(), YS) -> mark nil(), active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)), active prefix X -> prefix active X, active prefix L -> mark cons(nil(), zWadr(L, prefix L)), app(X1, mark X2) -> mark app(X1, X2), app(mark X1, X2) -> mark app(X1, X2), app(ok X1, ok X2) -> ok app(X1, X2), 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, zWadr(X1, mark X2) -> mark zWadr(X1, X2), zWadr(mark X1, X2) -> mark zWadr(X1, X2), zWadr(ok X1, ok X2) -> ok zWadr(X1, X2), prefix mark X -> mark prefix X, prefix ok X -> ok prefix X, proper app(X1, X2) -> app(proper X1, proper X2), proper nil() -> ok nil(), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper zWadr(X1, X2) -> zWadr(proper X1, proper X2), proper prefix X -> prefix proper X, top mark X -> top proper X, top ok X -> top active X} EDG: { (active# zWadr(X1, X2) -> zWadr#(X1, active X2), zWadr#(ok X1, ok X2) -> zWadr#(X1, X2)) (active# zWadr(X1, X2) -> zWadr#(X1, active X2), zWadr#(X1, mark X2) -> zWadr#(X1, X2)) (proper# app(X1, X2) -> app#(proper X1, proper X2), app#(ok X1, ok X2) -> app#(X1, X2)) (proper# app(X1, X2) -> app#(proper X1, proper X2), app#(mark X1, X2) -> app#(X1, X2)) (proper# app(X1, X2) -> app#(proper X1, proper X2), app#(X1, mark X2) -> app#(X1, X2)) (proper# zWadr(X1, X2) -> zWadr#(proper X1, proper X2), zWadr#(ok X1, ok X2) -> zWadr#(X1, X2)) (proper# zWadr(X1, X2) -> zWadr#(proper X1, proper X2), zWadr#(mark X1, X2) -> zWadr#(X1, X2)) (proper# zWadr(X1, X2) -> zWadr#(proper X1, proper X2), zWadr#(X1, mark X2) -> zWadr#(X1, X2)) (active# zWadr(X1, X2) -> active# X2, active# prefix L -> zWadr#(L, prefix L)) (active# zWadr(X1, X2) -> active# X2, active# prefix L -> cons#(nil(), zWadr(L, prefix L))) (active# zWadr(X1, X2) -> active# X2, active# prefix X -> prefix# active X) (active# zWadr(X1, X2) -> active# X2, active# prefix X -> active# X) (active# zWadr(X1, X2) -> active# X2, active# zWadr(cons(X, XS), cons(Y, YS)) -> zWadr#(XS, YS)) (active# zWadr(X1, X2) -> active# X2, active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(app(Y, cons(X, nil())), zWadr(XS, YS))) (active# zWadr(X1, X2) -> active# X2, active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(X, nil())) (active# zWadr(X1, X2) -> active# X2, active# zWadr(cons(X, XS), cons(Y, YS)) -> app#(Y, cons(X, nil()))) (active# zWadr(X1, X2) -> active# X2, active# zWadr(X1, X2) -> zWadr#(active X1, X2)) (active# zWadr(X1, X2) -> active# X2, active# zWadr(X1, X2) -> zWadr#(X1, active X2)) (active# zWadr(X1, X2) -> active# X2, active# zWadr(X1, X2) -> active# X2) (active# zWadr(X1, X2) -> active# X2, active# zWadr(X1, X2) -> active# X1) (active# zWadr(X1, X2) -> active# X2, active# s X -> s# active X) (active# zWadr(X1, X2) -> active# X2, active# s X -> active# X) (active# zWadr(X1, X2) -> active# X2, active# from X -> s# X) (active# zWadr(X1, X2) -> active# X2, active# from X -> from# s X) (active# zWadr(X1, X2) -> active# X2, active# from X -> from# active X) (active# zWadr(X1, X2) -> active# X2, active# from X -> cons#(X, from s X)) (active# zWadr(X1, X2) -> active# X2, active# from X -> active# X) (active# zWadr(X1, X2) -> active# X2, active# cons(X1, X2) -> cons#(active X1, X2)) (active# zWadr(X1, X2) -> active# X2, active# cons(X1, X2) -> active# X1) (active# zWadr(X1, X2) -> active# X2, active# app(cons(X, XS), YS) -> cons#(X, app(XS, YS))) (active# zWadr(X1, X2) -> active# X2, active# app(cons(X, XS), YS) -> app#(XS, YS)) (active# zWadr(X1, X2) -> active# X2, active# app(X1, X2) -> app#(active X1, X2)) (active# zWadr(X1, X2) -> active# X2, active# app(X1, X2) -> app#(X1, active X2)) (active# zWadr(X1, X2) -> active# X2, active# app(X1, X2) -> active# X2) (active# zWadr(X1, X2) -> active# X2, active# app(X1, X2) -> active# X1) (proper# cons(X1, X2) -> proper# X2, proper# prefix X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# prefix X -> prefix# proper X) (proper# cons(X1, X2) -> proper# X2, proper# zWadr(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# zWadr(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# zWadr(X1, X2) -> zWadr#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# from X -> from# proper X) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# app(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# app(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# app(X1, X2) -> app#(proper X1, proper X2)) (active# from X -> from# s X, from# ok X -> from# X) (active# from X -> from# s X, from# mark X -> from# X) (active# prefix X -> prefix# active X, prefix# ok X -> prefix# X) (active# prefix X -> prefix# active X, prefix# mark X -> prefix# X) (proper# s X -> s# proper X, s# ok X -> s# X) (proper# s X -> s# proper X, s# mark X -> s# X) (top# mark X -> top# proper X, top# ok X -> top# active X) (top# mark X -> top# proper X, top# ok X -> active# X) (top# mark X -> top# proper X, top# mark X -> top# proper X) (top# mark X -> top# proper X, top# mark X -> proper# X) (active# zWadr(cons(X, XS), cons(Y, YS)) -> app#(Y, cons(X, nil())), app#(ok X1, ok X2) -> app#(X1, X2)) (active# zWadr(cons(X, XS), cons(Y, YS)) -> app#(Y, cons(X, nil())), app#(X1, mark X2) -> app#(X1, X2)) (active# from X -> active# X, active# prefix L -> zWadr#(L, prefix L)) (active# from X -> active# X, active# prefix L -> cons#(nil(), zWadr(L, prefix L))) (active# from X -> active# X, active# prefix X -> prefix# active X) (active# from X -> active# X, active# prefix X -> active# X) (active# from X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> zWadr#(XS, YS)) (active# from X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(app(Y, cons(X, nil())), zWadr(XS, YS))) (active# from X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(X, nil())) (active# from X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> app#(Y, cons(X, nil()))) (active# from X -> active# X, active# zWadr(X1, X2) -> zWadr#(active X1, X2)) (active# from X -> active# X, active# zWadr(X1, X2) -> zWadr#(X1, active X2)) (active# from X -> active# X, active# zWadr(X1, X2) -> active# X2) (active# from X -> active# X, active# zWadr(X1, X2) -> active# X1) (active# from X -> active# X, active# s X -> s# active X) (active# from X -> active# X, active# s X -> active# X) (active# from X -> active# X, active# from X -> s# X) (active# from X -> active# X, active# from X -> from# s X) (active# from X -> active# X, active# from X -> from# active X) (active# from X -> active# X, active# from X -> cons#(X, from s X)) (active# from X -> active# X, active# from X -> active# X) (active# from X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# from X -> active# X, active# cons(X1, X2) -> active# X1) (active# from X -> active# X, active# app(cons(X, XS), YS) -> cons#(X, app(XS, YS))) (active# from X -> active# X, active# app(cons(X, XS), YS) -> app#(XS, YS)) (active# from X -> active# X, active# app(X1, X2) -> app#(active X1, X2)) (active# from X -> active# X, active# app(X1, X2) -> app#(X1, active X2)) (active# from X -> active# X, active# app(X1, X2) -> active# X2) (active# from X -> active# X, active# app(X1, X2) -> active# X1) (active# s X -> active# X, active# prefix L -> zWadr#(L, prefix L)) (active# s X -> active# X, active# prefix L -> cons#(nil(), zWadr(L, prefix L))) (active# s X -> active# X, active# prefix X -> prefix# active X) (active# s X -> active# X, active# prefix X -> active# X) (active# s X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> zWadr#(XS, YS)) (active# s X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(app(Y, cons(X, nil())), zWadr(XS, YS))) (active# s X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(X, nil())) (active# s X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> app#(Y, cons(X, nil()))) (active# s X -> active# X, active# zWadr(X1, X2) -> zWadr#(active X1, X2)) (active# s X -> active# X, active# zWadr(X1, X2) -> zWadr#(X1, active X2)) (active# s X -> active# X, active# zWadr(X1, X2) -> active# X2) (active# s X -> active# X, active# zWadr(X1, X2) -> active# X1) (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# from X -> 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 -> cons#(X, from s X)) (active# s X -> active# X, active# from X -> active# X) (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# app(cons(X, XS), YS) -> cons#(X, app(XS, YS))) (active# s X -> active# X, active# app(cons(X, XS), YS) -> app#(XS, YS)) (active# s X -> active# X, active# app(X1, X2) -> app#(active