MAYBE Time: 2.036003 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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# 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), active# minus(X1, X2) -> active# X1, active# minus(X1, X2) -> active# X2, active# minus(X1, X2) -> minus#(X1, active X2), active# minus(X1, X2) -> minus#(active X1, X2), active# minus(s X, s Y) -> minus#(X, Y), active# quot(X1, X2) -> active# X1, active# quot(X1, X2) -> active# X2, active# quot(X1, X2) -> quot#(X1, active X2), active# quot(X1, X2) -> quot#(active X1, X2), active# quot(s X, s Y) -> s# quot(minus(X, Y), s Y), active# quot(s X, s Y) -> minus#(X, Y), active# quot(s X, s Y) -> quot#(minus(X, Y), s Y), active# zWquot(X1, X2) -> active# X1, active# zWquot(X1, X2) -> active# X2, active# zWquot(X1, X2) -> zWquot#(X1, active X2), active# zWquot(X1, X2) -> zWquot#(active X1, X2), active# zWquot(cons(X, XS), cons(Y, YS)) -> cons#(quot(X, Y), zWquot(XS, YS)), active# zWquot(cons(X, XS), cons(Y, YS)) -> quot#(X, Y), active# zWquot(cons(X, XS), cons(Y, YS)) -> zWquot#(XS, YS), sel#(X1, mark X2) -> sel#(X1, X2), sel#(mark X1, X2) -> sel#(X1, X2), sel#(ok X1, ok X2) -> sel#(X1, X2), minus#(X1, mark X2) -> minus#(X1, X2), minus#(mark X1, X2) -> minus#(X1, X2), minus#(ok X1, ok X2) -> minus#(X1, X2), quot#(X1, mark X2) -> quot#(X1, X2), quot#(mark X1, X2) -> quot#(X1, X2), quot#(ok X1, ok X2) -> quot#(X1, X2), zWquot#(X1, mark X2) -> zWquot#(X1, X2), zWquot#(mark X1, X2) -> zWquot#(X1, X2), zWquot#(ok X1, ok X2) -> zWquot#(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# sel(X1, X2) -> sel#(proper X1, proper X2), proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# minus(X1, X2) -> minus#(proper X1, proper X2), proper# minus(X1, X2) -> proper# X1, proper# minus(X1, X2) -> proper# X2, proper# quot(X1, X2) -> quot#(proper X1, proper X2), proper# quot(X1, X2) -> proper# X1, proper# quot(X1, X2) -> proper# X2, proper# zWquot(X1, X2) -> zWquot#(proper X1, proper X2), proper# zWquot(X1, X2) -> proper# X1, proper# zWquot(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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(proper X1, proper X2)} EDG: { (active# from X -> from# s X, from# ok X -> from# X) (active# from X -> from# s X, from# mark X -> from# X) (active# s X -> s# active X, s# ok X -> s# X) (active# s X -> s# active X, s# mark X -> s# X) (proper# s X -> s# proper X, s# ok X -> s# X) (proper# s X -> s# proper X, s# mark X -> s# X) (top# ok X -> top# active X, top# ok X -> top# active X) (top# ok X -> top# active X, top# ok X -> active# X) (top# ok X -> top# active X, top# mark X -> top# proper X) (top# ok X -> top# active X, top# mark X -> proper# X) (active# zWquot(cons(X, XS), cons(Y, YS)) -> cons#(quot(X, Y), zWquot(XS, YS)), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# zWquot(cons(X, XS), cons(Y, YS)) -> cons#(quot(X, Y), zWquot(XS, YS)), cons#(mark X1, X2) -> cons#(X1, X2)) (active# minus(X1, X2) -> active# X2, active# zWquot(cons(X, XS), cons(Y, YS)) -> zWquot#(XS, YS)) (active# minus(X1, X2) -> active# X2, active# zWquot(cons(X, XS), cons(Y, YS)) -> quot#(X, Y)) (active# minus(X1, X2) -> active# X2, active# zWquot(cons(X, XS), cons(Y, YS)) -> cons#(quot(X, Y), zWquot(XS, YS))) (active# minus(X1, X2) -> active# X2, active# zWquot(X1, X2) -> zWquot#(active X1, X2)) (active# minus(X1, X2) -> active# X2, active# zWquot(X1, X2) -> zWquot#(X1, active X2)) (active# minus(X1, X2) -> active# X2, active# zWquot(X1, X2) -> active# X2) (active# minus(X1, X2) -> active# X2, active# zWquot(X1, X2) -> active# X1) (active# minus(X1, X2) -> active# X2, active# quot(s X, s Y) -> quot#(minus(X, Y), s Y)) (active# minus(X1, X2) -> active# X2, active# quot(s X, s Y) -> minus#(X, Y)) (active# minus(X1, X2) -> active# X2, active# quot(s X, s Y) -> s# quot(minus(X, Y), s Y)) (active# minus(X1, X2) -> active# X2, active# quot(X1, X2) -> quot#(active X1, X2)) (active# minus(X1, X2) -> active# X2, active# quot(X1, X2) -> quot#(X1, active X2)) (active# minus(X1, X2) -> active# X2, active# quot(X1, X2) -> active# X2) (active# minus(X1, X2) -> active# X2, active# quot(X1, X2) -> active# X1) (active# minus(X1, X2) -> active# X2, active# minus(s X, s Y) -> minus#(X, Y)) (active# minus(X1, X2) -> active# X2, active# minus(X1, X2) -> minus#(active X1, X2)) (active# minus(X1, X2) -> active# X2, active# minus(X1, X2) -> minus#(X1, active X2)) (active# minus(X1, X2) -> active# X2, active# minus(X1, X2) -> active# X2) (active# minus(X1, X2) -> active# X2, active# minus(X1, X2) -> active# X1) (active# minus(X1, X2) -> active# X2, active# sel(s N, cons(X, XS)) -> sel#(N, XS)) (active# minus(X1, X2) -> active# X2, active# sel(X1, X2) -> sel#(active X1, X2)) (active# minus(X1, X2) -> active# X2, active# sel(X1, X2) -> sel#(X1, active X2)) (active# minus(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X2) (active# minus(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X1) (active# minus(X1, X2) -> active# X2, active# s X -> active# X) (active# minus(X1, X2) -> active# X2, active# s X -> s# active X) (active# minus(X1, X2) -> active# X2, active# from X -> active# X) (active# minus(X1, X2) -> active# X2, active# from X -> s# X) (active# minus(X1, X2) -> active# X2, active# from X -> from# active X) (active# minus(X1, X2) -> active# X2, active# from X -> from# s X) (active# minus(X1, X2) -> active# X2, active# from X -> cons#(X, from s X)) (active# minus(X1, X2) -> active# X2, active# cons(X1, X2) -> active# X1) (active# minus(X1, X2) -> active# X2, active# cons(X1, X2) -> cons#(active X1, X2)) (active# zWquot(X1, X2) -> active# X2, active# zWquot(cons(X, XS), cons(Y, YS)) -> zWquot#(XS, YS)) (active# zWquot(X1, X2) -> active# X2, active# zWquot(cons(X, XS), cons(Y, YS)) -> quot#(X, Y)) (active# zWquot(X1, X2) -> active# X2, active# zWquot(cons(X, XS), cons(Y, YS)) -> cons#(quot(X, Y), zWquot(XS, YS))) (active# zWquot(X1, X2) -> active# X2, active# zWquot(X1, X2) -> zWquot#(active X1, X2)) (active# zWquot(X1, X2) -> active# X2, active# zWquot(X1, X2) -> zWquot#(X1, active X2)) (active# zWquot(X1, X2) -> active# X2, active# zWquot(X1, X2) -> active# X2) (active# zWquot(X1, X2) -> active# X2, active# zWquot(X1, X2) -> active# X1) (active# zWquot(X1, X2) -> active# X2, active# quot(s X, s Y) -> quot#(minus(X, Y), s Y)) (active# zWquot(X1, X2) -> active# X2, active# quot(s X, s Y) -> minus#(X, Y)) (active# zWquot(X1, X2) -> active# X2, active# quot(s X, s Y) -> s# quot(minus(X, Y), s Y)) (active# zWquot(X1, X2) -> active# X2, active# quot(X1, X2) -> quot#(active X1, X2)) (active# zWquot(X1, X2) -> active# X2, active# quot(X1, X2) -> quot#(X1, active X2)) (active# zWquot(X1, X2) -> active# X2, active# quot(X1, X2) -> active# X2) (active# zWquot(X1, X2) -> active# X2, active# quot(X1, X2) -> active# X1) (active# zWquot(X1, X2) -> active# X2, active# minus(s X, s Y) -> minus#(X, Y)) (active# zWquot(X1, X2) -> active# X2, active# minus(X1, X2) -> minus#(active X1, X2)) (active# zWquot(X1, X2) -> active# X2, active# minus(X1, X2) -> minus#(X1, active X2)) (active# zWquot(X1, X2) -> active# X2, active# minus(X1, X2) -> active# X2) (active# zWquot(X1, X2) -> active# X2, active# minus(X1, X2) -> active# X1) (active# zWquot(X1, X2) -> active# X2, active# sel(s N, cons(X, XS)) -> sel#(N, XS)) (active# zWquot(X1, X2) -> active# X2, active# sel(X1, X2) -> sel#(active X1, X2)) (active# zWquot(X1, X2) -> active# X2, active# sel(X1, X2) -> sel#(X1, active X2)) (active# zWquot(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X2) (active# zWquot(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X1) (active# zWquot(X1, X2) -> active# X2, active# s X -> active# X) (active# zWquot(X1, X2) -> active# X2, active# s X -> s# active X) (active# zWquot(X1, X2) -> active# X2, active# from X -> active# X) (active# zWquot(X1, X2) -> active# X2, active# from X -> s# X) (active# zWquot(X1, X2) -> active# X2, active# from X -> from# active X) (active# zWquot(X1, X2) -> active# X2, active# from X -> from# s X) (active# zWquot(X1, X2) -> active# X2, active# from X -> cons#(X, from s X)) (active# zWquot(X1, X2) -> active# X2, active# cons(X1, X2) -> active# X1) (active# zWquot(X1, X2) -> active# X2, active# cons(X1, X2) -> cons#(active