MAYBE Time: 0.687148 TRS: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} DP: DP: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2), f# mark X -> f# X, f# ok X -> f# X, g# mark X -> g# X, g# ok X -> g# X, active# cons(X1, X2) -> cons#(active X1, X2), active# cons(X1, X2) -> active# X1, active# f X -> cons#(X, f g X), active# f X -> f# g X, active# f X -> f# active X, active# f X -> g# X, active# f X -> active# X, active# g X -> g# active X, active# g X -> active# X, active# g s X -> g# X, active# g s X -> s# g X, active# g s X -> s# s g X, active# g 0() -> s# 0(), active# s X -> active# X, active# s X -> s# 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 X, cons(Y, Z)) -> sel#(X, Z), s# mark X -> s# X, s# ok X -> s# X, sel#(X1, mark X2) -> sel#(X1, X2), sel#(mark X1, X2) -> sel#(X1, X2), sel#(ok X1, ok X2) -> sel#(X1, X2), proper# cons(X1, X2) -> cons#(proper X1, proper X2), proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> f# proper X, proper# f X -> proper# X, proper# g X -> g# proper X, proper# g 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, 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), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} UR: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), a(x, y) -> x, a(x, y) -> y} EDG: { (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (sel#(mark X1, X2) -> sel#(X1, X2), sel#(ok X1, ok X2) -> sel#(X1, X2)) (sel#(mark X1, X2) -> sel#(X1, X2), sel#(mark X1, X2) -> sel#(X1, X2)) (sel#(mark X1, X2) -> sel#(X1, X2), sel#(X1, mark X2) -> sel#(X1, X2)) (active# f X -> f# g X, f# ok X -> f# X) (active# f X -> f# g X, f# mark X -> f# X) (active# g X -> g# active X, g# ok X -> g# X) (active# g X -> g# active X, g# mark X -> g# X) (active# s X -> s# active X, s# ok X -> s# X) (active# s X -> s# active X, s# mark X -> s# X) (proper# g X -> g# proper X, g# ok X -> g# X) (proper# g X -> g# proper X, g# mark X -> g# X) (top# mark X -> top# proper X, top# ok X -> top# active X) (top# mark X -> top# proper X, top# ok X -> active# X) (top# mark X -> top# proper X, top# mark X -> top# proper X) (top# mark X -> top# proper X, top# mark X -> proper# X) (active# sel(X1, X2) -> sel#(X1, active X2), sel#(ok X1, ok X2) -> sel#(X1, X2)) (active# sel(X1, X2) -> sel#(X1, active X2), sel#(mark X1, X2) -> sel#(X1, X2)) (active# sel(X1, X2) -> sel#(X1, active X2), sel#(X1, mark X2) -> sel#(X1, X2)) (proper# sel(X1, X2) -> sel#(proper X1, proper X2), sel#(ok X1, ok X2) -> sel#(X1, X2)) (proper# sel(X1, X2) -> sel#(proper X1, proper X2), sel#(mark X1, X2) -> sel#(X1, X2)) (proper# sel(X1, X2) -> sel#(proper X1, proper X2), sel#(X1, mark X2) -> sel#(X1, X2)) (proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# cons(X1, X2) -> proper# X2, proper# g X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# g X -> g# proper X) (proper# cons(X1, X2) -> proper# X2, proper# f X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# f X -> f# proper X) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# cons(X1, X2) -> active# X1, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (active# cons(X1, X2) -> active# X1, active# sel(X1, X2) -> sel#(active X1, X2)) (active# cons(X1, X2) -> active# X1, active# sel(X1, X2) -> sel#(X1, active X2)) (active# cons(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2) (active# cons(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# s X -> s# active X) (active# cons(X1, X2) -> active# X1, active# s X -> active# X) (active# cons(X1, X2) -> active# X1, active# g 0() -> s# 0()) (active# cons(X1, X2) -> active# X1, active# g s X -> s# s g X) (active# cons(X1, X2) -> active# X1, active# g s X -> s# g X) (active# cons(X1, X2) -> active# X1, active# g s X -> g# X) (active# cons(X1, X2) -> active# X1, active# g X -> active# X) (active# cons(X1, X2) -> active# X1, active# g X -> g# active X) (active# cons(X1, X2) -> active# X1, active# f X -> active# X) (active# cons(X1, X2) -> active# X1, active# f X -> g# X) (active# cons(X1, X2) -> active# X1, active# f X -> f# active X) (active# cons(X1, X2) -> active# X1, active# f X -> f# g X) (active# cons(X1, X2) -> active# X1, active# f X -> cons#(X, f g X)) (active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (proper# cons(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# cons(X1, X2) -> proper# X1, proper# g X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# g X -> g# proper X) (proper# cons(X1, X2) -> proper# X1, proper# f X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# f X -> f# proper X) (proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# g s X -> s# s g X, s# ok X -> s# X) (active# g s X -> s# s g X, s# mark X -> s# X) (active# f X -> cons#(X, f g X), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# f X -> cons#(X, f g X), cons#(mark X1, X2) -> cons#(X1, X2)) (f# ok X -> f# X, f# ok X -> f# X) (f# ok X -> f# X, f# mark X -> f# X) (g# ok X -> g# X, g# ok X -> g# X) (g# ok X -> g# X, g# mark X -> g# X) (active# f X -> active# X, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (active# f X -> active# X, active# sel(X1, X2) -> sel#(active X1, X2)) (active# f X -> active# X, active# sel(X1, X2) -> sel#(X1, active X2)) (active# f X -> active# X, active# sel(X1, X2) -> active# X2) (active# f X -> active# X, active# sel(X1, X2) -> active# X1) (active# f X -> active# X, active# s X -> s# active X) (active# f X -> active# X, active# s X -> active# X) (active# f X -> active# X, active# g 0() -> s# 0()) (active# f X -> active# X, active# g s X -> s# s g X) (active# f X -> active# X, active# g s X -> s# g X) (active# f X -> active# X, active# g s X -> g# X) (active# f X -> active# X, active# g X -> active# X) (active# f X -> active# X, active# g X -> g# active X) (active# f X -> active# X, active# f X -> active# X) (active# f X -> active# X, active# f X -> g# X) (active# f X -> active# X, active# f X -> f# active X) (active# f X -> active# X, active# f X -> f# g X) (active# f X -> active# X, active# f X -> cons#(X, f g X)) (active# f X -> active# X, active# cons(X1, X2) -> active# X1) (active# f X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# g s X -> g# X, g# ok X -> g# X) (active# g s X -> g# X, g# mark X -> g# X) (s# mark X -> s# X, s# ok X -> s# X) (s# mark X -> s# X, s# mark X -> s# X) (proper# f X -> proper# X, proper# sel(X1, X2) -> proper# X2) (proper# f X -> proper# X, proper# sel(X1, X2) -> proper# X1) (proper# f X -> proper# X, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# f X -> proper# X, proper# s X -> proper# X) (proper# f X -> proper# X, proper# s X -> s# proper X) (proper# f X -> proper# X, proper# g X -> proper# X) (proper# f X -> proper# X, proper# g X -> g# proper X) (proper# f X -> proper# X, proper# f X -> proper# X) (proper# f X -> proper# X, proper# f X -> f# proper X) (proper# f X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# f X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# f X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# s X -> proper# X, proper# sel(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# sel(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# s X -> proper# X, proper# s X -> proper# X) (proper# s X -> proper# X, proper# s X -> s# proper X) (proper# s X -> proper# X, proper# g X -> proper# X) (proper# s X -> proper# X, proper# g X -> g# proper X) (proper# s X -> proper# X, proper# f X -> proper# X) (proper# s X -> proper# X, proper# f X -> f# proper X) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (top# ok X -> active# X, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (top# ok X -> active# X, active# sel(X1, X2) -> sel#(active X1, X2)) (top# ok X -> active# X, active# sel(X1, X2) -> sel#(X1, active X2)) (top# ok X -> active# X, active# sel(X1, X2) -> active# X2) (top# ok X -> active# X, active# sel(X1, X2) -> active# X1) (top# ok X -> active# X, active# s X -> s# active X) (top# ok X -> active# X, active# s X -> active# X) (top# ok X -> active# X, active# g 0() -> s# 0()) (top# ok X -> active# X, active# g s X -> s# s g X) (top# ok X -> active# X, active# g s X -> s# g X) (top# ok X -> active# X, active# g s X -> g# X) (top# ok X -> active# X, active# g X -> active# X) (top# ok X -> active# X, active# g X -> g# active X) (top# ok X -> active# X, active# f X -> active# X) (top# ok X -> active# X, active# f X -> g# X) (top# ok X -> active# X, active# f X -> f# active X) (top# ok X -> active# X, active# f X -> f# g X) (top# ok X -> active# X, active# f X -> cons#(X, f g X)) (top# ok X -> active# X, active# cons(X1, X2) -> active# X1) (top# ok X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# cons(X1, X2) -> cons#(active X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# cons(X1, X2) -> cons#(active X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (active# sel(X1, X2) -> sel#(active X1, X2), sel#(X1, mark X2) -> sel#(X1, X2)) (active# sel(X1, X2) -> sel#(active X1, X2), sel#(mark X1, X2) -> sel#(X1, X2)) (active# sel(X1, X2) -> sel#(active X1, X2), sel#(ok X1, ok X2) -> sel#(X1, X2)) (top# mark X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# f X -> f# proper X) (top# mark X -> proper# X, proper# f X -> proper# X) (top# mark X -> proper# X, proper# g X -> g# proper X) (top# mark X -> proper# X, proper# g X -> proper# X) (top# mark X -> proper# X, proper# s X -> s# proper X) (top# mark X -> proper# X, proper# s X -> proper# X) (top# mark X -> proper# X, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (top# mark X -> proper# X, proper# sel(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# sel(X1, X2) -> proper# X2) (proper# g X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# g X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# g X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# g X -> proper# X, proper# f X -> f# proper X) (proper# g X -> proper# X, proper# f X -> proper# X) (proper# g X -> proper# X, proper# g X -> g# proper X) (proper# g X -> proper# X, proper# g X -> proper# X) (proper# g X -> proper# X, proper# s X -> s# proper X) (proper# g X -> proper# X, proper# s X -> proper# X) (proper# g X -> proper# X, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# g X -> proper# X, proper# sel(X1, X2) -> proper# X1) (proper# g X -> proper# X, proper# sel(X1, X2) -> proper# X2) (s# ok X -> s# X, s# mark X -> s# X) (s# ok X -> s# X, s# ok X -> s# X) (active# s X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# s X -> active# X, active# cons(X1, X2) -> active# X1) (active# s X -> active# X, active# f X -> cons#(X, f g X)) (active# s X -> active# X, active# f X -> f# g X) (active# s X -> active# X, active# f X -> f# active X) (active# s X -> active# X, active# f X -> g# X) (active# s X -> active# X, active# f X -> active# X) (active# s X -> active# X, active# g X -> g# active X) (active# s X -> active# X, active# g X -> active# X) (active# s X -> active# X, active# g s X -> g# X) (active# s X -> active# X, active# g s X -> s# g X) (active# s X -> active# X, active# g s X -> s# s g X) (active# s X -> active# X, active# g 0() -> s# 0()) (active# s X -> active# X, active# s X -> active# X) (active# s X -> active# X, active# s X -> s# active X) (active# s X -> active# X, active# sel(X1, X2) -> active# X1) (active# s X -> active# X, active# sel(X1, X2) -> active# X2) (active# s X -> active# X, active# sel(X1, X2) -> sel#(X1, active X2)) (active# s X -> active# X, active# sel(X1, X2) -> sel#(active X1, X2)) (active# s X -> active# X, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (active# g X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# g X -> active# X, active# cons(X1, X2) -> active# X1) (active# g X -> active# X, active# f X -> cons#(X, f g X)) (active# g X -> active# X, active# f X -> f# g X) (active# g X -> active# X, active# f X -> f# active X) (active# g X -> active# X, active# f X -> g# X) (active# g X -> active# X, active# f X -> active# X) (active# g X -> active# X, active# g X -> g# active X) (active# g X -> active# X, active# g X -> active# X) (active# g X -> active# X, active# g s X -> g# X) (active# g X -> active# X, active# g s X -> s# g X) (active# g X -> active# X, active# g s X -> s# s g X) (active# g X -> active# X, active# g 0() -> s# 0()) (active# g X -> active# X, active# s X -> active# X) (active# g X -> active# X, active# s X -> s# active X) (active# g X -> active# X, active# sel(X1, X2) -> active# X1) (active# g X -> active# X, active# sel(X1, X2) -> active# X2) (active# g X -> active# X, active# sel(X1, X2) -> sel#(X1, active X2)) (active# g X -> active# X, active# sel(X1, X2) -> sel#(active X1, X2)) (active# g X -> active# X, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (active# f X -> g# X, g# mark X -> g# X) (active# f X -> g# X, g# ok X -> g# X) (g# mark X -> g# X, g# mark X -> g# X) (g# mark X -> g# X, g# ok X -> g# X) (f# mark X -> f# X, f# mark X -> f# X) (f# mark X -> f# X, f# ok X -> f# X) (active# sel(s X, cons(Y, Z)) -> sel#(X, Z), sel#(X1, mark X2) -> sel#(X1, X2)) (active# sel(s X, cons(Y, Z)) -> sel#(X, Z), sel#(mark X1, X2) -> sel#(X1, X2)) (active# sel(s X, cons(Y, Z)) -> sel#(X, Z), sel#(ok X1, ok X2) -> sel#(X1, X2)) (proper# sel(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# sel(X1, X2) -> proper# X1, proper# f X -> f# proper X) (proper# sel(X1, X2) -> proper# X1, proper# f X -> proper# X) (proper# sel(X1, X2) -> proper# X1, proper# g X -> g# proper X) (proper# sel(X1, X2) -> proper# X1, proper# g X -> proper# X) (proper# sel(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# sel(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2) (active# sel(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# sel(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X1, active# f X -> cons#(X, f g X)) (active# sel(X1, X2) -> active# X1, active# f X -> f# g X) (active# sel(X1, X2) -> active# X1, active# f X -> f# active X) (active# sel(X1, X2) -> active# X1, active# f X -> g# X) (active# sel(X1, X2) -> active# X1, active# f X -> active# X) (active# sel(X1, X2) -> active# X1, active# g X -> g# active X) (active# sel(X1, X2) -> active# X1, active# g X -> active# X) (active# sel(X1, X2) -> active# X1, active# g s X -> g# X) (active# sel(X1, X2) -> active# X1, active# g s X -> s# g X) (active# sel(X1, X2) -> active# X1, active# g s X -> s# s g X) (active# sel(X1, X2) -> active# X1, active# g 0() -> s# 0()) (active# sel(X1, X2) -> active# X1, active# s X -> active# X) (active# sel(X1, X2) -> active# X1, active# s X -> s# active X) (active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2) (active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> sel#(X1, active X2)) (active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> sel#(active X1, X2)) (active# sel(X1, X2) -> active# X1, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (proper# sel(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# sel(X1, X2) -> proper# X2, proper# f X -> f# proper X) (proper# sel(X1, X2) -> proper# X2, proper# f X -> proper# X) (proper# sel(X1, X2) -> proper# X2, proper# g X -> g# proper X) (proper# sel(X1, X2) -> proper# X2, proper# g X -> proper# X) (proper# sel(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# sel(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# sel(X1, X2) -> proper# X2, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X2) (active# sel(X1, X2) -> active# X2, active# cons(X1, X2) -> cons#(active X1, X2)) (active# sel(X1, X2) -> active# X2, active# cons(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X2, active# f X -> cons#(X, f g X)) (active# sel(X1, X2) -> active# X2, active# f X -> f# g X) (active# sel(X1, X2) -> active# X2, active# f X -> f# active X) (active# sel(X1, X2) -> active# X2, active# f X -> g# X) (active# sel(X1, X2) -> active# X2, active# f X -> active# X) (active# sel(X1, X2) -> active# X2, active# g X -> g# active X) (active# sel(X1, X2) -> active# X2, active# g X -> active# X) (active# sel(X1, X2) -> active# X2, active# g s X -> g# X) (active# sel(X1, X2) -> active# X2, active# g s X -> s# g X) (active# sel(X1, X2) -> active# X2, active# g s X -> s# s g X) (active# sel(X1, X2) -> active# X2, active# g 0() -> s# 0()) (active# sel(X1, X2) -> active# X2, active# s