X1, X2)) (active# s X -> active# X, active# app(X1, X2) -> app#(X1, active X2)) (active# s X -> active# X, active# app(X1, X2) -> active# X2) (active# s X -> active# X, active# app(X1, X2) -> active# X1) (from# mark X -> from# X, from# ok X -> from# X) (from# mark X -> from# X, from# mark X -> from# X) (s# mark X -> s# X, s# ok X -> s# X) (s# mark X -> s# X, s# mark X -> s# X) (prefix# mark X -> prefix# X, prefix# ok X -> prefix# X) (prefix# mark X -> prefix# X, prefix# mark X -> prefix# X) (proper# from X -> proper# X, proper# prefix X -> proper# X) (proper# from X -> proper# X, proper# prefix X -> prefix# proper X) (proper# from X -> proper# X, proper# zWadr(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# zWadr(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# zWadr(X1, X2) -> zWadr#(proper X1, proper X2)) (proper# from X -> proper# X, proper# s X -> proper# X) (proper# from X -> proper# X, proper# s X -> s# proper X) (proper# from X -> proper# X, proper# from X -> proper# X) (proper# from X -> proper# X, proper# from X -> from# proper X) (proper# from X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# from X -> proper# X, proper# app(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# app(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# app(X1, X2) -> app#(proper X1, proper X2)) (proper# prefix X -> proper# X, proper# prefix X -> proper# X) (proper# prefix X -> proper# X, proper# prefix X -> prefix# proper X) (proper# prefix X -> proper# X, proper# zWadr(X1, X2) -> proper# X2) (proper# prefix X -> proper# X, proper# zWadr(X1, X2) -> proper# X1) (proper# prefix X -> proper# X, proper# zWadr(X1, X2) -> zWadr#(proper X1, proper X2)) (proper# prefix X -> proper# X, proper# s X -> proper# X) (proper# prefix X -> proper# X, proper# s X -> s# proper X) (proper# prefix X -> proper# X, proper# from X -> proper# X) (proper# prefix X -> proper# X, proper# from X -> from# proper X) (proper# prefix X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# prefix X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# prefix X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# prefix X -> proper# X, proper# app(X1, X2) -> proper# X2) (proper# prefix X -> proper# X, proper# app(X1, X2) -> proper# X1) (proper# prefix X -> proper# X, proper# app(X1, X2) -> app#(proper X1, proper X2)) (top# ok X -> active# X, active# prefix L -> zWadr#(L, prefix L)) (top# ok X -> active# X, active# prefix L -> cons#(nil(), zWadr(L, prefix L))) (top# ok X -> active# X, active# prefix X -> prefix# active X) (top# ok X -> active# X, active# prefix X -> active# X) (top# ok X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> zWadr#(XS, YS)) (top# ok X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(app(Y, cons(X, nil())), zWadr(XS, YS))) (top# ok X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(X, nil())) (top# ok X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> app#(Y, cons(X, nil()))) (top# ok X -> active# X, active# zWadr(X1, X2) -> zWadr#(active X1, X2)) (top# ok X -> active# X, active# zWadr(X1, X2) -> zWadr#(X1, active X2)) (top# ok X -> active# X, active# zWadr(X1, X2) -> active# X2) (top# ok X -> active# X, active# zWadr(X1, X2) -> active# X1) (top# ok X -> active# X, active# s X -> s# active X) (top# ok X -> active# X, active# s X -> active# X) (top# ok X -> active# X, active# from X -> s# X) (top# ok X -> active# X, active# from X -> from# s X) (top# ok X -> active# X, active# from X -> from# active X) (top# ok X -> active# X, active# from X -> cons#(X, from s X)) (top# ok X -> active# X, active# from X -> active# X) (top# ok X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (top# ok X -> active# X, active# cons(X1, X2) -> active# X1) (top# ok X -> active# X, active# app(cons(X, XS), YS) -> cons#(X, app(XS, YS))) (top# ok X -> active# X, active# app(cons(X, XS), YS) -> app#(XS, YS)) (top# ok X -> active# X, active# app(X1, X2) -> app#(active X1, X2)) (top# ok X -> active# X, active# app(X1, X2) -> app#(X1, active X2)) (top# ok X -> active# X, active# app(X1, X2) -> active# X2) (top# ok X -> active# X, active# app(X1, X2) -> active# X1) (active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(app(Y, cons(X, nil())), zWadr(XS, YS)), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(app(Y, cons(X, nil())), zWadr(XS, YS)), cons#(mark X1, X2) -> cons#(X1, X2)) (active# app(X1, X2) -> app#(active X1, X2), app#(ok X1, ok X2) -> app#(X1, X2)) (active# app(X1, X2) -> app#(active X1, X2), app#(mark X1, X2) -> app#(X1, X2)) (active# zWadr(X1, X2) -> zWadr#(active X1, X2), zWadr#(ok X1, ok X2) -> zWadr#(X1, X2)) (active# zWadr(X1, X2) -> zWadr#(active X1, X2), zWadr#(mark X1, X2) -> zWadr#(X1, X2)) (active# cons(X1, X2) -> active# X1, active# prefix L -> zWadr#(L, prefix L)) (active# cons(X1, X2) -> active# X1, active# prefix L -> cons#(nil(), zWadr(L, prefix L))) (active# cons(X1, X2) -> active# X1, active# prefix X -> prefix# active X) (active# cons(X1, X2) -> active# X1, active# 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-> proper# X1) (proper# zWadr(X1, X2) -> proper# X1, proper# app(X1, X2) -> app#(proper X1, proper X2)) (app#(mark X1, X2) -> app#(X1, X2), app#(ok X1, ok X2) -> app#(X1, X2)) (app#(mark X1, X2) -> app#(X1, X2), app#(mark X1, X2) -> app#(X1, X2)) (app#(mark X1, X2) -> app#(X1, X2), app#(X1, mark X2) -> app#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (zWadr#(X1, mark X2) -> zWadr#(X1, X2), zWadr#(ok X1, ok X2) -> zWadr#(X1, X2)) (zWadr#(X1, mark X2) -> zWadr#(X1, X2), zWadr#(mark X1, X2) -> zWadr#(X1, X2)) (zWadr#(X1, mark X2) -> zWadr#(X1, X2), zWadr#(X1, mark X2) -> zWadr#(X1, X2)) (zWadr#(ok X1, ok X2) -> zWadr#(X1, X2), zWadr#(ok X1, ok X2) -> zWadr#(X1, X2)) (zWadr#(ok X1, ok X2) -> zWadr#(X1, X2), zWadr#(mark X1, X2) -> zWadr#(X1, X2)) (zWadr#(ok X1, ok X2) -> zWadr#(X1, X2), zWadr#(X1, mark X2) -> zWadr#(X1, X2)) (active# zWadr(cons(X, XS), cons(Y, YS)) -> 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X1, ok X2) -> app#(X1, X2)) (app#(X1, mark X2) -> app#(X1, X2), app#(X1, mark X2) -> app#(X1, X2)) (app#(X1, mark X2) -> app#(X1, X2), app#(mark X1, X2) -> app#(X1, X2)) (app#(X1, mark X2) -> app#(X1, X2), app#(ok X1, ok X2) -> app#(X1, X2)) (proper# cons(X1, X2) -> proper# X1, proper# app(X1, X2) -> app#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X1, proper# app(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# app(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) -> 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nil())) (active# zWadr(X1, X2) -> active# X1, active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(app(Y, cons(X, nil())), zWadr(XS, YS))) (active# zWadr(X1, X2) -> active# X1, active# zWadr(cons(X, XS), cons(Y, YS)) -> zWadr#(XS, YS)) (active# zWadr(X1, X2) -> active# X1, active# prefix X -> active# X) (active# zWadr(X1, X2) -> active# X1, active# prefix X -> prefix# active X) (active# zWadr(X1, X2) -> active# X1, active# prefix L -> cons#(nil(), zWadr(L, prefix L))) (active# zWadr(X1, X2) -> active# X1, active# prefix L -> zWadr#(L, prefix L)) (active# app(X1, X2) -> active# X1, active# app(X1, X2) -> active# X1) (active# app(X1, X2) -> active# X1, active# app(X1, X2) -> active# X2) (active# app(X1, X2) -> active# X1, active# app(X1, X2) -> app#(X1, active X2)) (active# app(X1, X2) -> active# X1, active# app(X1, X2) -> app#(active X1, X2)) (active# app(X1, X2) -> active# X1, active# app(cons(X, XS), YS) -> app#(XS, YS)) (active# app(X1, X2) -> active# X1, active# app(cons(X, XS), YS) -> 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(proper# s X -> proper# X, proper# app(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# app(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# from X -> from# proper X) (proper# s X -> proper# X, proper# from X -> proper# X) (proper# s X -> proper# X, proper# s X -> s# proper X) (proper# s X -> proper# X, proper# s X -> proper# X) (proper# s X -> proper# X, proper# zWadr(X1, X2) -> zWadr#(proper X1, proper X2)) (proper# s X -> proper# X, proper# zWadr(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# zWadr(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# prefix X -> prefix# proper X) (proper# s X -> proper# X, proper# prefix X -> proper# X) (prefix# ok X -> prefix# X, prefix# mark X -> prefix# X) (prefix# ok X -> prefix# X, prefix# ok X -> prefix# X) (s# ok X -> s# X, s# mark X -> s# X) (s# ok