X1, X2)) (proper# sel(X1, X2) -> proper# X2, proper# zWquot(X1, X2) -> proper# X2) (proper# sel(X1, X2) -> proper# X2, proper# zWquot(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X2, proper# zWquot(X1, X2) -> zWquot#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X2, proper# quot(X1, X2) -> proper# X2) (proper# sel(X1, X2) -> proper# X2, proper# quot(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X2, proper# quot(X1, X2) -> quot#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X2, proper# minus(X1, X2) -> proper# X2) (proper# sel(X1, X2) -> proper# X2, proper# minus(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X2, proper# minus(X1, X2) -> minus#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X2) (proper# sel(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X2, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# sel(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# sel(X1, X2) -> proper# X2, proper# from X -> proper# X) (proper# sel(X1, X2) -> proper# X2, proper# from X -> from# proper X) (proper# sel(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# sel(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# quot(X1, X2) -> proper# X2, proper# zWquot(X1, X2) -> proper# X2) (proper# quot(X1, X2) -> proper# X2, proper# zWquot(X1, X2) -> proper# X1) (proper# quot(X1, X2) -> proper# X2, proper# zWquot(X1, X2) -> zWquot#(proper X1, proper X2)) (proper# quot(X1, X2) -> proper# X2, proper# quot(X1, X2) -> proper# X2) (proper# quot(X1, X2) -> proper# X2, proper# quot(X1, X2) -> proper# X1) (proper# quot(X1, X2) -> proper# X2, proper# quot(X1, X2) -> quot#(proper X1, proper X2)) (proper# quot(X1, X2) -> proper# X2, proper# minus(X1, X2) -> proper# X2) (proper# quot(X1, X2) -> proper# X2, proper# minus(X1, X2) -> proper# X1) (proper# quot(X1, X2) -> proper# X2, proper# minus(X1, X2) -> minus#(proper X1, proper X2)) (proper# quot(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X2) (proper# quot(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1) (proper# quot(X1, X2) -> proper# X2, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# quot(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# quot(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# quot(X1, X2) -> proper# X2, proper# from X -> proper# X) (proper# quot(X1, X2) -> proper# X2, proper# from X -> from# proper X) (proper# quot(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# quot(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# quot(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# cons(X1, X2) -> cons#(active X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# cons(X1, X2) -> cons#(active X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (active# minus(X1, X2) -> minus#(active X1, X2), minus#(ok X1, ok X2) -> minus#(X1, X2)) (active# minus(X1, X2) -> minus#(active X1, X2), minus#(mark X1, X2) -> minus#(X1, X2)) (active# zWquot(X1, X2) -> zWquot#(active X1, X2), zWquot#(ok X1, ok X2) -> zWquot#(X1, X2)) (active# zWquot(X1, X2) -> zWquot#(active X1, X2), zWquot#(mark X1, X2) -> zWquot#(X1, X2)) (active# sel(X1, X2) -> sel#(X1, active X2), sel#(ok X1, ok X2) -> sel#(X1, X2)) (active# sel(X1, X2) -> sel#(X1, active X2), sel#(X1, mark X2) -> sel#(X1, X2)) (active# quot(X1, X2) -> quot#(X1, active X2), quot#(ok X1, ok X2) -> quot#(X1, X2)) (active# quot(X1, X2) -> quot#(X1, active X2), quot#(X1, mark X2) -> quot#(X1, X2)) (active# zWquot(X1, X2) -> zWquot#(X1, active X2), zWquot#(ok X1, ok X2) -> zWquot#(X1, X2)) (active# zWquot(X1, X2) -> zWquot#(X1, active X2), zWquot#(X1, mark X2) -> zWquot#(X1, X2)) (proper# sel(X1, X2) -> sel#(proper X1, proper X2), sel#(ok X1, ok X2) -> sel#(X1, X2)) (proper# sel(X1, X2) -> 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X2)) (minus#(mark X1, X2) -> minus#(X1, X2), minus#(ok X1, ok X2) -> minus#(X1, X2)) (minus#(mark X1, X2) -> minus#(X1, X2), minus#(mark X1, X2) -> minus#(X1, X2)) (minus#(mark X1, X2) -> minus#(X1, X2), minus#(X1, mark X2) -> minus#(X1, X2)) (quot#(X1, mark X2) -> quot#(X1, X2), quot#(ok X1, ok X2) -> quot#(X1, X2)) (quot#(X1, mark X2) -> quot#(X1, X2), quot#(mark X1, X2) -> quot#(X1, X2)) (quot#(X1, mark X2) -> quot#(X1, X2), quot#(X1, mark X2) -> quot#(X1, X2)) (quot#(ok X1, ok X2) -> quot#(X1, X2), quot#(ok X1, ok X2) -> quot#(X1, X2)) (quot#(ok X1, ok X2) -> quot#(X1, X2), quot#(mark X1, X2) -> quot#(X1, X2)) (quot#(ok X1, ok X2) -> quot#(X1, X2), quot#(X1, mark X2) -> quot#(X1, X2)) (zWquot#(mark X1, X2) -> zWquot#(X1, X2), zWquot#(ok X1, ok X2) -> zWquot#(X1, X2)) (zWquot#(mark X1, X2) -> zWquot#(X1, X2), zWquot#(mark X1, X2) -> zWquot#(X1, X2)) (zWquot#(mark X1, X2) -> zWquot#(X1, X2), zWquot#(X1, mark X2) -> zWquot#(X1, X2)) (from# mark X -> from# X, from# ok X -> from# X) 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-> cons#(proper X1, proper X2)) (proper# zWquot(X1, X2) -> proper# X1, proper# zWquot(X1, X2) -> proper# X2) (proper# zWquot(X1, X2) -> proper# X1, proper# zWquot(X1, X2) -> proper# X1) (proper# zWquot(X1, X2) -> proper# X1, proper# zWquot(X1, X2) -> zWquot#(proper X1, proper X2)) (proper# zWquot(X1, X2) -> proper# X1, proper# quot(X1, X2) -> proper# X2) (proper# zWquot(X1, X2) -> proper# X1, proper# quot(X1, X2) -> proper# X1) (proper# zWquot(X1, X2) -> proper# X1, proper# quot(X1, X2) -> quot#(proper X1, proper X2)) (proper# zWquot(X1, X2) -> proper# X1, proper# minus(X1, X2) -> proper# X2) (proper# zWquot(X1, X2) -> proper# X1, proper# minus(X1, X2) -> proper# X1) (proper# zWquot(X1, X2) -> proper# X1, proper# minus(X1, X2) -> minus#(proper X1, proper X2)) (proper# zWquot(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2) (proper# zWquot(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X1) (proper# zWquot(X1, X2) -> proper# X1, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# zWquot(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# zWquot(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# zWquot(X1, X2) -> proper# X1, proper# from X -> proper# X) (proper# zWquot(X1, X2) -> proper# X1, proper# from X -> from# proper X) (proper# zWquot(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# zWquot(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# zWquot(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# quot(s X, s Y) -> s# quot(minus(X, Y), s Y), s# ok X -> s# X) (active# quot(s X, s Y) -> s# quot(minus(X, Y), s Y), s# mark X -> s# X) (active# sel(s N, cons(X, XS)) -> sel#(N, XS), sel#(X1, mark X2) -> sel#(X1, X2)) (proper# quot(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# quot(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# quot(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# quot(X1, X2) -> proper# X1, proper# from X -> from# proper X) (proper# quot(X1, X2) -> proper# X1, proper# from X -> proper# X) (proper# quot(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# quot(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# quot(X1, X2) -> proper# X1, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# quot(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X1) (proper# quot(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2) (proper# quot(X1, X2) -> proper# X1, proper# minus(X1, X2) -> minus#(proper X1, proper X2)) (proper# quot(X1, X2) -> proper# X1, proper# minus(X1, X2) -> proper# X1) (proper# quot(X1, X2) -> proper# X1, proper# minus(X1, X2) -> proper# X2) (proper# quot(X1, X2) -> proper# X1, proper# quot(X1, X2) -> quot#(proper X1, proper X2)) (proper# quot(X1, X2) -> proper# X1, proper# quot(X1, X2) -> proper# X1) (proper# quot(X1, X2) -> proper# X1, proper# quot(X1, X2) -> proper# X2) (proper# quot(X1, X2) -> proper# X1, 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(active# minus(X1, X2) -> active# X1, active# quot(X1, X2) -> quot#(active X1, X2)) (active# minus(X1, X2) -> active# X1, active# quot(s X, s Y) -> s# quot(minus(X, Y), s Y)) (active# minus(X1, X2) -> active# X1, active# quot(s X, s Y) -> minus#(X, Y)) (active# minus(X1, X2) -> active# X1, active# quot(s X, s Y) -> quot#(minus(X, Y), s Y)) (active# minus(X1, X2) -> active# X1, active# zWquot(X1, X2) -> active# X1) (active# minus(X1, X2) -> active# X1, active# zWquot(X1, X2) -> active# X2) (active# minus(X1, X2) -> active# X1, active# zWquot(X1, X2) -> zWquot#(X1, active X2)) (active# minus(X1, X2) -> active# X1, active# zWquot(X1, X2) -> zWquot#(active X1, X2)) (active# minus(X1, X2) -> active# X1, active# zWquot(cons(X, XS), cons(Y, YS)) -> cons#(quot(X, Y), zWquot(XS, YS))) (active# minus(X1, X2) -> active# X1, active# zWquot(cons(X, XS), cons(Y, YS)) -> quot#(X, Y)) (active# minus(X1, X2) -> active# X1, active# zWquot(cons(X, XS), cons(Y, YS)) -> zWquot#(XS, YS)) (active# cons(X1, 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(proper# minus(X1, X2) -> proper# X2, proper# zWquot(X1, X2) -> proper# X1) (proper# minus(X1, X2) -> proper# X2, proper# zWquot(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# from X -> from# proper