X -> active# X) (active# sel(X1, X2) -> active# X2, active# s X -> s# active X) (active# sel(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X2) (active# sel(X1, X2) -> active# X2, active# sel(X1, X2) -> sel#(X1, active X2)) (active# sel(X1, X2) -> active# X2, active# sel(X1, X2) -> sel#(active X1, X2)) (active# sel(X1, X2) -> active# X2, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (proper# cons(X1, X2) -> cons#(proper X1, proper X2), cons#(mark X1, X2) -> cons#(X1, X2)) (proper# cons(X1, X2) -> cons#(proper X1, proper X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (top# ok X -> top# active X, top# mark X -> proper# X) (top# ok X -> top# active X, top# mark X -> top# proper X) (top# ok X -> top# active X, top# ok X -> active# X) (top# ok X -> top# active X, top# ok X -> top# active X) (proper# s X -> s# proper X, s# mark X -> s# X) (proper# s X -> s# proper X, s# ok X -> s# X) (proper# f X -> f# proper X, f# mark X -> f# X) (proper# f X -> f# proper X, f# ok X -> f# X) (active# g s X -> s# g X, s# mark X -> s# X) (active# g s X -> s# g X, s# ok X -> s# X) (active# f X -> f# active X, f# mark X -> f# X) (active# f X -> f# active X, f# ok X -> f# X) (sel#(ok X1, ok X2) -> sel#(X1, X2), sel#(X1, mark X2) -> sel#(X1, X2)) (sel#(ok X1, ok X2) -> sel#(X1, X2), sel#(mark X1, X2) -> sel#(X1, X2)) (sel#(ok X1, ok X2) -> sel#(X1, X2), sel#(ok X1, ok X2) -> sel#(X1, X2)) (sel#(X1, mark X2) -> sel#(X1, X2), sel#(X1, mark X2) -> sel#(X1, X2)) (sel#(X1, mark X2) -> sel#(X1, X2), sel#(mark X1, X2) -> sel#(X1, X2)) (sel#(X1, mark X2) -> sel#(X1, X2), sel#(ok X1, ok X2) -> sel#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) } STATUS: arrows: 0.860118 SCCS (8): Scc: {top# mark X -> top# proper X, top# ok X -> top# active X} Scc: {active# cons(X1, X2) -> active# X1, active# f X -> active# X, active# g X -> active# X, active# s X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2} Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> proper# X, proper# g X -> proper# X, proper# s X -> proper# X, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2} Scc: {s# mark X -> s# X, s# ok X -> s# X} Scc: {g# mark X -> g# X, g# ok X -> g# X} Scc: {f# mark X -> f# X, f# ok X -> f# X} 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 (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), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} Fail SCC (6): Strict: {active# cons(X1, X2) -> active# X1, active# f X -> active# X, active# g 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), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = x0 + x1 + 1, [mark](x0) = 0, [f](x0) = x0, [g](x0) = x0, [active](x0) = 0, [s](x0) = x0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [active#](x0) = x0 Strict: active# sel(X1, X2) -> active# X2 1 + 1X1 + 1X2 >= 0 + 1X2 active# sel(X1, X2) -> active# X1 1 + 1X1 + 1X2 >= 0 + 1X1 active# s X -> active# X 0 + 1X >= 0 + 1X active# g X -> active# X 0 + 1X >= 0 + 1X active# f X -> active# X 0 + 1X >= 0 + 1X active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper s X -> s proper X 0 + 0X >= 0 + 0X proper g X -> g proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 0 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 0 + 0X >= 0 + 0X active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z 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 g 0() -> mark s 0() 0 >= 0 active g s X -> mark s s g X 0 + 0X >= 0 + 0X active g X -> g active X 0 + 0X >= 0 + 0X active f X -> f active X 0 + 0X >= 0 + 0X active f X -> mark cons(X, f g X) 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 g ok X -> ok g X 1 + 1X >= 1 + 1X g mark X -> mark g X 0 + 0X >= 0 + 0X f ok X -> ok f X 1 + 1X >= 1 + 1X f mark X -> mark f X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1, active# f X -> active# X, active# g X -> active# X, active# s X -> active# X} SCC (4): Strict: {active# cons(X1, X2) -> active# X1, active# f X -> active# X, active# g 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), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = x0 + 1, [mark](x0) = 0, [f](x0) = x0, [g](x0) = x0, [active](x0) = 0, [s](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [active#](x0) = x0 Strict: active# s X -> active# X 1 + 1X >= 0 + 1X active# g X -> active# X 0 + 1X >= 0 + 1X active# f X -> active# X 0 + 1X >= 0 + 1X active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper s X -> s proper X 0 + 0X >= 1 + 0X proper g X -> g proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 0 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 1 + 0X >= 0 + 0X active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active s X -> s active X 0 + 0X >= 1 + 0X active g 0() -> mark s 0() 0 >= 0 active g s X -> mark s s g X 0 + 0X >= 0 + 0X active g X -> g active X 0 + 0X >= 0 + 0X active f X -> f active X 0 + 0X >= 0 + 0X active f X -> mark cons(X, f g X) 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 g ok X -> ok g X 1 + 1X >= 1 + 1X g mark X -> mark g X 0 + 0X >= 0 + 0X f ok X -> ok f X 1 + 1X >= 1 + 1X f mark X -> mark f X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1, active# f X -> active# X, active# g X -> active# X} SCC (3): Strict: {active# cons(X1, X2) -> active# X1, active# f X -> active# X, active# g X -> active# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = 0, [mark](x0) = 0, [f](x0) = x0, [g](x0) = x0 + 1, [active](x0) = 0, [s](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [active#](x0) = x0 Strict: active# g X -> active# X 1 + 1X >= 0 + 1X active# f X -> active# X 0 + 1X >= 0 + 1X active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper s X -> s proper X 0 + 0X >= 1 + 0X proper g X -> g proper X 0 + 0X >= 1 + 0X proper f X -> f proper X 0 + 0X >= 0 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 1 + 0X >= 0 + 0X active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 1 + 0X active g 0() -> mark s 0() 0 >= 0 active g s X -> mark s s g X 0 + 0X >= 0 + 0X active g X -> g active X 0 + 0X >= 1 + 0X active f X -> f active X 0 + 0X >= 0 + 0X active f X -> mark cons(X, f g X) 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 g ok X -> ok g X 2 + 1X >= 2 + 1X g mark X -> mark g X 1 + 0X >= 0 + 0X f ok X -> ok f X 1 + 1X >= 1 + 1X f mark X -> mark f X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1, active# f X -> active# X} SCC (2): Strict: {active# cons(X1, X2) -> active# X1, active# f X -> active# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = 0, [mark](x0) = 0, [f](x0) = x0 + 1, [g](x0) = 0, [active](x0) = 0, [s](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [active#](x0) = x0 Strict: active# f X -> active# X 1 + 1X >= 0 + 1X active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper s X -> s proper X 0 + 0X >= 0 + 0X proper g X -> g proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 1 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 0 + 0X active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 0 + 0X active g 0() -> mark s 0() 0 >= 0 active g s X -> mark s s g X 0 + 0X >= 0 + 0X active g X -> g active X 0 + 0X >= 0 + 0X active f X -> f active X 0 + 0X >= 1 + 0X active f X -> mark cons(X, f g X) 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 g ok X -> ok g X 0 + 0X >= 1 + 0X g mark X -> mark g X 0 + 0X >= 0 + 0X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f 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), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [f](x0) = x0 + 1, [g](x0) = 0, [active](x0) = x0 + 1, [s](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [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 sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper s X -> s proper X 0 + 0X >= 1 + 0X proper g X -> g proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 1 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X active sel(0(), cons(X, Y)) -> mark X 3 + 1X + 0Y >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 1Y + 0Z >= 2 + 0X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active s X -> s active X 2 + 1X >= 2 + 1X active g 0() -> mark s 0() 1 >= 3 active g s X -> mark s s g X 1 + 0X >= 3 + 0X active g X -> g active X 1 + 0X >= 0 + 0X active f X -> f active X 2 + 1X >= 2 + 1X active f X -> mark cons(X, f g X) 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 g ok X -> ok g X 0 + 0X >= 1 + 0X g mark X -> mark g X 0 + 0X >= 1 + 0X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f 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 (7): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> proper# X, proper# g 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), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = x0 + x1 + 1, [mark](x0) = 0, [f](x0) = x0, [g](x0) = x0, [active](x0) = 0, [s](x0) = x0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [proper#](x0) = x0 Strict: proper# sel(X1, X2) -> proper# X2 1 + 1X1 + 1X2 >= 0 + 1X2 proper# sel(X1, X2) -> proper# X1 1 + 1X1 + 1X2 >= 0 + 1X1 proper# s X -> proper# X 0 + 1X >= 0 + 1X proper# g X -> proper# X 0 + 1X >= 0 + 1X proper# f X -> proper# X 0 + 1X >= 0 + 1X proper# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper s X -> s proper X 0 + 0X >= 0 + 0X proper g X -> g proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 0 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 0 + 0X >= 0 + 0X active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z 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 g 0() -> mark s 0() 0 >= 0 active g s X -> mark s s g X 0 + 0X >= 0 + 0X active g X -> g active X 0 + 0X >= 0 + 0X active f X -> f active X 0 + 0X >= 0 + 0X active f X -> mark cons(X, f g X) 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 g ok X -> ok g X 1 + 1X >= 1 + 1X g mark X -> mark g X 0 + 0X >= 0 + 0X f ok X -> ok f X 1 + 1X >= 1 + 1X f mark X -> mark f X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> proper# X, proper# g X -> proper# X, proper# s X -> proper# X} SCC (5): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> proper# X, proper# g 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), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = x0 + 1, [mark](x0) = 0, [f](x0) = x0, [g](x0) = x0, [active](x0) = 0, [s](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [proper#](x0) = x0 Strict: proper# s X -> proper# X 1 + 1X >= 0 + 1X proper# g X -> proper# X 0 + 1X >= 0 + 1X proper# f X -> proper# X 0 + 1X >= 0 + 1X proper# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper s X -> s proper X 0 + 0X >= 1 + 0X proper g X -> g proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 0 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 1 + 0X >= 0 + 0X active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active s X -> s active X 0 + 0X >= 1 + 0X