X -> s# X, s# ok X -> s# X) (from# ok X -> from# X, from# mark X -> from# X) (from# ok X -> from# X, from# ok X -> from# X) (active# prefix X -> active# X, active# app(X1, X2) -> active# X1) (active# prefix X -> active# X, active# app(X1, X2) -> active# X2) (active# prefix X -> active# X, active# app(X1, X2) -> app#(X1, active X2)) (active# prefix X -> active# X, active# app(X1, X2) -> app#(active X1, X2)) (active# prefix X -> active# X, active# app(cons(X, XS), YS) -> app#(XS, YS)) (active# prefix X -> active# X, active# app(cons(X, XS), YS) -> cons#(X, app(XS, YS))) (active# prefix X -> active# X, active# cons(X1, X2) -> active# X1) (active# prefix X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# prefix X -> active# X, active# from X -> active# X) (active# prefix X -> active# X, active# from X -> cons#(X, from s X)) (active# prefix X -> active# X, active# from X -> from# active X) (active# prefix X -> active# X, active# from X -> from# s X) (active# prefix X -> active# X, active# from X -> s# X) (active# prefix X -> active# X, active# s X -> active# X) (active# prefix X -> active# X, active# s X -> s# active X) (active# prefix X -> active# X, active# zWadr(X1, X2) -> active# X1) (active# prefix X -> active# X, active# zWadr(X1, X2) -> active# X2) (active# prefix X -> active# X, active# zWadr(X1, X2) -> zWadr#(X1, active X2)) (active# prefix X -> active# X, active# zWadr(X1, X2) -> zWadr#(active X1, X2)) (active# prefix X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> app#(Y, cons(X, nil()))) (active# prefix X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(X, nil())) (active# prefix X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(app(Y, cons(X, nil())), zWadr(XS, YS))) (active# prefix X -> active# X, active# zWadr(cons(X, XS), cons(Y, YS)) -> zWadr#(XS, YS)) (active# prefix X -> active# X, active# prefix X -> active# X) (active# prefix X -> active# X, active# prefix X -> prefix# active X) (active# prefix X -> active# X, active# prefix L -> cons#(nil(), zWadr(L, prefix L))) (active# prefix X -> active# X, active# prefix L -> zWadr#(L, prefix L)) (top# ok X -> top# active X, top# mark X -> proper# X) (top# ok X -> top# active X, top# mark X -> top# proper X) (top# ok X -> top# active X, top# ok X -> active# X) (top# ok X -> top# active X, top# ok X -> top# active X) (proper# prefix X -> prefix# proper X, prefix# mark X -> prefix# X) (proper# prefix X -> prefix# proper X, prefix# ok X -> prefix# X) (proper# from X -> from# proper X, from# mark X -> from# X) (proper# from X -> from# proper X, from# ok X -> from# X) (active# s X -> s# active X, s# mark X -> s# X) (active# s X -> s# active X, s# ok X -> s# X) (active# from X -> from# active X, from# mark X -> from# X) (active# from X -> from# active X, from# ok X -> from# X) (proper# zWadr(X1, X2) -> proper# X2, proper# app(X1, X2) -> app#(proper X1, proper X2)) (proper# zWadr(X1, X2) -> proper# X2, proper# app(X1, X2) -> proper# X1) (proper# zWadr(X1, X2) -> proper# X2, proper# app(X1, X2) -> proper# X2) (proper# zWadr(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# zWadr(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# zWadr(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# zWadr(X1, X2) -> proper# X2, proper# from X -> from# proper X) (proper# zWadr(X1, X2) -> proper# X2, proper# from X -> proper# X) (proper# zWadr(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# zWadr(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# zWadr(X1, X2) -> proper# X2, proper# zWadr(X1, X2) -> zWadr#(proper X1, proper X2)) (proper# zWadr(X1, X2) -> proper# X2, proper# zWadr(X1, X2) -> proper# X1) (proper# zWadr(X1, X2) -> proper# X2, proper# zWadr(X1, X2) -> proper# X2) (proper# zWadr(X1, X2) -> proper# X2, proper# prefix X -> prefix# proper X) (proper# zWadr(X1, X2) -> proper# X2, proper# prefix X -> proper# X) (proper# app(X1, X2) -> proper# X2, proper# app(X1, X2) -> app#(proper X1, proper X2)) (proper# app(X1, X2) -> proper# X2, proper# app(X1, X2) -> proper# X1) (proper# app(X1, X2) -> proper# X2, proper# app(X1, X2) -> proper# X2) (proper# app(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# app(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# app(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# app(X1, X2) -> proper# X2, proper# from X -> from# proper X) (proper# app(X1, X2) -> proper# X2, proper# from X -> proper# X) (proper# app(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# app(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# app(X1, X2) -> proper# X2, proper# zWadr(X1, X2) -> zWadr#(proper X1, proper X2)) (proper# app(X1, X2) -> proper# X2, proper# zWadr(X1, X2) -> proper# X1) (proper# app(X1, X2) -> proper# X2, proper# zWadr(X1, X2) -> proper# X2) (proper# app(X1, X2) -> proper# X2, proper# prefix X -> prefix# proper X) (proper# app(X1, X2) -> proper# X2, proper# prefix X -> proper# X) (active# app(X1, X2) -> active# X2, active# app(X1, X2) -> active# X1) (active# app(X1, X2) -> active# X2, active# app(X1, X2) -> active# X2) (active# app(X1, X2) -> active# X2, active# app(X1, X2) -> app#(X1, active X2)) (active# app(X1, X2) -> active# X2, active# app(X1, X2) -> app#(active X1, X2)) (active# app(X1, X2) -> active# X2, active# app(cons(X, XS), YS) -> app#(XS, YS)) (active# app(X1, X2) -> active# X2, active# app(cons(X, XS), YS) -> cons#(X, app(XS, YS))) (active# app(X1, X2) -> active# X2, active# cons(X1, X2) -> active# X1) (active# app(X1, X2) -> active# X2, active# cons(X1, X2) -> cons#(active X1, X2)) (active# app(X1, X2) -> active# X2, active# from X -> active# X) (active# app(X1, X2) -> active# X2, active# from X -> cons#(X, from s X)) (active# app(X1, X2) -> active# X2, active# from X -> from# active X) (active# app(X1, X2) -> active# X2, active# from X -> from# s X) (active# app(X1, X2) -> active# X2, active# from X -> s# X) (active# app(X1, X2) -> active# X2, active# s X -> active# X) (active# app(X1, X2) -> active# X2, active# s X -> s# active X) (active# app(X1, X2) -> active# X2, active# zWadr(X1, X2) -> active# X1) (active# app(X1, X2) -> active# X2, active# zWadr(X1, X2) -> active# X2) (active# app(X1, X2) -> active# X2, active# zWadr(X1, X2) -> zWadr#(X1, active X2)) (active# app(X1, X2) -> active# X2, active# zWadr(X1, X2) -> zWadr#(active X1, X2)) (active# app(X1, X2) -> active# X2, active# zWadr(cons(X, XS), cons(Y, YS)) -> app#(Y, cons(X, nil()))) (active# app(X1, X2) -> active# X2, active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(X, nil())) (active# app(X1, X2) -> active# X2, active# zWadr(cons(X, XS), cons(Y, YS)) -> cons#(app(Y, cons(X, nil())), zWadr(XS, YS))) (active# app(X1, X2) -> active# X2, active# zWadr(cons(X, XS), cons(Y, YS)) -> zWadr#(XS, YS)) (active# app(X1, X2) -> active# X2, active# prefix X -> active# X) (active# app(X1, X2) -> active# X2, active# prefix X -> prefix# active X) (active# app(X1, X2) -> active# X2, active# prefix L -> cons#(nil(), zWadr(L, prefix L))) (active# app(X1, X2) -> active# X2, active# prefix L -> zWadr#(L, prefix L)) (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# prefix L -> zWadr#(L, prefix L), zWadr#(X1, mark X2) -> zWadr#(X1, X2)) (active# app(X1, X2) -> app#(X1, active X2), app#(X1, mark X2) -> app#(X1, X2)) (active# app(X1, X2) -> app#(X1, active X2), app#(ok X1, ok X2) -> app#(X1, X2)) } STATUS: arrows: 0.867222 SCCS (9): Scc: {top# mark X -> top# proper X, top# ok X -> top# active X} Scc: { proper# app(X1, X2) -> proper# X1, proper# app(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# s X -> proper# X, proper# zWadr(X1, X2) -> proper# X1, proper# zWadr(X1, X2) -> proper# X2, proper# prefix X -> proper# X} Scc: { active# app(X1, X2) -> active# X1, active# app(X1, X2) -> active# X2, active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# zWadr(X1, X2) -> active# X1, active# zWadr(X1, X2) -> active# X2, active# prefix X -> active# X} Scc: {prefix# mark X -> prefix# X, prefix# ok X -> prefix# 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: { zWadr#(X1, mark X2) -> zWadr#(X1, X2), zWadr#(mark X1, X2) -> zWadr#(X1, X2), zWadr#(ok X1, ok X2) -> zWadr#(X1, X2)} Scc: { app#(X1, mark X2) -> app#(X1, X2), app#(mark X1, X2) -> app#(X1, X2), app#(ok X1, ok X2) -> app#(X1, X2)} SCC (2): Strict: {top# mark X -> top# proper X, top# ok X -> top# active X} Weak: { active app(X1, X2) -> app(X1, active X2), active app(X1, X2) -> app(active