X) (proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# cons(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# minus(X1, X2) -> minus#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# minus(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# minus(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# quot(X1, X2) -> quot#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# quot(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# quot(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# zWquot(X1, X2) -> zWquot#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# zWquot(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# zWquot(X1, X2) -> proper# X2) (active# quot(X1, X2) -> active# X2, active# cons(X1, X2) -> cons#(active X1, X2)) (active# quot(X1, X2) -> active# X2, active# cons(X1, X2) -> active# X1) (active# quot(X1, X2) -> active# X2, active# from X -> cons#(X, from s X)) (active# quot(X1, X2) -> active# X2, active# from X -> from# s X) (active# quot(X1, X2) -> active# X2, active# from X -> from# active X) (active# quot(X1, X2) -> 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X2, active# sel(X1, X2) -> sel#(X1, active X2)) (active# sel(X1, X2) -> active# X2, active# sel(X1, X2) -> sel#(active X1, X2)) (active# sel(X1, X2) -> active# X2, active# sel(s N, cons(X, XS)) -> sel#(N, XS)) (active# sel(X1, X2) -> active# X2, active# minus(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X2, active# minus(X1, X2) -> active# X2) (active# sel(X1, X2) -> active# X2, active# minus(X1, X2) -> minus#(X1, active X2)) (active# sel(X1, X2) -> active# X2, active# minus(X1, X2) -> minus#(active X1, X2)) (active# sel(X1, X2) -> active# X2, active# minus(s X, s Y) -> minus#(X, Y)) (active# sel(X1, X2) -> active# X2, active# quot(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X2, active# quot(X1, X2) -> active# X2) (active# sel(X1, X2) -> active# X2, active# quot(X1, X2) -> quot#(X1, active X2)) (active# sel(X1, X2) -> active# X2, active# quot(X1, X2) -> quot#(active X1, X2)) (active# sel(X1, X2) -> active# X2, active# quot(s X, s Y) -> s# quot(minus(X, Y), s Y)) (active# sel(X1, X2) -> active# X2, active# quot(s X, s Y) -> minus#(X, Y)) (active# sel(X1, X2) -> active# X2, active# quot(s X, s Y) -> quot#(minus(X, Y), s Y)) (active# sel(X1, X2) -> active# X2, active# zWquot(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X2, active# zWquot(X1, X2) -> active# X2) (active# sel(X1, X2) -> active# X2, active# zWquot(X1, X2) -> zWquot#(X1, active X2)) (active# sel(X1, X2) -> active# X2, active# zWquot(X1, X2) -> zWquot#(active X1, X2)) (active# sel(X1, X2) -> active# X2, active# zWquot(cons(X, XS), cons(Y, YS)) -> cons#(quot(X, Y), zWquot(XS, YS))) (active# sel(X1, X2) -> active# X2, active# zWquot(cons(X, XS), cons(Y, YS)) -> quot#(X, Y)) (active# sel(X1, X2) -> active# X2, active# zWquot(cons(X, XS), cons(Y, YS)) -> zWquot#(XS, YS)) (top# mark X -> top# proper X, top# mark X -> proper# X) (top# mark X -> top# proper X, top# mark X -> top# proper X) (top# mark X -> top# proper X, top# ok X -> active# X) (top# mark X -> top# proper X, top# ok X -> top# active X) (proper# from X -> from# proper X, from# mark X -> from# X) (proper# from X -> from# proper X, from# ok X -> from# X) (active# from X -> from# active X, from# mark X -> from# X) (active# from X -> from# active X, from# ok X -> from# X) (active# zWquot(cons(X, XS), cons(Y, YS)) -> quot#(X, Y), quot#(ok X1, ok X2) -> quot#(X1, X2)) } STATUS: arrows: 0.862491 SCCS (10): Scc: {top# mark X -> top# proper X, top# ok X -> top# active X} Scc: { active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2, active# minus(X1, X2) -> active# X1, active# minus(X1, X2) -> active# X2, active# quot(X1, X2) -> active# X1, active# quot(X1, X2) -> active# X2, active# zWquot(X1, X2) -> active# X1, active# zWquot(X1, X2) -> active# X2} Scc: { proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# s X -> proper# X, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# minus(X1, X2) -> proper# X1, proper# minus(X1, X2) -> proper# X2, proper# quot(X1, X2) -> proper# X1, proper# quot(X1, X2) -> proper# X2, proper# zWquot(X1, X2) -> proper# X1, proper# zWquot(X1, X2) -> proper# X2} Scc: { zWquot#(X1, mark X2) -> zWquot#(X1, X2), zWquot#(mark X1, X2) -> zWquot#(X1, X2), zWquot#(ok X1, ok X2) -> zWquot#(X1, X2)} Scc: { minus#(X1, mark X2) -> minus#(X1, X2), minus#(mark X1, X2) -> minus#(X1, X2), minus#(ok X1, ok X2) -> minus#(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: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)} Scc: {s# mark X -> s# X, s# ok X -> s# X} Scc: {from# mark X -> from# X, from# ok X -> from# X} Scc: { quot#(X1, mark X2) -> quot#(X1, X2), quot#(mark X1, X2) -> quot#(X1, X2), quot#(ok X1, ok X2) -> quot#(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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} Fail SCC (11): Strict: { active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2, active# minus(X1, X2) -> active# X1, active# minus(X1, X2) -> active# X2, active# quot(X1, X2) -> active# X1, active# quot(X1, X2) -> active# X2, active# zWquot(X1, X2) -> active# X1, active# zWquot(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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + x1, [minus](x0, x1) = x0 + x1, [quot](x0, x1) = x0 + x1, [zWquot](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [nil] = 1, [active#](x0) = x0 Strict: active# zWquot(X1, X2) -> active# X2 1 + 1X1 + 1X2 >= 0 + 1X2 active# zWquot(X1, X2) -> active# X1 1 + 1X1 + 1X2 >= 0 + 1X1 active# quot(X1, X2) -> active# X2 0 + 1X1 + 1X2 >= 0 + 1X2 active# quot(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 active# minus(X1, X2) -> active# X2 0 + 1X1 + 1X2 >= 0 + 1X2 active# minus(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 active# sel(X1, X2) -> active# X2 0 + 1X1 + 1X2 >= 0 + 1X2 active# sel(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 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 + 0X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 minus(mark X1, X2) -> mark minus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 minus(X1, mark X2) -> mark minus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 active zWquot(nil(), XS) -> mark nil() 0 + 0XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 0 + 0X + 0XS + 0Y + 0YS >= 0 + 1X + 0XS + 1Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 0 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 0 + 0Y >= 0 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 0 + 0X + 0Y >= 0 + 1X + 2Y active quot(X1, X2) -> quot(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 active minus(s X, s Y) -> mark minus(X, Y) 0 + 0X + 0Y >= 0 + 1X + 1Y active minus(X1, X2) -> minus(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active minus(X1, X2) -> minus(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 active minus(X, 0()) -> mark 0() 0 + 0X >= 0 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 + 1XS + 1N 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 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 + 1X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 0 + 1X >= 0 + 1X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 0 + 1X >= 0 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 SCCS (1): Scc: { active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2, active# minus(X1, X2) -> active# X1, active# minus(X1, X2) -> active# X2, active# quot(X1, X2) -> active# X1, active# quot(X1, X2) -> active# X2} SCC (9): Strict: { active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2, active# minus(X1, X2) -> active# X1, active# minus(X1, X2) -> active# X2, active# quot(X1, X2) -> active# X1, active# quot(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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + x1, [minus](x0, x1) = x0 + x1, [quot](x0, x1) = x0 + x1 + 1, [zWquot](x0, x1) = x0 + 1, [mark](x0) = x0, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [nil] = 1, [active#](x0) = x0 Strict: active# quot(X1, X2) -> active# X2 1 + 1X1 + 1X2 >= 0 + 1X2 active# quot(X1, X2) -> active# X1 1 + 1X1 + 1X2 >= 0 + 1X1 active# minus(X1, X2) -> active# X2 0 + 1X1 + 1X2 >= 0 + 1X2 active# minus(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 active# sel(X1, X2) -> active# X2 0 + 1X1 + 1X2 >= 0 + 1X2 active# sel(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 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 + 0X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 minus(mark X1, X2) -> mark minus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 minus(X1, mark X2) -> mark minus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 active zWquot(nil(), XS) -> mark nil() 0 + 0XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 0 + 0X + 0XS + 0Y + 0YS >= 1 + 1X + 0XS + 1Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 0 