active g 0() -> mark s 0() 0 >= 0 active g s X -> mark s s g X 0 + 0X >= 0 + 0X active g X -> g active X 0 + 0X >= 0 + 0X active f X -> f active X 0 + 0X >= 0 + 0X active f X -> mark cons(X, f g X) 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 g ok X -> ok g X 1 + 1X >= 1 + 1X g mark X -> mark g X 0 + 0X >= 0 + 0X f ok X -> ok f X 1 + 1X >= 1 + 1X f mark X -> mark f X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> proper# X, proper# g X -> proper# X} SCC (4): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> proper# X, proper# g X -> proper# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = 0, [mark](x0) = 0, [f](x0) = x0, [g](x0) = x0 + 1, [active](x0) = 0, [s](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [proper#](x0) = x0 Strict: proper# g X -> proper# X 1 + 1X >= 0 + 1X proper# f X -> proper# X 0 + 1X >= 0 + 1X proper# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper s X -> s proper X 0 + 0X >= 1 + 0X proper g X -> g proper X 0 + 0X >= 1 + 0X proper f X -> f proper X 0 + 0X >= 0 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 1 + 0X >= 0 + 0X active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 1 + 0X active g 0() -> mark s 0() 0 >= 0 active g s X -> mark s s g X 0 + 0X >= 0 + 0X active g X -> g active X 0 + 0X >= 1 + 0X active f X -> f active X 0 + 0X >= 0 + 0X active f X -> mark cons(X, f g X) 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 g ok X -> ok g X 2 + 1X >= 2 + 1X g mark X -> mark g X 1 + 0X >= 0 + 0X f ok X -> ok f X 1 + 1X >= 1 + 1X f mark X -> mark f X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> proper# X} SCC (3): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> proper# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = 0, [mark](x0) = 0, [f](x0) = x0 + 1, [g](x0) = 0, [active](x0) = 0, [s](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [proper#](x0) = x0 Strict: proper# f X -> proper# X 1 + 1X >= 0 + 1X proper# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper s X -> s proper X 0 + 0X >= 0 + 0X proper g X -> g proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 1 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 0 + 0X active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 0 + 0X active g 0() -> mark s 0() 0 >= 0 active g s X -> mark s s g X 0 + 0X >= 0 + 0X active g X -> g active X 0 + 0X >= 0 + 0X active f X -> f active X 0 + 0X >= 1 + 0X active f X -> mark cons(X, f g X) 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 g ok X -> ok g X 0 + 0X >= 1 + 0X g mark X -> mark g X 0 + 0X >= 0 + 0X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f 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), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1 + 1, [sel](x0, x1) = 0, [mark](x0) = x0 + 1, [f](x0) = x0 + 1, [g](x0) = x0 + 1, [active](x0) = 0, [s](x0) = 0, [proper](x0) = 0, [ok](x0) = 0, [top](x0) = 0, [0] = 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 sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 0 proper s X -> s proper X 0 + 0X >= 0 + 0X proper g X -> g proper X 0 + 0X >= 1 + 0X proper f X -> f proper X 0 + 0X >= 1 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 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 s ok X -> ok s X 0 + 0X >= 0 + 0X s mark X -> mark s X 0 + 0X >= 1 + 0X active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 1 + 0X + 0Z active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 0 + 0X active g 0() -> mark s 0() 0 >= 1 active g s X -> mark s s g X 0 + 0X >= 1 + 0X active g X -> g active X 0 + 0X >= 1 + 0X active f X -> f active X 0 + 0X >= 1 + 0X active f X -> mark cons(X, f g X) 0 + 0X >= 4 + 2X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 g ok X -> ok g X 1 + 0X >= 0 + 0X g mark X -> mark g X 2 + 1X >= 2 + 1X f ok X -> ok f X 1 + 0X >= 0 + 0X f mark X -> mark f 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 (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), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = 0, [sel](x0, x1) = 0, [mark](x0) = x0, [f](x0) = 0, [g](x0) = 0, [active](x0) = 0, [s](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [s#](x0) = x0 Strict: s# ok X -> s# X 1 + 1X >= 0 + 1X s# mark X -> s# X 0 + 1X >= 0 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper s X -> s proper X 0 + 0X >= 1 + 0X proper g X -> g proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 0 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 1 + 1X >= 1 + 1X active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 1 + 0X active g 0() -> mark s 0() 0 >= 2 active g s X -> mark s s g X 0 + 0X >= 2 + 0X active g X -> g active X 0 + 0X >= 0 + 0X active f X -> f active X 0 + 0X >= 0 + 0X active f X -> mark cons(X, f g X) 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 g ok X -> ok g X 0 + 0X >= 1 + 0X g mark X -> mark g X 0 + 0X >= 0 + 0X f ok X -> ok f X 0 + 0X >= 1 + 0X f mark X -> mark f 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), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [f](x0) = x0 + 1, [g](x0) = 0, [active](x0) = x0 + 1, [s](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [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 sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper s X -> s proper X 0 + 0X >= 1 + 0X proper g X -> g proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 1 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X