X1, X2), active app(nil(), YS) -> mark YS, active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)), 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 zWadr(XS, nil()) -> mark nil(), active zWadr(X1, X2) -> zWadr(X1, active X2), active zWadr(X1, X2) -> zWadr(active X1, X2), active zWadr(nil(), YS) -> mark nil(), active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)), active prefix X -> prefix active X, active prefix L -> mark cons(nil(), zWadr(L, prefix L)), app(X1, mark X2) -> mark app(X1, X2), app(mark X1, X2) -> mark app(X1, X2), app(ok X1, ok X2) -> ok app(X1, X2), 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, zWadr(X1, mark X2) -> mark zWadr(X1, X2), zWadr(mark X1, X2) -> mark zWadr(X1, X2), zWadr(ok X1, ok X2) -> ok zWadr(X1, X2), prefix mark X -> mark prefix X, prefix ok X -> ok prefix X, proper app(X1, X2) -> app(proper X1, proper X2), proper nil() -> ok nil(), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper zWadr(X1, X2) -> zWadr(proper X1, proper X2), proper prefix X -> prefix proper X, top mark X -> top proper X, top ok X -> top active X} Fail SCC (9): Strict: { proper# app(X1, X2) -> proper# X1, proper# app(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# s X -> proper# X, proper# zWadr(X1, X2) -> proper# X1, proper# zWadr(X1, X2) -> proper# X2, proper# prefix X -> proper# X} Weak: { active app(X1, X2) -> app(X1, active X2), active app(X1, X2) -> app(active X1, X2), active app(nil(), YS) -> mark YS, active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)), 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 zWadr(XS, nil()) -> mark nil(), active zWadr(X1, X2) -> zWadr(X1, active X2), active zWadr(X1, X2) -> zWadr(active X1, X2), active zWadr(nil(), YS) -> mark nil(), active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)), active prefix X -> prefix active X, active prefix L -> mark cons(nil(), zWadr(L, prefix L)), app(X1, mark X2) -> mark app(X1, X2), app(mark X1, X2) -> mark app(X1, X2), app(ok X1, ok X2) -> ok app(X1, X2), 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, zWadr(X1, mark X2) -> mark zWadr(X1, X2), zWadr(mark X1, X2) -> mark zWadr(X1, X2), zWadr(ok X1, ok X2) -> ok zWadr(X1, X2), prefix mark X -> mark prefix X, prefix ok X -> ok prefix X, proper app(X1, X2) -> app(proper X1, proper X2), proper nil() -> ok nil(), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper zWadr(X1, X2) -> zWadr(proper X1, proper X2), proper prefix X -> prefix proper X, 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: [app](x0, x1) = x0 + x1 + 1, [cons](x0, x1) = x0 + x1 + 1, [zWadr](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [active](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [prefix](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0, [top](x0) = 0, [nil] = 0, [proper#](x0) = x0 + 1 Strict: proper# prefix X -> proper# X 2 + 1X >= 1 + 1X proper# zWadr(X1, X2) -> proper# X2 2 + 1X1 + 1X2 >= 1 + 1X2 proper# zWadr(X1, X2) -> proper# X1 2 + 1X1 + 1X2 >= 1 + 1X1 proper# s X -> proper# X 2 + 1X >= 1 + 1X proper# from X -> proper# X 2 + 1X >= 1 + 1X proper# cons(X1, X2) -> proper# X2 2 + 1X1 + 1X2 >= 1 + 1X2 proper# cons(X1, X2) -> proper# X1 2 + 1X1 + 1X2 >= 1 + 1X1 proper# app(X1, X2) -> proper# X2 2 + 1X1 + 1X2 >= 1 + 1X2 proper# app(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 prefix X -> prefix proper X 0 + 0X >= 1 + 0X proper zWadr(X1, X2) -> zWadr(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 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 proper nil() -> ok nil() 0 >= 0 proper app(X1, X2) -> app(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 prefix ok X -> ok prefix X 1 + 1X >= 1 + 1X prefix mark X -> mark prefix X 1 + 1X >= 1 + 1X zWadr(ok X1, ok X2) -> ok zWadr(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 zWadr(mark X1, X2) -> mark zWadr(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 zWadr(X1, mark X2) -> mark zWadr(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 1 + 1X >= 1 + 1X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 1 + 1X >= 1 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 app(ok X1, ok X2) -> ok app(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 app(mark X1, X2) -> mark app(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 app(X1, mark X2) -> mark app(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active prefix L -> mark cons(nil(), zWadr(L, prefix L)) 2 + 1L >= 3 + 2L active prefix X -> prefix active X 2 + 1X >= 2 + 1X active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)) 4 + 1YS + 1X + 1XS + 1Y >= 4 + 1YS + 1X + 1XS + 1Y active zWadr(nil(), YS) -> mark nil() 2 + 1YS >= 0 active zWadr(X1, X2) -> zWadr(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active zWadr(X1, X2) -> zWadr(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active zWadr(XS, nil()) -> mark nil() 2 + 1XS >= 0 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 >= 3 + 2X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)) 3 + 1YS + 1X + 1XS >= 2 + 1YS + 1X + 1XS active app(nil(), YS) -> mark YS 2 + 1YS >= 0 + 1YS active app(X1, X2) -> app(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active app(X1, X2) -> app(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 Qed SCC (8): Strict: { active# app(X1, X2) -> active# X1, active# app(X1, X2) -> active# X2, active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# zWadr(X1, X2) -> active# X1, active# zWadr(X1, X2) -> active# X2, active# prefix X -> active# X} Weak: { active app(X1, X2) -> app(X1, active X2), active app(X1, X2) -> app(active X1, X2), active app(nil(), YS) -> mark YS, active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)), 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 zWadr(XS, nil()) -> mark nil(), active zWadr(X1, X2) -> zWadr(X1, active X2), active zWadr(X1, X2) -> zWadr(active X1, X2), active zWadr(nil(), YS) -> mark nil(), active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)), active prefix X -> prefix active X, active prefix L -> mark cons(nil(), zWadr(L, prefix L)), app(X1, mark X2) -> mark app(X1, X2), app(mark X1, X2) -> mark app(X1, X2), app(ok X1, ok X2) -> ok app(X1, X2), 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, zWadr(X1, mark X2) -> mark zWadr(X1, X2), zWadr(mark X1, X2) -> mark zWadr(X1, X2), zWadr(ok X1, ok X2) -> ok zWadr(X1, X2), prefix mark X -> mark prefix X, prefix ok X -> ok prefix X, proper app(X1, X2) -> app(proper X1, proper X2), proper nil() -> ok nil(), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper zWadr(X1, X2) -> zWadr(proper X1, proper X2), proper prefix X -> prefix proper X, 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: [app](x0, x1) = x0 + x1 + 1, [cons](x0, x1) = x0 + x1 + 1, [zWadr](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [active](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [prefix](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0, [top](x0) = 0, [nil] = 0, [active#](x0) = x0 + 1 Strict: active# prefix X -> active# X 2 + 1X >= 1 + 1X active# zWadr(X1, X2) -> active# X2 2 + 1X1 + 1X2 >= 1 + 1X2 active# zWadr(X1, X2) -> active# X1 2 + 1X1 + 1X2 >= 1 + 1X1 active# s X -> active# X 2 + 1X >= 1 + 1X active# from X -> active# X 2 + 1X >= 1 + 1X active# cons(X1, X2) -> active# X1 2 + 1X1 + 1X2 >= 1 + 1X1 active# app(X1, X2) -> active# X2 2 + 1X1 + 1X2 >= 1 + 1X2 active# app(X1, X2) -> active# 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 prefix X -> prefix proper X 0 + 0X >= 1 + 0X proper zWadr(X1, X2) -> zWadr(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 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 proper nil() -> ok nil() 0 >= 0 proper app(X1, X2) -> app(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 prefix ok X -> ok prefix X 1 + 1X >= 1 + 1X prefix mark X -> mark prefix X 1 + 1X >= 1 + 1X zWadr(ok X1, ok X2) -> ok zWadr(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 zWadr(mark X1, X2) -> mark zWadr(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 zWadr(X1, mark X2) -> mark zWadr(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 1 + 1X >= 1 + 1X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 1 + 1X >= 1 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 app(ok X1, ok X2) -> ok app(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 app(mark X1, X2) -> mark app(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 app(X1, mark X2) -> mark