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 0 + 0Y >= 0 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 0 + 0X + 0Y >= 1 + 1X + 2Y active quot(X1, X2) -> quot(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active minus(s X, s Y) -> mark minus(X, Y) 0 + 0X + 0Y >= 0 + 1X + 1Y active minus(X1, X2) -> minus(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active minus(X1, X2) -> minus(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 active minus(X, 0()) -> mark 0() 0 + 0X >= 0 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 + 1XS + 1N 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 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 + 1X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 0 + 1X >= 0 + 1X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 0 + 1X >= 0 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 SCCS (1): Scc: { active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2, active# minus(X1, X2) -> active# X1, active# minus(X1, X2) -> active# X2} SCC (7): Strict: { active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2, active# minus(X1, X2) -> active# X1, active# minus(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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + x1, [minus](x0, x1) = x0 + x1 + 1, [quot](x0, x1) = 0, [zWquot](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = 0, [top](x0) = 0, [0] = 0, [nil] = 1, [active#](x0) = x0 Strict: active# minus(X1, X2) -> active# X2 1 + 1X1 + 1X2 >= 0 + 1X2 active# minus(X1, X2) -> active# X1 1 + 1X1 + 1X2 >= 0 + 1X1 active# sel(X1, X2) -> active# X2 0 + 1X1 + 1X2 >= 0 + 1X2 active# sel(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 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 + 0X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 0 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 0 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 quot(mark X1, X2) -> mark quot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(X1, mark X2) -> mark quot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 minus(mark X1, X2) -> mark minus(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 minus(X1, mark X2) -> mark minus(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 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 active zWquot(nil(), XS) -> mark nil() 0 + 0XS >= 2 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 0 + 0X + 0XS + 0Y + 0YS >= 1 + 0X + 0XS + 0Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 0 + 0XS >= 2 active quot(0(), s Y) -> mark 0() 0 + 0Y >= 1 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 0 + 0X + 0Y >= 1 + 0X + 0Y active quot(X1, X2) -> quot(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active quot(X1, X2) -> quot(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active minus(s X, s Y) -> mark minus(X, Y) 0 + 0X + 0Y >= 2 + 1X + 1Y active minus(X1, X2) -> minus(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active minus(X1, X2) -> minus(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active minus(X, 0()) -> mark 0() 0 + 0X >= 1 active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 1 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 1 + 1XS + 1N 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 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 + 1X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 0 + 0X >= 0 + 0X s mark X -> mark s X 1 + 1X >= 1 + 1X from ok X -> ok from X 0 + 0X >= 0 + 0X from mark X -> mark from X 1 + 1X >= 1 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2} SCC (5): Strict: {active# cons(X1, X2) -> active# X1, active# from X -> active# X, active# s X -> active# X, 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + x1 + 1, [minus](x0, x1) = x0 + 1, [quot](x0, x1) = x0 + 1, [zWquot](x0, x1) = x0 + 1, [mark](x0) = 1, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 1, [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# 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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 proper nil() -> ok nil() 2 >= 2 proper quot(X1, X2) -> quot(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 proper 0() -> ok 0() 2 >= 2 proper sel(X1, X2) -> sel(proper X1, proper X2) 2 + 1X1 + 1X2 >= 3 + 1X1 + 1X2 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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 quot(mark X1, X2) -> mark quot(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(X1, mark X2) -> mark quot(X1, X2) 1 + 1X1 + 0X2 >= 1 + 0X1 + 0X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 1X1 + 0X2 >= 1 + 0X1 + 0X2 active zWquot(nil(), XS) -> mark nil() 0 + 0XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 0 + 0X + 0XS + 0Y + 0YS >= 1 + 0X + 0XS + 0Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 0 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 0 + 0Y >= 1 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 0 + 0X + 0Y >= 1 + 0X + 0Y active quot(X1, X2) -> quot(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active quot(X1, X2) -> quot(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active minus(s X, s Y) -> mark minus(X, Y) 0 + 0X + 0Y >= 1 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active minus(X1, X2) -> minus(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 0 + 0X >= 1 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 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} 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = 0, [minus](x0, x1) = x0 + 1, [quot](x0, x1) = x0 + x1, [zWquot](x0, x1) = x0 + 1, [mark](x0) = 1, [from](x0) = x0, [s](x0) = x0 + 1, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 1, [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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 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 >= 0 + 0X1 + 0X2 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 quot(X1, mark X2) -> mark quot(X1, X2) 1 + 1X1 + 0X2 >= 1 + 0X1 + 0X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 2 + 0X1 + 0X2 >= 1 + 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 >= 1 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWquot(nil(), XS) -> mark nil() 0 + 0XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 0 + 0X + 0XS + 0Y + 0YS >= 1 + 0X + 0XS + 0Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 0 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 0 + 0Y >= 1 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 0 + 0X + 0Y >= 1 + 0X + 0Y active quot(X1, X2) -> quot(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 active minus(s X, s Y) -> mark minus(X, Y) 0 + 0X + 0Y >= 1 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active minus(X1, X2) -> minus(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 0 + 0X >= 1 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 >= 0 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 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 >= 1 + 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 2 + 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} 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = 0, [minus](x0, x1) = x0 + 1, [quot](x0, x1) = 0, [zWquot](x0, x1) = 0, [mark](x0) = 0, [from](x0) = x0 + 1, [s](x0) = 0, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(mark X1, X2) -> mark quot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 quot(X1, mark X2) -> mark quot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 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 active zWquot(nil(), XS) -> mark nil() 0 + 0XS >= 0 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 0 + 0X + 0XS + 0Y + 0YS >= 0 + 0X + 0XS + 0Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 0 + 0XS >= 0 active quot(0(), s Y) -> mark 0() 0 + 0Y >= 0 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active quot(X1, X2) -> quot(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active quot(X1, X2) -> quot(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active minus(s X, s Y) -> mark minus(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active minus(X1, X2) -> minus(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 0 + 0X >= 0 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 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + 1, [minus](x0, x1) = 1, [quot](x0, x1) = x0 + 1, [zWquot](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [nil] = 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 >= 1 + 0X proper zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 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 active zWquot(nil(), XS) -> mark nil() 2 + 1XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 3 + 0X + 0XS + 1Y + 0YS >= 3 + 0X + 0XS + 1Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active zWquot(XS, nil()) -> mark nil() 2 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 3 + 1Y >= 2 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 3 + 0X + 1Y >= 4 + 0X + 1Y active quot(X1, X2) -> quot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active minus(s X, s Y) -> mark minus(X, Y) 2 + 0X + 0Y >= 2 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X1, X2) -> minus(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 2 + 0X >= 2 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 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 (12): Strict: { proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# s X -> proper# X, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# minus(X1, X2) -> proper# X1, proper# minus(X1, X2) -> proper# X2, proper# quot(X1, X2) -> proper# X1, proper# quot(X1, X2) -> proper# X2, proper# zWquot(X1, X2) -> proper# X1, proper# zWquot(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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + x1, [minus](x0, x1) = x0 + x1, [quot](x0, x1) = x0 + x1, [zWquot](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [nil] = 1, [proper#](x0) = x0 Strict: proper# zWquot(X1, X2) -> proper# X2 1 + 1X1 + 1X2 >= 0 + 1X2 proper# zWquot(X1, X2) -> proper# X1 1 + 1X1 + 1X2 >= 0 + 1X1 proper# quot(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# quot(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 proper# minus(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# minus(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 proper# sel(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# sel(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 minus(mark X1, X2) -> mark minus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 minus(X1, mark X2) -> mark minus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 active zWquot(nil(), XS) -> mark nil() 0 + 0XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 0 + 0X + 0XS + 0Y + 0YS >= 1 + 1X + 1XS + 1Y + 1YS active zWquot(X1, X2) -> zWquot(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 0 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 0 + 0Y >= 0 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 0 + 0X + 0Y >= 0 + 1X + 2Y active quot(X1, X2) -> quot(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 active minus(s X, s Y) -> mark minus(X, Y) 0 + 0X + 0Y >= 0 + 1X + 1Y active minus(X1, X2) -> minus(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active minus(X1, X2) -> minus(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 active minus(X, 0()) -> mark 0() 0 + 0X >= 0 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 + 1XS + 1N 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 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 + 2X 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 + 1X >= 0 + 1X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 0 + 1X >= 0 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 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# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# minus(X1, X2) -> proper# X1, proper# minus(X1, X2) -> proper# X2, proper# quot(X1, X2) -> proper# X1, proper# quot(X1, X2) -> proper# X2} 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# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# minus(X1, X2) -> proper# X1, proper# minus(X1, X2) -> proper# X2, proper# quot(X1, X2) -> proper# X1, proper# quot(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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + x1, [minus](x0, x1) = x0 + x1, [quot](x0, x1) = x0 + x1 + 1, [zWquot](x0, x1) = x0 + 1, [mark](x0) = x0, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [nil] = 1, [proper#](x0) = x0 Strict: proper# quot(X1, X2) -> proper# X2 1 + 1X1 + 1X2 >= 0 + 1X2 proper# quot(X1, X2) -> proper# X1 1 + 1X1 + 1X2 >= 0 + 1X1 proper# minus(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# minus(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 proper# sel(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# sel(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 minus(mark X1, X2) -> mark minus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 minus(X1, mark X2) -> mark minus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 active zWquot(nil(), XS) -> mark nil() 0 + 0XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 0 + 0X + 0XS + 0Y + 0YS >= 2 + 1X + 0XS + 1Y + 1YS active zWquot(X1, X2) -> zWquot(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 0 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 0 + 0Y >= 0 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 0 + 0X + 0Y >= 1 + 1X + 2Y active quot(X1, X2) -> quot(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active minus(s X, s Y) -> mark minus(X, Y) 0 + 0X + 0Y >= 0 + 1X + 1Y active minus(X1, X2) -> minus(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active minus(X1, X2) -> minus(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 active minus(X, 0()) -> mark 0() 0 + 0X >= 0 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 + 1XS + 1N 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 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 + 2X 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 + 1X >= 0 + 1X from ok X -> ok from X 1 + 1X >= 1 + 1X from mark X -> mark from X 0 + 1X >= 0 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 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# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# minus(X1, X2) -> proper# X1, proper# minus(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# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# minus(X1, X2) -> proper# X1, proper# minus(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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + x1, [minus](x0, x1) = x0 + x1 + 1, [quot](x0, x1) = 0, [zWquot](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [nil] = 1, [proper#](x0) = x0 Strict: proper# minus(X1, X2) -> proper# X2 1 + 1X1 + 1X2 >= 0 + 1X2 proper# minus(X1, X2) -> proper# X1 1 + 1X1 + 1X2 >= 0 + 1X1 proper# sel(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# sel(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(mark X1, X2) -> mark quot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(X1, mark X2) -> mark quot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 minus(mark X1, X2) -> mark minus(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 minus(X1, mark X2) -> mark minus(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 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 active zWquot(nil(), XS) -> mark nil() 0 + 0XS >= 2 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 0 + 0X + 0XS + 0Y + 0YS >= 2 + 0X + 0XS + 0Y + 1YS active zWquot(X1, X2) -> zWquot(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 0 + 0XS >= 2 active quot(0(), s Y) -> mark 0() 0 + 0Y >= 1 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 0 + 0X + 0Y >= 1 + 0X + 0Y active quot(X1, X2) -> quot(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active quot(X1, X2) -> quot(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active minus(s X, s Y) -> mark minus(X, Y) 0 + 0X + 0Y >= 2 + 1X + 1Y active minus(X1, X2) -> minus(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active minus(X1, X2) -> minus(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active minus(X, 0()) -> mark 0() 0 + 0X >= 1 active sel(0(), cons(X, XS)) -> mark X 0 + 0X + 0XS >= 1 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 0 + 0X + 0XS + 0N >= 1 + 1XS + 1N 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 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 + 2X 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 + 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) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 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# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2} 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# 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + x1 + 1, [minus](x0, x1) = x0 + 1, [quot](x0, x1) = x0 + 1, [zWquot](x0, x1) = x0 + 1, [mark](x0) = 1, [from](x0) = x0, [s](x0) = x0, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 1, [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# 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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 quot(mark X1, X2) -> mark quot(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(X1, mark X2) -> mark quot(X1, X2) 1 + 1X1 + 0X2 >= 1 + 0X1 + 0X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 