active sel(0(), cons(X, Y)) -> mark X 3 + 1X + 0Y >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 1Y + 0Z >= 2 + 0X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active s X -> s active X 2 + 1X >= 2 + 1X active g 0() -> mark s 0() 1 >= 3 active g s X -> mark s s g X 1 + 0X >= 3 + 0X active g X -> g active X 1 + 0X >= 0 + 0X active f X -> f active X 2 + 1X >= 2 + 1X active f X -> mark cons(X, f g X) 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 g ok X -> ok g X 0 + 0X >= 1 + 0X g mark X -> mark g X 0 + 0X >= 1 + 0X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f 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: {g# mark X -> g# X, g# ok X -> g# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = 0, [sel](x0, x1) = 0, [mark](x0) = x0, [f](x0) = 0, [g](x0) = 0, [active](x0) = 0, [s](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [g#](x0) = x0 Strict: g# ok X -> g# X 1 + 1X >= 0 + 1X g# mark X -> g# X 0 + 1X >= 0 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper s X -> s proper X 0 + 0X >= 1 + 0X proper g X -> g proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 0 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 1 + 1X >= 1 + 1X active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 1 + 0X active g 0() -> mark s 0() 0 >= 2 active g s X -> mark s s g X 0 + 0X >= 2 + 0X active g X -> g active X 0 + 0X >= 0 + 0X active f X -> f active X 0 + 0X >= 0 + 0X active f X -> mark cons(X, f g X) 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 g ok X -> ok g X 0 + 0X >= 1 + 0X g mark X -> mark g X 0 + 0X >= 0 + 0X f ok X -> ok f X 0 + 0X >= 1 + 0X f mark X -> mark f 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: {g# mark X -> g# X} SCC (1): Strict: {g# mark X -> g# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [f](x0) = x0 + 1, [g](x0) = 0, [active](x0) = x0 + 1, [s](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [g#](x0) = x0 Strict: g# mark X -> g# 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 sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper s X -> s proper X 0 + 0X >= 1 + 0X proper g X -> g proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 1 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X active sel(0(), cons(X, Y)) -> mark X 3 + 1X + 0Y >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 1Y + 0Z >= 2 + 0X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active s X -> s active X 2 + 1X >= 2 + 1X active g 0() -> mark s 0() 1 >= 3 active g s X -> mark s s g X 1 + 0X >= 3 + 0X active g X -> g active X 1 + 0X >= 0 + 0X active f X -> f active X 2 + 1X >= 2 + 1X active f X -> mark cons(X, f g X) 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 g ok X -> ok g X 0 + 0X >= 1 + 0X g mark X -> mark g X 0 + 0X >= 1 + 0X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f 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: {f# mark X -> f# X, f# ok X -> f# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = 0, [sel](x0, x1) = 0, [mark](x0) = x0, [f](x0) = 0, [g](x0) = 0, [active](x0) = 0, [s](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [f#](x0) = x0 Strict: f# ok X -> f# X 1 + 1X >= 0 + 1X f# mark X -> f# X 0 + 1X >= 0 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper s X -> s proper X 0 + 0X >= 1 + 0X proper g X -> g proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 0 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 1 + 1X >= 1 + 1X active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(X1, X2) -> sel(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 1 + 0X active g 0() -> mark s 0() 0 >= 2 active g s X -> mark s s g X 0 + 0X >= 2 + 0X active g X -> g active X 0 + 0X >= 0 + 0X active f X -> f active X 0 + 0X >= 0 + 0X active f X -> mark cons(X, f g X) 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 g ok X -> ok g X 0 + 0X >= 1 + 0X g mark X -> mark g X 0 + 0X >= 0 + 0X f ok X -> ok f X 0 + 0X >= 1 + 0X f mark X -> mark f 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: {f# mark X -> f# X} SCC (1): Strict: {f# mark X -> f# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [f](x0) = x0 + 1, [g](x0) = 0, [active](x0) = x0 + 1, [s](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [f#](x0) = x0 Strict: f# mark X -> f# 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 sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper s X -> s proper X 0 + 0X >= 1 + 0X proper g X -> g proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 1 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X active sel(0(), cons(X, Y)) -> mark X 3 + 1X + 0Y >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 1Y + 0Z >= 2 + 0X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active s X -> s active X 2 + 1X >= 2 + 1X active g 0() -> mark s 0() 1 >= 3 active g s X -> mark s s g X 1 + 0X >= 3 + 0X active g X -> g active X 1 + 0X >= 0 + 0X active f X -> f active X 2 + 1X >= 2 + 1X active f X -> mark cons(X, f g X) 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 g ok X -> ok g X 0 + 0X >= 1 + 0X g mark X -> mark g X 0 + 0X >= 1 + 0X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f 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), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [f](x0) = 0, [g](x0) = x0 + 1, [active](x0) = x0 + 1, [s](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [sel#](x0, x1) = x0 + 1 Strict: sel#(ok