app(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active prefix L -> mark cons(nil(), zWadr(L, prefix L)) 2 + 1L >= 3 + 2L active prefix X -> prefix active X 2 + 1X >= 2 + 1X active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)) 4 + 1YS + 1X + 1XS + 1Y >= 4 + 1YS + 1X + 1XS + 1Y active zWadr(nil(), YS) -> mark nil() 2 + 1YS >= 0 active zWadr(X1, X2) -> zWadr(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active zWadr(X1, X2) -> zWadr(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active zWadr(XS, nil()) -> mark nil() 2 + 1XS >= 0 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 >= 3 + 2X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)) 3 + 1YS + 1X + 1XS >= 2 + 1YS + 1X + 1XS active app(nil(), YS) -> mark YS 2 + 1YS >= 0 + 1YS active app(X1, X2) -> app(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active app(X1, X2) -> app(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 Qed SCC (2): Strict: {prefix# mark X -> prefix# X, prefix# ok X -> prefix# X} Weak: { active app(X1, X2) -> app(X1, active X2), active app(X1, X2) -> app(active X1, X2), active app(nil(), YS) -> mark YS, active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)), 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 zWadr(XS, nil()) -> mark nil(), active zWadr(X1, X2) -> zWadr(X1, active X2), active zWadr(X1, X2) -> zWadr(active X1, X2), active zWadr(nil(), YS) -> mark nil(), active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)), active prefix X -> prefix active X, active prefix L -> mark cons(nil(), zWadr(L, prefix L)), app(X1, mark X2) -> mark app(X1, X2), app(mark X1, X2) -> mark app(X1, X2), app(ok X1, ok X2) -> ok app(X1, X2), 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, zWadr(X1, mark X2) -> mark zWadr(X1, X2), zWadr(mark X1, X2) -> mark zWadr(X1, X2), zWadr(ok X1, ok X2) -> ok zWadr(X1, X2), prefix mark X -> mark prefix X, prefix ok X -> ok prefix X, proper app(X1, X2) -> app(proper X1, proper X2), proper nil() -> ok nil(), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper zWadr(X1, X2) -> zWadr(proper X1, proper X2), proper prefix X -> prefix proper X, 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: [app](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [zWadr](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [from](x0) = 0, [s](x0) = x0 + 1, [prefix](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [prefix#](x0) = x0 + 1 Strict: prefix# ok X -> prefix# X 2 + 1X >= 1 + 1X prefix# mark X -> prefix# X 2 + 1X >= 1 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper prefix X -> prefix proper X 0 + 0X >= 1 + 0X proper zWadr(X1, X2) -> zWadr(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 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 proper nil() -> ok nil() 0 >= 2 proper app(X1, X2) -> app(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 prefix ok X -> ok prefix X 2 + 1X >= 2 + 1X prefix mark X -> mark prefix X 2 + 1X >= 2 + 1X zWadr(ok X1, ok X2) -> ok zWadr(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 zWadr(mark X1, X2) -> mark zWadr(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 zWadr(X1, mark X2) -> mark zWadr(X1, X2) 1 + 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 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(ok X1, ok X2) -> ok app(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(mark X1, X2) -> mark app(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(X1, mark X2) -> mark app(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active prefix L -> mark cons(nil(), zWadr(L, prefix L)) 2 + 1L >= 3 + 1L active prefix X -> prefix active X 2 + 1X >= 2 + 1X active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)) 3 + 0YS + 0X + 1XS + 0Y >= 3 + 0YS + 0X + 1XS + 0Y active zWadr(nil(), YS) -> mark nil() 3 + 0YS >= 2 active zWadr(X1, X2) -> zWadr(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active zWadr(X1, X2) -> zWadr(X1, active X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active zWadr(XS, nil()) -> mark nil() 2 + 1XS >= 2 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 + 0X active cons(X1, X2) -> cons(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)) 2 + 1YS + 0X + 0XS >= 3 + 1YS + 0X + 0XS active app(nil(), YS) -> mark YS 2 + 1YS >= 1 + 1YS active app(X1, X2) -> app(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(X1, X2) -> app(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 Qed SCC (2): Strict: {s# mark X -> s# X, s# ok X -> s# X} Weak: { active app(X1, X2) -> app(X1, active X2), active app(X1, X2) -> app(active X1, X2), active app(nil(), YS) -> mark YS, active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)), 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 zWadr(XS, nil()) -> mark nil(), active zWadr(X1, X2) -> zWadr(X1, active X2), active zWadr(X1, X2) -> zWadr(active X1, X2), active zWadr(nil(), YS) -> mark nil(), active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)), active prefix X -> prefix active X, active prefix L -> mark cons(nil(), zWadr(L, prefix L)), app(X1, mark X2) -> mark app(X1, X2), app(mark X1, X2) -> mark app(X1, X2), app(ok X1, ok X2) -> ok app(X1, X2), 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, zWadr(X1, mark X2) -> mark zWadr(X1, X2), zWadr(mark X1, X2) -> mark zWadr(X1, X2), zWadr(ok X1, ok X2) -> ok zWadr(X1, X2), prefix mark X -> mark prefix X, prefix ok X -> ok prefix X, proper app(X1, X2) -> app(proper X1, proper X2), proper nil() -> ok nil(), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper zWadr(X1, X2) -> zWadr(proper X1, proper X2), proper prefix X -> prefix proper X, 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: [app](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [zWadr](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [from](x0) = 0, [s](x0) = x0 + 1, [prefix](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [s#](x0) = x0 + 1 Strict: s# ok X -> s# X 2 + 1X >= 1 + 1X s# mark X -> s# X 2 + 1X >= 1 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper prefix X -> prefix proper X 0 + 0X >= 1 + 0X proper zWadr(X1, X2) -> zWadr(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 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 proper nil() -> ok nil() 0 >= 2 proper app(X1, X2) -> app(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 prefix ok X -> ok prefix X 2 + 1X >= 2 + 1X prefix mark X -> mark prefix X 2 + 1X >= 2 + 1X zWadr(ok X1, ok X2) -> ok zWadr(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 zWadr(mark X1, X2) -> mark zWadr(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 zWadr(X1, mark X2) -> mark zWadr(X1, X2) 1 + 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 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(ok X1, ok X2) -> ok app(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(mark X1, X2) -> mark app(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(X1, mark X2) -> mark app(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active prefix L -> mark cons(nil(), zWadr(L, prefix L)) 2 + 1L >= 3 + 1L active prefix X -> prefix active X 2 + 1X >= 2 + 1X active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)) 3 + 0YS + 0X + 1XS + 0Y >= 3 + 0YS + 0X + 1XS + 0Y active zWadr(nil(), YS) -> mark nil() 3 + 0YS >= 2 active zWadr(X1, X2) -> zWadr(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active zWadr(X1, X2) -> zWadr(X1, active X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active zWadr(XS, nil()) -> mark nil() 2 + 1XS >= 2 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 + 0X active cons(X1, X2) -> cons(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)) 2 + 1YS + 0X + 0XS >= 3 + 1YS + 0X + 0XS active app(nil(), YS) -> mark YS 2 + 1YS >= 1 + 1YS active app(X1, X2) -> app(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(X1, X2) -> app(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 Qed SCC (2): Strict: {from# mark X -> from# X, from# ok X -> from# X} Weak: { active app(X1, X2) -> app(X1, active X2), active app(X1, X2) -> app(active X1, X2), active app(nil(), YS) -> mark YS, active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)), 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 zWadr(XS, nil()) -> mark nil(), active zWadr(X1, X2) -> zWadr(X1, active X2), active zWadr(X1, X2) -> zWadr(active X1, X2), active zWadr(nil(), YS) -> mark nil(), active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)), active