1X1 + 0X2 >= 1 + 0X1 + 0X2 active zWquot(nil(), XS) -> mark nil() 0 + 0XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 0 + 0X + 0XS + 0Y + 0YS >= 1 + 0X + 0XS + 0Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 0 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 0 + 0Y >= 1 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 0 + 0X + 0Y >= 1 + 0X + 0Y active quot(X1, X2) -> quot(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active quot(X1, X2) -> quot(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active minus(s X, s Y) -> mark minus(X, Y) 0 + 0X + 0Y >= 1 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active minus(X1, X2) -> minus(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 0 + 0X >= 1 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 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} 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = 0, [minus](x0, x1) = x0 + 1, [quot](x0, x1) = x0 + x1, [zWquot](x0, x1) = x0 + 1, [mark](x0) = 1, [from](x0) = x0, [s](x0) = x0 + 1, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 1, [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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 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 >= 0 + 0X1 + 0X2 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 quot(X1, mark X2) -> mark quot(X1, X2) 1 + 1X1 + 0X2 >= 1 + 0X1 + 0X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 2 + 0X1 + 0X2 >= 1 + 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 >= 1 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWquot(nil(), XS) -> mark nil() 0 + 0XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 0 + 0X + 0XS + 0Y + 0YS >= 1 + 0X + 0XS + 0Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 0 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 0 + 0Y >= 1 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 0 + 0X + 0Y >= 1 + 0X + 0Y active quot(X1, X2) -> quot(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 active minus(s X, s Y) -> mark minus(X, Y) 0 + 0X + 0Y >= 1 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active minus(X1, X2) -> minus(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 0 + 0X >= 1 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 >= 0 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 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 >= 1 + 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 2 + 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} 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = 0, [minus](x0, x1) = x0 + 1, [quot](x0, x1) = x0, [zWquot](x0, x1) = 0, [mark](x0) = 0, [from](x0) = x0 + 1, [s](x0) = 0, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 quot(X1, mark X2) -> mark quot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 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 active zWquot(nil(), XS) -> mark nil() 0 + 0XS >= 0 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 0 + 0X + 0XS + 0Y + 0YS >= 0 + 0X + 0XS + 0Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 0 + 0XS >= 0 active quot(0(), s Y) -> mark 0() 0 + 0Y >= 0 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active quot(X1, X2) -> quot(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active minus(s X, s Y) -> mark minus(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active minus(X1, X2) -> minus(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 0 + 0X >= 0 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 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + 1, [minus](x0, x1) = 1, [quot](x0, x1) = 0, [zWquot](x0, x1) = 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = 0, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = 0, [top](x0) = 0, [0] = 1, [nil] = 1, [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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 0 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 0 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 quot(mark X1, X2) -> mark quot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(X1, mark X2) -> mark quot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 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 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active zWquot(nil(), XS) -> mark nil() 2 + 0XS >= 2 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 2 + 0X + 0XS + 0Y + 0YS >= 3 + 0X + 0XS + 0Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 2 + 0XS >= 2 active quot(0(), s Y) -> mark 0() 1 + 0Y >= 2 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 1 + 0X + 0Y >= 1 + 0X + 0Y active quot(X1, X2) -> quot(active X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active quot(X1, X2) -> quot(X1, active X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active minus(s X, s Y) -> mark minus(X, Y) 2 + 0X + 0Y >= 2 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X1, X2) -> minus(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 2 + 0X >= 2 active sel(0(), cons(X, XS)) -> mark X 3 + 1X + 1XS >= 1 + 1X active sel(s N, cons(X, XS)) -> mark sel(N, XS) 3 + 1X + 1XS + 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 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 (3): Strict: { zWquot#(X1, mark X2) -> zWquot#(X1, X2), zWquot#(mark X1, X2) -> zWquot#(X1, X2), zWquot#(ok X1, ok X2) -> zWquot#(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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + 1, [minus](x0, x1) = 1, [quot](x0, x1) = x0 + 1, [zWquot](x0, x1) = 0, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 1, [zWquot#](x0, x1) = x0 + 1 Strict: zWquot#(ok X1, ok X2) -> zWquot#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 zWquot#(mark X1, X2) -> zWquot#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 zWquot#(X1, mark X2) -> zWquot#(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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 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 active zWquot(nil(), XS) -> mark nil() 1 + 0XS >= 2 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 1 + 0X + 0XS + 0Y + 0YS >= 3 + 0X + 0XS + 1Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 1 + 0XS >= 2 active quot(0(), s Y) -> mark 0() 3 + 1Y >= 2 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 3 + 0X + 1Y >= 4 + 0X + 1Y active quot(X1, X2) -> quot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active minus(s X, s Y) -> mark minus(X, Y) 2 + 0X + 0Y >= 2 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X1, X2) -> minus(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 2 + 0X >= 2 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 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: {zWquot#(X1, mark X2) -> zWquot#(X1, X2)} SCC (1): Strict: {zWquot#(X1, mark X2) -> zWquot#(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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + 1, [minus](x0, x1) = 1, [quot](x0, x1) = x0 + 1, [zWquot](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [nil] = 0, [zWquot#](x0, x1) = x0 Strict: zWquot#(X1, mark X2) -> zWquot#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 1 + 0X proper zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 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 active zWquot(nil(), XS) -> mark nil() 2 + 1XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 3 + 0X + 0XS + 1Y + 0YS >= 3 + 0X + 0XS + 1Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active zWquot(XS, nil()) -> mark nil() 2 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 3 + 1Y >= 2 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 3 + 0X + 1Y >= 4 + 0X + 1Y active quot(X1, X2) -> quot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active minus(s X, s Y) -> mark minus(X, Y) 2 + 0X + 0Y >= 2 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X1, X2) -> minus(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 2 + 0X >= 2 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 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: { minus#(X1, mark X2) -> minus#(X1, X2), minus#(mark X1, X2) -> minus#(X1, X2), minus#(ok X1, ok X2) -> minus#(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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + 1, [minus](x0, x1) = 1, [quot](x0, x1) = x0 + 1, [zWquot](x0, x1) = 0, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 1, [minus#](x0, x1) = x0 + 1 Strict: minus#(ok X1, ok X2) -> minus#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 minus#(mark X1, X2) -> minus#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 minus#(X1, mark X2) -> minus#(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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 