X1, ok X2) -> sel#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel#(mark X1, X2) -> sel#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel#(X1, mark X2) -> sel#(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper s X -> s proper X 0 + 0X >= 0 + 0X proper g X -> g proper X 0 + 0X >= 1 + 0X proper f X -> f proper X 0 + 0X >= 0 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 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 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 1 + 0X active sel(0(), cons(X, Y)) -> mark X 3 + 1X + 0Y >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 1Y + 0Z >= 2 + 0X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active s X -> s active X 1 + 0X >= 0 + 0X active g 0() -> mark s 0() 2 >= 1 active g s X -> mark s s g X 2 + 0X >= 1 + 0X active g X -> g active X 2 + 1X >= 2 + 1X active f X -> f active X 1 + 0X >= 0 + 0X active f X -> mark cons(X, f g X) 1 + 0X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 g ok X -> ok g X 2 + 1X >= 2 + 1X g mark X -> mark g X 2 + 1X >= 2 + 1X f ok X -> ok f X 0 + 0X >= 1 + 0X f mark X -> mark f X 0 + 0X >= 1 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 SCCS (1): Scc: {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), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [f](x0) = x0 + 1, [g](x0) = 0, [active](x0) = x0 + 1, [s](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [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 sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper s X -> s proper X 0 + 0X >= 1 + 0X proper g X -> g proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 1 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X active sel(0(), cons(X, Y)) -> mark X 3 + 1X + 0Y >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 1Y + 0Z >= 2 + 0X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active s X -> s active X 2 + 1X >= 2 + 1X active g 0() -> mark s 0() 1 >= 3 active g s X -> mark s s g X 1 + 0X >= 3 + 0X active g X -> g active X 1 + 0X >= 0 + 0X active f X -> f active X 2 + 1X >= 2 + 1X active f X -> mark cons(X, f g X) 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 g ok X -> ok g X 0 + 0X >= 1 + 0X g mark X -> mark g X 0 + 0X >= 1 + 0X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f 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), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [f](x0) = x0 + 1, [g](x0) = x0 + 1, [active](x0) = x0 + 1, [s](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [cons#](x0, x1) = x0 Strict: cons#(ok X1, ok X2) -> cons#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons#(mark X1, X2) -> cons#(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 1 proper s X -> s proper X 0 + 0X >= 0 + 0X proper g X -> g proper X 0 + 0X >= 1 + 0X proper f X -> f proper X 0 + 0X >= 1 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 1 + 0X active sel(0(), cons(X, Y)) -> mark X 3 + 1X + 0Y >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 1Y + 0Z >= 2 + 0X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active s X -> s active X 1 + 0X >= 0 + 0X active g 0() -> mark s 0() 2 >= 1 active g s X -> mark s s g X 2 + 0X >= 1 + 0X active g X -> g active X 2 + 1X >= 2 + 1X active f X -> f active X 2 + 1X >= 2 + 1X active f X -> mark cons(X, f g X) 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 g ok X -> ok g X 2 + 1X >= 2 + 1X g mark X -> mark g X 2 + 1X >= 2 + 1X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f 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), f mark X -> mark f X, f ok X -> ok f X, g mark X -> mark g X, g ok X -> ok g X, active cons(X1, X2) -> cons(active X1, X2), active f X -> mark cons(X, f g X), active f X -> f active X, active g X -> g active X, active g s X -> mark s s g X, active g 0() -> mark s 0(), 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 X, cons(Y, Z)) -> mark sel(X, Z), active sel(0(), cons(X, Y)) -> mark X, s mark X -> mark s X, s ok X -> ok s X, sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), proper cons(X1, X2) -> cons(proper X1, proper X2), proper f X -> f proper X, proper g X -> g proper X, proper s X -> s proper X, proper 0() -> ok 0(), proper sel(X1, X2) -> sel(proper X1, proper X2), top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [f](x0) = x0 + 1, [g](x0) = 0, [active](x0) = x0 + 1, [s](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [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 sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper 0() -> ok 0() 0 >= 2 proper s X -> s proper X 0 + 0X >= 1 + 0X proper g X -> g proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 1 + 0X proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X active sel(0(), cons(X, Y)) -> mark X 3 + 1X + 0Y >= 1 + 1X active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 1Y + 0Z >= 2 + 0X + 1Z active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 active s X -> s active X 2 + 1X >= 2 + 1X active g 0() -> mark s 0() 1 >= 3 active g s X -> mark s s g X 1 + 0X >= 3 + 0X active g X -> g active X 1 + 0X >= 0 + 0X active f X -> f active X 2 + 1X >= 2 + 1X active f X -> mark cons(X, f g X) 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 g ok X -> ok g X 0 + 0X >= 1 + 0X g mark X -> mark g X 0 + 0X >= 1 + 0X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f 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