prefix X -> prefix active X, active prefix L -> mark cons(nil(), zWadr(L, prefix L)), app(X1, mark X2) -> mark app(X1, X2), app(mark X1, X2) -> mark app(X1, X2), app(ok X1, ok X2) -> ok app(X1, X2), 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, zWadr(X1, mark X2) -> mark zWadr(X1, X2), zWadr(mark X1, X2) -> mark zWadr(X1, X2), zWadr(ok X1, ok X2) -> ok zWadr(X1, X2), prefix mark X -> mark prefix X, prefix ok X -> ok prefix X, proper app(X1, X2) -> app(proper X1, proper X2), proper nil() -> ok nil(), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper zWadr(X1, X2) -> zWadr(proper X1, proper X2), proper prefix X -> prefix proper X, 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: [app](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [zWadr](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [from](x0) = 0, [s](x0) = x0 + 1, [prefix](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [from#](x0) = x0 + 1 Strict: from# ok X -> from# X 2 + 1X >= 1 + 1X from# mark X -> from# X 2 + 1X >= 1 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper prefix X -> prefix proper X 0 + 0X >= 1 + 0X proper zWadr(X1, X2) -> zWadr(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 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 proper nil() -> ok nil() 0 >= 2 proper app(X1, X2) -> app(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 prefix ok X -> ok prefix X 2 + 1X >= 2 + 1X prefix mark X -> mark prefix X 2 + 1X >= 2 + 1X zWadr(ok X1, ok X2) -> ok zWadr(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 zWadr(mark X1, X2) -> mark zWadr(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 zWadr(X1, mark X2) -> mark zWadr(X1, X2) 1 + 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 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(ok X1, ok X2) -> ok app(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(mark X1, X2) -> mark app(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(X1, mark X2) -> mark app(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active prefix L -> mark cons(nil(), zWadr(L, prefix L)) 2 + 1L >= 3 + 1L active prefix X -> prefix active X 2 + 1X >= 2 + 1X active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)) 3 + 0YS + 0X + 1XS + 0Y >= 3 + 0YS + 0X + 1XS + 0Y active zWadr(nil(), YS) -> mark nil() 3 + 0YS >= 2 active zWadr(X1, X2) -> zWadr(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active zWadr(X1, X2) -> zWadr(X1, active X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active zWadr(XS, nil()) -> mark nil() 2 + 1XS >= 2 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 + 0X active cons(X1, X2) -> cons(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)) 2 + 1YS + 0X + 0XS >= 3 + 1YS + 0X + 0XS active app(nil(), YS) -> mark YS 2 + 1YS >= 1 + 1YS active app(X1, X2) -> app(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(X1, X2) -> app(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 Qed SCC (2): Strict: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)} Weak: { active app(X1, X2) -> app(X1, active X2), active app(X1, X2) -> app(active X1, X2), active app(nil(), YS) -> mark YS, active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)), 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 zWadr(XS, nil()) -> mark nil(), active zWadr(X1, X2) -> zWadr(X1, active X2), active zWadr(X1, X2) -> zWadr(active X1, X2), active zWadr(nil(), YS) -> mark nil(), active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)), active prefix X -> prefix active X, active prefix L -> mark cons(nil(), zWadr(L, prefix L)), app(X1, mark X2) -> mark app(X1, X2), app(mark X1, X2) -> mark app(X1, X2), app(ok X1, ok X2) -> ok app(X1, X2), 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, zWadr(X1, mark X2) -> mark zWadr(X1, X2), zWadr(mark X1, X2) -> mark zWadr(X1, X2), zWadr(ok X1, ok X2) -> ok zWadr(X1, X2), prefix mark X -> mark prefix X, prefix ok X -> ok prefix X, proper app(X1, X2) -> app(proper X1, proper X2), proper nil() -> ok nil(), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper zWadr(X1, X2) -> zWadr(proper X1, proper X2), proper prefix X -> prefix proper X, 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: [app](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [zWadr](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [from](x0) = 0, [s](x0) = x0 + 1, [prefix](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [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 prefix X -> prefix proper X 0 + 0X >= 1 + 0X proper zWadr(X1, X2) -> zWadr(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 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 proper nil() -> ok nil() 0 >= 2 proper app(X1, X2) -> app(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 prefix ok X -> ok prefix X 2 + 1X >= 2 + 1X prefix mark X -> mark prefix X 2 + 1X >= 2 + 1X zWadr(ok X1, ok X2) -> ok zWadr(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 zWadr(mark X1, X2) -> mark zWadr(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 zWadr(X1, mark X2) -> mark zWadr(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 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 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(ok X1, ok X2) -> ok app(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(mark X1, X2) -> mark app(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(X1, mark X2) -> mark app(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active prefix L -> mark cons(nil(), zWadr(L, prefix L)) 2 + 1L >= 3 + 0L active prefix X -> prefix active X 2 + 1X >= 2 + 1X active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)) 2 + 0YS + 0X + 0XS + 0Y >= 3 + 0YS + 0X + 0XS + 0Y active zWadr(nil(), YS) -> mark nil() 2 + 0YS >= 2 active zWadr(X1, X2) -> zWadr(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWadr(X1, X2) -> zWadr(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWadr(XS, nil()) -> mark nil() 2 + 0XS >= 2 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 + 0X active cons(X1, X2) -> cons(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)) 2 + 1YS + 0X + 0XS >= 3 + 1YS + 0X + 0XS active app(nil(), YS) -> mark YS 2 + 1YS >= 1 + 1YS active app(X1, X2) -> app(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(X1, X2) -> app(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 SCCS (1): Scc: {cons#(mark X1, X2) -> cons#(X1, X2)} SCC (1): Strict: {cons#(mark X1, X2) -> cons#(X1, X2)} Weak: { active app(X1, X2) -> app(X1, active X2), active app(X1, X2) -> app(active X1, X2), active app(nil(), YS) -> mark YS, active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)), 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 zWadr(XS, nil()) -> mark nil(), active zWadr(X1, X2) -> zWadr(X1, active X2), active zWadr(X1, X2) -> zWadr(active X1, X2), active zWadr(nil(), YS) -> mark nil(), active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)), active prefix X -> prefix active X, active prefix L -> mark cons(nil(), zWadr(L, prefix L)), app(X1, mark X2) -> mark app(X1, X2), app(mark X1, X2) -> mark app(X1, X2), app(ok X1, ok X2) -> ok app(X1, X2), 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, zWadr(X1, mark X2) -> mark zWadr(X1, X2), zWadr(mark X1, X2) -> mark zWadr(X1, X2), zWadr(ok X1, ok X2) -> ok zWadr(X1, X2), prefix mark X -> mark prefix X, prefix ok X -> ok prefix X, proper app(X1, X2) -> app(proper X1, proper X2), proper nil() -> ok nil(), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper zWadr(X1, X2) -> zWadr(proper X1, proper X2), proper prefix X -> prefix proper X, 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: [app](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [zWadr](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [from](x0) = 0, [s](x0) = x0 + 1, [prefix](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = 0, [top](x0) = x0 + 1, [nil] = 1, [cons#](x0, x1) = x0 + 1 Strict: cons#(mark X1, X2) -> cons#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 Weak: top ok X -> top active X 1 + 0X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper prefix X -> prefix proper X 2 + 1X >= 2 + 1X proper zWadr(X1, X2) -> zWadr(proper X1, proper X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s X -> s proper X 2 + 1X >= 2 + 1X proper from X -> from proper X 1 + 0X >= 0 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 proper nil() -> ok nil() 2 >= 0 proper