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 active zWquot(nil(), XS) -> mark nil() 1 + 0XS >= 2 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 1 + 0X + 0XS + 0Y + 0YS >= 3 + 0X + 0XS + 1Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 1 + 0XS >= 2 active quot(0(), s Y) -> mark 0() 3 + 1Y >= 2 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 3 + 0X + 1Y >= 4 + 0X + 1Y active quot(X1, X2) -> quot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active minus(s X, s Y) -> mark minus(X, Y) 2 + 0X + 0Y >= 2 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X1, X2) -> minus(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 2 + 0X >= 2 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 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: {minus#(X1, mark X2) -> minus#(X1, X2)} SCC (1): Strict: {minus#(X1, mark X2) -> minus#(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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + 1, [minus](x0, x1) = 1, [quot](x0, x1) = x0 + 1, [zWquot](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [nil] = 0, [minus#](x0, x1) = x0 Strict: minus#(X1, mark X2) -> minus#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 1 + 0X proper zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 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 active zWquot(nil(), XS) -> mark nil() 2 + 1XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 3 + 0X + 0XS + 1Y + 0YS >= 3 + 0X + 0XS + 1Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active zWquot(XS, nil()) -> mark nil() 2 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 3 + 1Y >= 2 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 3 + 0X + 1Y >= 4 + 0X + 1Y active quot(X1, X2) -> quot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active minus(s X, s Y) -> mark minus(X, Y) 2 + 0X + 0Y >= 2 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X1, X2) -> minus(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 2 + 0X >= 2 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 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + 1, [minus](x0, x1) = 1, [quot](x0, x1) = x0 + 1, [zWquot](x0, x1) = 0, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 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 active zWquot(nil(), XS) -> mark nil() 1 + 0XS >= 2 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 1 + 0X + 0XS + 0Y + 0YS >= 3 + 0X + 0XS + 1Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 1 + 0XS >= 2 active quot(0(), s Y) -> mark 0() 3 + 1Y >= 2 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 3 + 0X + 1Y >= 4 + 0X + 1Y active quot(X1, X2) -> quot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active minus(s X, s Y) -> mark minus(X, Y) 2 + 0X + 0Y >= 2 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X1, X2) -> minus(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 2 + 0X >= 2 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 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + 1, [minus](x0, x1) = 1, [quot](x0, x1) = x0 + 1, [zWquot](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [nil] = 0, [sel#](x0, x1) = x0 Strict: sel#(X1, mark X2) -> sel#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 1 + 0X proper zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 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 active zWquot(nil(), XS) -> mark nil() 2 + 1XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 3 + 0X + 0XS + 1Y + 0YS >= 3 + 0X + 0XS + 1Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active zWquot(XS, nil()) -> mark nil() 2 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 3 + 1Y >= 2 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 3 + 0X + 1Y >= 4 + 0X + 1Y active quot(X1, X2) -> quot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active minus(s X, s Y) -> mark minus(X, Y) 2 + 0X + 0Y >= 2 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X1, X2) -> minus(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 2 + 0X >= 2 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 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + 1, [minus](x0, x1) = 1, [quot](x0, x1) = x0 + 1, [zWquot](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 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 active zWquot(nil(), XS) -> mark nil() 2 + 1XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 3 + 0X + 0XS + 1Y + 0YS >= 3 + 0X + 0XS + 1Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active zWquot(XS, nil()) -> mark nil() 2 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 3 + 1Y >= 2 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 3 + 0X + 1Y >= 4 + 0X + 1Y active quot(X1, X2) -> quot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active minus(s X, s Y) -> mark minus(X, Y) 2 + 0X + 0Y >= 2 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X1, X2) -> minus(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 2 + 0X >= 2 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 s X -> s active X 2 + 1X >= 2 + 1X active from X -> from active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X from ok X -> ok from X 2 + 1X >= 2 + 1X from mark X -> mark from X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 SCCS (1): Scc: {cons#(mark X1, X2) -> cons#(X1, X2)} SCC (1): Strict: {cons#(mark X1, X2) -> cons#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), from mark X -> mark from X, from ok X -> ok from X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active from X -> mark cons(X, from s X), active from X -> from active X, active s X -> s active X, active 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + 1, [minus](x0, x1) = 1, [quot](x0, x1) = x0 + 1, [zWquot](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [nil] = 0, [cons#](x0, x1) = x0 Strict: cons#(mark X1, X2) -> cons#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 1 + 0X proper zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 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 active zWquot(nil(), XS) -> mark nil() 2 + 1XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 3 + 0X + 0XS + 1Y + 0YS >= 3 + 0X + 0XS + 1Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active zWquot(XS, nil()) -> mark nil() 2 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 3 + 1Y >= 2 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 3 + 0X + 1Y >= 4 + 0X + 1Y active quot(X1, X2) -> quot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active minus(s X, s Y) -> mark minus(X, Y) 2 + 0X + 0Y >= 2 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X1, X2) -> minus(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 2 + 0X >= 2 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 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = 0, [minus](x0, x1) = x0 + 1, [quot](x0, x1) = 0, [zWquot](x0, x1) = 0, [mark](x0) = x0, [from](x0) = 0, [s](x0) = 0, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 0, [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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(mark X1, X2) -> mark quot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 quot(X1, mark X2) -> mark quot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 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 active zWquot(nil(), XS) -> mark nil() 0 + 0XS >= 0 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 0 + 0X + 0XS + 0Y + 0YS >= 0 + 0X + 0XS + 0Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 0 + 0XS >= 0 active quot(0(), s Y) -> mark 0() 0 + 0Y >= 1 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active quot(X1, X2) -> quot(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active quot(X1, X2) -> quot(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active minus(s X, s Y) -> mark minus(X, Y) 0 + 0X + 0Y >= 1 + 0X + 1Y active minus(X1, X2) -> minus(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active minus(X1, X2) -> minus(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 0 + 0X >= 1 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 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + 1, [minus](x0, x1) = 1, [quot](x0, x1) = x0 + 1, [zWquot](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [nil] = 0, [s#](x0) = x0 Strict: s# mark X -> s# X 1 + 1X >= 0 + 1X Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 1 + 0X proper zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 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 active zWquot(nil(), XS) -> mark nil() 2 + 1XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 3 + 0X + 0XS + 1Y + 0YS >= 3 + 0X + 0XS + 1Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active zWquot(XS, nil()) -> mark