app(X1, X2) -> app(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 prefix ok X -> ok prefix X 1 + 0X >= 0 + 0X prefix mark X -> mark prefix X 2 + 1X >= 2 + 1X zWadr(ok X1, ok X2) -> ok zWadr(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 zWadr(mark X1, X2) -> mark zWadr(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 zWadr(X1, mark X2) -> mark zWadr(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 s ok X -> ok s X 1 + 0X >= 0 + 0X s mark X -> mark s X 2 + 1X >= 2 + 1X from ok X -> ok from X 0 + 0X >= 0 + 0X from mark X -> mark from X 0 + 0X >= 1 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(ok X1, ok X2) -> ok app(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 app(mark X1, X2) -> mark app(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(X1, mark X2) -> mark app(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active prefix L -> mark cons(nil(), zWadr(L, prefix L)) 2 + 1L >= 3 + 0L active prefix X -> prefix active X 2 + 1X >= 2 + 1X active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)) 2 + 0YS + 0X + 0XS + 0Y >= 3 + 0YS + 0X + 0XS + 0Y active zWadr(nil(), YS) -> mark nil() 2 + 0YS >= 2 active zWadr(X1, X2) -> zWadr(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWadr(X1, X2) -> zWadr(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWadr(XS, nil()) -> mark nil() 2 + 0XS >= 2 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 + 0X active cons(X1, X2) -> cons(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)) 2 + 1YS + 0X + 0XS >= 3 + 1YS + 0X + 0XS active app(nil(), YS) -> mark YS 2 + 1YS >= 1 + 1YS active app(X1, X2) -> app(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(X1, X2) -> app(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 Qed SCC (3): Strict: { zWadr#(X1, mark X2) -> zWadr#(X1, X2), zWadr#(mark X1, X2) -> zWadr#(X1, X2), zWadr#(ok X1, ok X2) -> zWadr#(X1, X2)} Weak: { active app(X1, X2) -> app(X1, active X2), active app(X1, X2) -> app(active X1, X2), active app(nil(), YS) -> mark YS, active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)), 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 zWadr(XS, nil()) -> mark nil(), active zWadr(X1, X2) -> zWadr(X1, active X2), active zWadr(X1, X2) -> zWadr(active X1, X2), active zWadr(nil(), YS) -> mark nil(), active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)), active prefix X -> prefix active X, active prefix L -> mark cons(nil(), zWadr(L, prefix L)), app(X1, mark X2) -> mark app(X1, X2), app(mark X1, X2) -> mark app(X1, X2), app(ok X1, ok X2) -> ok app(X1, X2), 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, zWadr(X1, mark X2) -> mark zWadr(X1, X2), zWadr(mark X1, X2) -> mark zWadr(X1, X2), zWadr(ok X1, ok X2) -> ok zWadr(X1, X2), prefix mark X -> mark prefix X, prefix ok X -> ok prefix X, proper app(X1, X2) -> app(proper X1, proper X2), proper nil() -> ok nil(), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper zWadr(X1, X2) -> zWadr(proper X1, proper X2), proper prefix X -> prefix proper X, 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: [app](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [zWadr](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [from](x0) = 0, [s](x0) = x0 + 1, [prefix](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [zWadr#](x0, x1) = x0 + 1 Strict: zWadr#(ok X1, ok X2) -> zWadr#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 zWadr#(mark X1, X2) -> zWadr#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 zWadr#(X1, mark X2) -> zWadr#(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 prefix X -> prefix proper X 0 + 0X >= 1 + 0X proper zWadr(X1, X2) -> zWadr(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 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 proper nil() -> ok nil() 0 >= 2 proper app(X1, X2) -> app(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 prefix ok X -> ok prefix X 2 + 1X >= 2 + 1X prefix mark X -> mark prefix X 2 + 1X >= 2 + 1X zWadr(ok X1, ok X2) -> ok zWadr(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 zWadr(mark X1, X2) -> mark zWadr(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 zWadr(X1, mark X2) -> mark zWadr(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 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 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(ok X1, ok X2) -> ok app(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(mark X1, X2) -> mark app(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(X1, mark X2) -> mark app(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active prefix L -> mark cons(nil(), zWadr(L, prefix L)) 2 + 1L >= 3 + 0L active prefix X -> prefix active X 2 + 1X >= 2 + 1X active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)) 2 + 0YS + 0X + 0XS + 0Y >= 3 + 0YS + 0X + 0XS + 0Y active zWadr(nil(), YS) -> mark nil() 2 + 0YS >= 2 active zWadr(X1, X2) -> zWadr(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWadr(X1, X2) -> zWadr(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWadr(XS, nil()) -> mark nil() 2 + 0XS >= 2 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 + 0X active cons(X1, X2) -> cons(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)) 2 + 1YS + 0X + 0XS >= 3 + 1YS + 0X + 0XS active app(nil(), YS) -> mark YS 2 + 1YS >= 1 + 1YS active app(X1, X2) -> app(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(X1, X2) -> app(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 SCCS (1): Scc: {zWadr#(X1, mark X2) -> zWadr#(X1, X2)} SCC (1): Strict: {zWadr#(X1, mark X2) -> zWadr#(X1, X2)} Weak: { active app(X1, X2) -> app(X1, active X2), active app(X1, X2) -> app(active X1, X2), active app(nil(), YS) -> mark YS, active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)), 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 zWadr(XS, nil()) -> mark nil(), active zWadr(X1, X2) -> zWadr(X1, active X2), active zWadr(X1, X2) -> zWadr(active X1, X2), active zWadr(nil(), YS) -> mark nil(), active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)), active prefix X -> prefix active X, active prefix L -> mark cons(nil(), zWadr(L, prefix L)), app(X1, mark X2) -> mark app(X1, X2), app(mark X1, X2) -> mark app(X1, X2), app(ok X1, ok X2) -> ok app(X1, X2), 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, zWadr(X1, mark X2) -> mark zWadr(X1, X2), zWadr(mark X1, X2) -> mark zWadr(X1, X2), zWadr(ok X1, ok X2) -> ok zWadr(X1, X2), prefix mark X -> mark prefix X, prefix ok X -> ok prefix X, proper app(X1, X2) -> app(proper X1, proper X2), proper nil() -> ok nil(), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper zWadr(X1, X2) -> zWadr(proper X1, proper X2), proper prefix X -> prefix proper X, 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: [app](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [zWadr](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [from](x0) = 0, [s](x0) = x0 + 1, [prefix](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = 0, [top](x0) = x0 + 1, [nil] = 1, [zWadr#](x0, x1) = x0 + 1 Strict: zWadr#(X1, mark X2) -> zWadr#(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 Weak: top ok X -> top active X 1 + 0X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper prefix X -> prefix proper X 2 + 1X >= 2 + 1X proper zWadr(X1, X2) -> zWadr(proper X1, proper X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s X -> s proper X 2 + 1X >= 2 + 1X proper from X -> from proper X 1 + 0X >= 0 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 proper nil() -> ok nil() 2 >= 0 proper app(X1, X2) -> app(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 prefix ok X -> ok prefix X 1 + 0X >= 0 + 0X prefix mark X -> mark prefix X 2 + 1X >= 2 + 1X zWadr(ok X1, ok X2) -> ok zWadr(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 zWadr(mark X1, X2) -> mark zWadr(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 zWadr(X1, mark X2) -> mark zWadr(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 s ok X -> ok s X 1 + 0X >= 0 + 0X s mark X -> mark s X 2 + 1X >= 2 + 1X from ok X -> ok from X 0 + 0X >= 0 + 0X from mark X -> mark from X 0 + 0X >= 1 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(ok X1, ok X2) -> ok app(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 app(mark X1, X2) -> mark app(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(X1, mark X2) -> mark app(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active prefix L -> mark