nil() 2 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 3 + 1Y >= 2 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 3 + 0X + 1Y >= 4 + 0X + 1Y active quot(X1, X2) -> quot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active minus(s X, s Y) -> mark minus(X, Y) 2 + 0X + 0Y >= 2 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X1, X2) -> minus(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 2 + 0X >= 2 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 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = 0, [minus](x0, x1) = x0 + 1, [quot](x0, x1) = 0, [zWquot](x0, x1) = 0, [mark](x0) = x0, [from](x0) = 0, [s](x0) = 0, [active](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 0, [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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(mark X1, X2) -> mark quot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 quot(X1, mark X2) -> mark quot(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 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 active zWquot(nil(), XS) -> mark nil() 0 + 0XS >= 0 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 0 + 0X + 0XS + 0Y + 0YS >= 0 + 0X + 0XS + 0Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 0 + 0XS >= 0 active quot(0(), s Y) -> mark 0() 0 + 0Y >= 1 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active quot(X1, X2) -> quot(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active quot(X1, X2) -> quot(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active minus(s X, s Y) -> mark minus(X, Y) 0 + 0X + 0Y >= 1 + 0X + 1Y active minus(X1, X2) -> minus(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active minus(X1, X2) -> minus(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 0 + 0X >= 1 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 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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + 1, [minus](x0, x1) = 1, [quot](x0, x1) = x0 + 1, [zWquot](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [nil] = 0, [from#](x0) = x0 Strict: from# mark X -> from# X 1 + 1X >= 0 + 1X Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 1 + 0X proper zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 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 active zWquot(nil(), XS) -> mark nil() 2 + 1XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 3 + 0X + 0XS + 1Y + 0YS >= 3 + 0X + 0XS + 1Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active zWquot(XS, nil()) -> mark nil() 2 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 3 + 1Y >= 2 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 3 + 0X + 1Y >= 4 + 0X + 1Y active quot(X1, X2) -> quot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active minus(s X, s Y) -> mark minus(X, Y) 2 + 0X + 0Y >= 2 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X1, X2) -> minus(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 2 + 0X >= 2 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 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: { quot#(X1, mark X2) -> quot#(X1, X2), quot#(mark X1, X2) -> quot#(X1, X2), quot#(ok X1, ok X2) -> quot#(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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + 1, [minus](x0, x1) = 1, [quot](x0, x1) = x0 + 1, [zWquot](x0, x1) = 0, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 1, [quot#](x0, x1) = x0 + 1 Strict: quot#(ok X1, ok X2) -> quot#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 quot#(mark X1, X2) -> quot#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 quot#(X1, mark X2) -> quot#(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 zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 2 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 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 active zWquot(nil(), XS) -> mark nil() 1 + 0XS >= 2 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 1 + 0X + 0XS + 0Y + 0YS >= 3 + 0X + 0XS + 1Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zWquot(XS, nil()) -> mark nil() 1 + 0XS >= 2 active quot(0(), s Y) -> mark 0() 3 + 1Y >= 2 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 3 + 0X + 1Y >= 4 + 0X + 1Y active quot(X1, X2) -> quot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active minus(s X, s Y) -> mark minus(X, Y) 2 + 0X + 0Y >= 2 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X1, X2) -> minus(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 2 + 0X >= 2 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 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: {quot#(X1, mark X2) -> quot#(X1, X2)} SCC (1): Strict: {quot#(X1, mark X2) -> quot#(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 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, active minus(X, 0()) -> mark 0(), active minus(X1, X2) -> minus(X1, active X2), active minus(X1, X2) -> minus(active X1, X2), active minus(s X, s Y) -> mark minus(X, Y), active quot(X1, X2) -> quot(X1, active X2), active quot(X1, X2) -> quot(active X1, X2), active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y), active quot(0(), s Y) -> mark 0(), active zWquot(XS, nil()) -> mark nil(), active zWquot(X1, X2) -> zWquot(X1, active X2), active zWquot(X1, X2) -> zWquot(active X1, X2), active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)), active zWquot(nil(), XS) -> mark nil(), 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), minus(X1, mark X2) -> mark minus(X1, X2), minus(mark X1, X2) -> mark minus(X1, X2), minus(ok X1, ok X2) -> ok minus(X1, X2), quot(X1, mark X2) -> mark quot(X1, X2), quot(mark X1, X2) -> mark quot(X1, X2), quot(ok X1, ok X2) -> ok quot(X1, X2), zWquot(X1, mark X2) -> mark zWquot(X1, X2), zWquot(mark X1, X2) -> mark zWquot(X1, X2), zWquot(ok X1, ok X2) -> ok zWquot(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper from X -> from proper X, proper s X -> s proper X, proper sel(X1, X2) -> sel(proper X1, proper X2), proper 0() -> ok 0(), proper minus(X1, X2) -> minus(proper X1, proper X2), proper quot(X1, X2) -> quot(proper X1, proper X2), proper nil() -> ok nil(), proper zWquot(X1, X2) -> zWquot(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, [sel](x0, x1) = x0 + 1, [minus](x0, x1) = 1, [quot](x0, x1) = x0 + 1, [zWquot](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [from](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [nil] = 0, [quot#](x0, x1) = x0 Strict: quot#(X1, mark X2) -> quot#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 1 + 0X proper zWquot(X1, X2) -> zWquot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper nil() -> ok nil() 0 >= 1 proper quot(X1, X2) -> quot(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper minus(X1, X2) -> minus(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper sel(X1, X2) -> sel(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 zWquot(ok X1, ok X2) -> ok zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(mark X1, X2) -> mark zWquot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 zWquot(X1, mark X2) -> mark zWquot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(ok X1, ok X2) -> ok quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(mark X1, X2) -> mark quot(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 quot(X1, mark X2) -> mark quot(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 minus(ok X1, ok X2) -> ok minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(mark X1, X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 minus(X1, mark X2) -> mark minus(X1, X2) 1 + 0X1 + 0X2 >= 2 + 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 active zWquot(nil(), XS) -> mark nil() 2 + 1XS >= 1 active zWquot(cons(X, XS), cons(Y, YS)) -> mark cons(quot(X, Y), zWquot(XS, YS)) 3 + 0X + 0XS + 1Y + 0YS >= 3 + 0X + 0XS + 1Y + 0YS active zWquot(X1, X2) -> zWquot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active zWquot(X1, X2) -> zWquot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active zWquot(XS, nil()) -> mark nil() 2 + 0XS >= 1 active quot(0(), s Y) -> mark 0() 3 + 1Y >= 2 active quot(s X, s Y) -> mark s quot(minus(X, Y), s Y) 3 + 0X + 1Y >= 4 + 0X + 1Y active quot(X1, X2) -> quot(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active quot(X1, X2) -> quot(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active minus(s X, s Y) -> mark minus(X, Y) 2 + 0X + 0Y >= 2 + 0X + 0Y active minus(X1, X2) -> minus(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X1, X2) -> minus(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active minus(X, 0()) -> mark 0() 2 + 0X >= 2 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 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