cons(nil(), zWadr(L, prefix L)) 2 + 1L >= 3 + 0L active prefix X -> prefix active X 2 + 1X >= 2 + 1X active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)) 2 + 0YS + 0X + 0XS + 0Y >= 3 + 0YS + 0X + 0XS + 0Y active zWadr(nil(), YS) -> mark nil() 2 + 0YS >= 2 active zWadr(X1, X2) -> zWadr(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWadr(X1, X2) -> zWadr(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWadr(XS, nil()) -> mark nil() 2 + 0XS >= 2 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 + 0X active cons(X1, X2) -> cons(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)) 2 + 1YS + 0X + 0XS >= 3 + 1YS + 0X + 0XS active app(nil(), YS) -> mark YS 2 + 1YS >= 1 + 1YS active app(X1, X2) -> app(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(X1, X2) -> app(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 Qed SCC (3): Strict: { app#(X1, mark X2) -> app#(X1, X2), app#(mark X1, X2) -> app#(X1, X2), app#(ok X1, ok X2) -> app#(X1, X2)} Weak: { active app(X1, X2) -> app(X1, active X2), active app(X1, X2) -> app(active X1, X2), active app(nil(), YS) -> mark YS, active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)), 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 zWadr(XS, nil()) -> mark nil(), active zWadr(X1, X2) -> zWadr(X1, active X2), active zWadr(X1, X2) -> zWadr(active X1, X2), active zWadr(nil(), YS) -> mark nil(), active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)), active prefix X -> prefix active X, active prefix L -> mark cons(nil(), zWadr(L, prefix L)), app(X1, mark X2) -> mark app(X1, X2), app(mark X1, X2) -> mark app(X1, X2), app(ok X1, ok X2) -> ok app(X1, X2), 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, zWadr(X1, mark X2) -> mark zWadr(X1, X2), zWadr(mark X1, X2) -> mark zWadr(X1, X2), zWadr(ok X1, ok X2) -> ok zWadr(X1, X2), prefix mark X -> mark prefix X, prefix ok X -> ok prefix X, proper app(X1, X2) -> app(proper X1, proper X2), proper nil() -> ok nil(), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper zWadr(X1, X2) -> zWadr(proper X1, proper X2), proper prefix X -> prefix proper X, 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: [app](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [zWadr](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [from](x0) = 0, [s](x0) = x0 + 1, [prefix](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [nil] = 1, [app#](x0, x1) = x0 + 1 Strict: app#(ok X1, ok X2) -> app#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 app#(mark X1, X2) -> app#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 app#(X1, mark X2) -> app#(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 prefix X -> prefix proper X 0 + 0X >= 1 + 0X proper zWadr(X1, X2) -> zWadr(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 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 proper nil() -> ok nil() 0 >= 2 proper app(X1, X2) -> app(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 prefix ok X -> ok prefix X 2 + 1X >= 2 + 1X prefix mark X -> mark prefix X 2 + 1X >= 2 + 1X zWadr(ok X1, ok X2) -> ok zWadr(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 zWadr(mark X1, X2) -> mark zWadr(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 zWadr(X1, mark X2) -> mark zWadr(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 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 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(ok X1, ok X2) -> ok app(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(mark X1, X2) -> mark app(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(X1, mark X2) -> mark app(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active prefix L -> mark cons(nil(), zWadr(L, prefix L)) 2 + 1L >= 3 + 0L active prefix X -> prefix active X 2 + 1X >= 2 + 1X active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)) 2 + 0YS + 0X + 0XS + 0Y >= 3 + 0YS + 0X + 0XS + 0Y active zWadr(nil(), YS) -> mark nil() 2 + 0YS >= 2 active zWadr(X1, X2) -> zWadr(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWadr(X1, X2) -> zWadr(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWadr(XS, nil()) -> mark nil() 2 + 0XS >= 2 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 + 0X active cons(X1, X2) -> cons(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)) 2 + 1YS + 0X + 0XS >= 3 + 1YS + 0X + 0XS active app(nil(), YS) -> mark YS 2 + 1YS >= 1 + 1YS active app(X1, X2) -> app(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(X1, X2) -> app(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 SCCS (1): Scc: {app#(X1, mark X2) -> app#(X1, X2)} SCC (1): Strict: {app#(X1, mark X2) -> app#(X1, X2)} Weak: { active app(X1, X2) -> app(X1, active X2), active app(X1, X2) -> app(active X1, X2), active app(nil(), YS) -> mark YS, active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)), 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 zWadr(XS, nil()) -> mark nil(), active zWadr(X1, X2) -> zWadr(X1, active X2), active zWadr(X1, X2) -> zWadr(active X1, X2), active zWadr(nil(), YS) -> mark nil(), active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)), active prefix X -> prefix active X, active prefix L -> mark cons(nil(), zWadr(L, prefix L)), app(X1, mark X2) -> mark app(X1, X2), app(mark X1, X2) -> mark app(X1, X2), app(ok X1, ok X2) -> ok app(X1, X2), 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, zWadr(X1, mark X2) -> mark zWadr(X1, X2), zWadr(mark X1, X2) -> mark zWadr(X1, X2), zWadr(ok X1, ok X2) -> ok zWadr(X1, X2), prefix mark X -> mark prefix X, prefix ok X -> ok prefix X, proper app(X1, X2) -> app(proper X1, proper X2), proper nil() -> ok nil(), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper zWadr(X1, X2) -> zWadr(proper X1, proper X2), proper prefix X -> prefix proper X, 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: [app](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [zWadr](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [from](x0) = 0, [s](x0) = x0 + 1, [prefix](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = 0, [top](x0) = x0 + 1, [nil] = 1, [app#](x0, x1) = x0 + 1 Strict: app#(X1, mark X2) -> app#(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 Weak: top ok X -> top active X 1 + 0X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper prefix X -> prefix proper X 2 + 1X >= 2 + 1X proper zWadr(X1, X2) -> zWadr(proper X1, proper X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s X -> s proper X 2 + 1X >= 2 + 1X proper from X -> from proper X 1 + 0X >= 0 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 proper nil() -> ok nil() 2 >= 0 proper app(X1, X2) -> app(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 prefix ok X -> ok prefix X 1 + 0X >= 0 + 0X prefix mark X -> mark prefix X 2 + 1X >= 2 + 1X zWadr(ok X1, ok X2) -> ok zWadr(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 zWadr(mark X1, X2) -> mark zWadr(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 zWadr(X1, mark X2) -> mark zWadr(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 s ok X -> ok s X 1 + 0X >= 0 + 0X s mark X -> mark s X 2 + 1X >= 2 + 1X from ok X -> ok from X 0 + 0X >= 0 + 0X from mark X -> mark from X 0 + 0X >= 1 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(ok X1, ok X2) -> ok app(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 app(mark X1, X2) -> mark app(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 app(X1, mark X2) -> mark app(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active prefix L -> mark cons(nil(), zWadr(L, prefix L)) 2 + 1L >= 3 + 0L active prefix X -> prefix active X 2 + 1X >= 2 + 1X active zWadr(cons(X, XS), cons(Y, YS)) -> mark cons(app(Y, cons(X, nil())), zWadr(XS, YS)) 2 + 0YS + 0X + 0XS + 0Y >= 3 + 0YS + 0X + 0XS + 0Y active zWadr(nil(), YS) -> mark nil() 2 + 0YS >= 2 active zWadr(X1, X2) -> zWadr(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWadr(X1, X2) -> zWadr(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWadr(XS, nil()) -> mark nil() 2 + 0XS >= 2 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 + 0X active cons(X1, X2) -> cons(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(cons(X, XS), YS) -> mark cons(X, app(XS, YS)) 2 + 1YS + 0X + 0XS >= 3 + 1YS + 0X + 0XS active app(nil(), YS) -> mark YS 2 + 1YS >= 1 + 1YS active app(X1, X2) -> app(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active app(X1, X2) -> app(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 Qed