MAYBE Time: 6.465943 TRS: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} DP: DP: { active# dbl X -> active# X, active# dbl X -> dbl# active X, active# dbl s X -> dbl# X, active# dbl s X -> s# dbl X, active# dbl s X -> s# s dbl X, active# dbls X -> active# X, active# dbls X -> dbls# active X, active# dbls cons(X, Y) -> dbl# X, active# dbls cons(X, Y) -> dbls# Y, active# dbls cons(X, Y) -> cons#(dbl X, dbls Y), 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), active# indx(X1, X2) -> active# X1, active# indx(X1, X2) -> indx#(active X1, X2), active# indx(cons(X, Y), Z) -> cons#(sel(X, Z), indx(Y, Z)), active# indx(cons(X, Y), Z) -> sel#(X, Z), active# indx(cons(X, Y), Z) -> indx#(Y, Z), active# from X -> s# X, active# from X -> cons#(X, from s X), active# from X -> from# s X, active# dbl1 X -> active# X, active# dbl1 X -> dbl1# active X, active# dbl1 s X -> dbl1# X, active# dbl1 s X -> s1# dbl1 X, active# dbl1 s X -> s1# s1 dbl1 X, active# s1 X -> active# X, active# s1 X -> s1# active X, active# sel1(X1, X2) -> active# X1, active# sel1(X1, X2) -> active# X2, active# sel1(X1, X2) -> sel1#(X1, active X2), active# sel1(X1, X2) -> sel1#(active X1, X2), active# sel1(s X, cons(Y, Z)) -> sel1#(X, Z), active# quote X -> active# X, active# quote X -> quote# active X, active# quote dbl X -> dbl1# X, active# quote s X -> s1# quote X, active# quote s X -> quote# X, active# quote sel(X, Y) -> sel1#(X, Y), dbl# mark X -> dbl# X, dbl# ok X -> dbl# X, s# ok X -> s# X, dbls# mark X -> dbls# X, dbls# ok X -> dbls# X, cons#(ok X1, ok X2) -> cons#(X1, X2), sel#(X1, mark X2) -> sel#(X1, X2), sel#(mark X1, X2) -> sel#(X1, X2), sel#(ok X1, ok X2) -> sel#(X1, X2), indx#(mark X1, X2) -> indx#(X1, X2), indx#(ok X1, ok X2) -> indx#(X1, X2), from# ok X -> from# X, dbl1# mark X -> dbl1# X, dbl1# ok X -> dbl1# X, s1# mark X -> s1# X, s1# ok X -> s1# X, sel1#(X1, mark X2) -> sel1#(X1, X2), sel1#(mark X1, X2) -> sel1#(X1, X2), sel1#(ok X1, ok X2) -> sel1#(X1, X2), quote# mark X -> quote# X, quote# ok X -> quote# X, proper# dbl X -> dbl# proper X, proper# dbl X -> proper# X, proper# s X -> s# proper X, proper# s X -> proper# X, proper# dbls X -> dbls# proper X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2), proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> sel#(proper X1, proper X2), proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> indx#(proper X1, proper X2), proper# indx(X1, X2) -> proper# X1, proper# indx(X1, X2) -> proper# X2, proper# from X -> from# proper X, proper# from X -> proper# X, proper# dbl1 X -> dbl1# proper X, proper# dbl1 X -> proper# X, proper# s1 X -> s1# proper X, proper# s1 X -> proper# X, proper# sel1(X1, X2) -> sel1#(proper X1, proper X2), proper# sel1(X1, X2) -> proper# X1, proper# sel1(X1, X2) -> proper# X2, proper# quote X -> quote# proper X, proper# quote X -> proper# X, top# mark X -> proper# X, top# mark X -> top# proper X, top# ok X -> active# X, top# ok X -> top# active X} TRS: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} UR: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, a(x, y) -> x, a(x, y) -> y} EDG: { (active# dbl s X -> s# dbl X, s# ok X -> s# X) (active# from X -> from# s X, from# ok X -> from# X) (active# dbl1 s X -> s1# dbl1 X, s1# ok X -> s1# X) (active# dbl1 s X -> s1# dbl1 X, s1# mark X -> s1# X) (active# quote X -> quote# active X, quote# ok X -> quote# X) (active# quote X -> quote# active X, quote# mark X -> quote# X) (proper# dbl X -> dbl# proper X, dbl# ok X -> dbl# X) (proper# dbl X -> dbl# proper X, dbl# mark X -> dbl# X) (proper# dbls X -> dbls# proper X, dbls# ok X -> dbls# X) (proper# dbls X -> dbls# proper X, dbls# mark X -> dbls# X) (proper# dbl1 X -> dbl1# proper X, dbl1# ok X -> dbl1# X) (proper# dbl1 X -> dbl1# proper X, dbl1# mark X -> dbl1# X) (proper# quote X -> quote# proper X, quote# ok X -> quote# X) (proper# quote X -> quote# proper X, quote# mark X -> quote# 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) (sel#(X1, mark X2) -> sel#(X1, X2), sel#(ok X1, ok 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#(X1, mark X2) -> sel#(X1, X2)) (sel#(ok X1, ok X2) -> sel#(X1, X2), sel#(ok X1, ok 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#(X1, mark X2) -> sel#(X1, X2)) (indx#(ok X1, ok X2) -> indx#(X1, X2), indx#(ok X1, ok X2) -> indx#(X1, X2)) (indx#(ok X1, ok X2) -> indx#(X1, X2), indx#(mark X1, X2) -> indx#(X1, X2)) (sel1#(mark X1, X2) -> sel1#(X1, X2), sel1#(ok X1, ok X2) -> sel1#(X1, X2)) (sel1#(mark X1, X2) -> sel1#(X1, X2), sel1#(mark X1, X2) -> sel1#(X1, X2)) (sel1#(mark X1, X2) -> sel1#(X1, X2), sel1#(X1, mark X2) -> sel1#(X1, X2)) (active# sel(X1, X2) -> active# X2, active# quote sel(X, Y) -> sel1#(X, Y)) (active# sel(X1, X2) -> active# X2, active# quote s X -> quote# X) (active# sel(X1, X2) -> active# X2, active# quote s X -> s1# quote X) (active# sel(X1, X2) -> active# X2, active# quote dbl X -> dbl1# X) (active# sel(X1, X2) -> active# X2, active# quote X -> quote# active X) (active# sel(X1, X2) -> active# X2, active# quote X -> active# X) (active# sel(X1, X2) -> active# X2, active# sel1(s X, cons(Y, Z)) -> sel1#(X, Z)) (active# sel(X1, X2) -> active# X2, active# sel1(X1, X2) -> sel1#(active X1, X2)) (active# sel(X1, X2) -> active# X2, active# sel1(X1, X2) -> sel1#(X1, active X2)) (active# sel(X1, X2) -> active# X2, active# sel1(X1, X2) -> active# X2) (active# sel(X1, X2) -> active# X2, active# sel1(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X2, active# s1 X -> s1# active X) (active# sel(X1, X2) -> active# X2, active# s1 X -> active# X) (active# sel(X1, X2) -> active# X2, active# dbl1 s X -> s1# s1 dbl1 X) (active# sel(X1, X2) -> active# X2, active# dbl1 s X -> s1# dbl1 X) (active# sel(X1, X2) -> active# X2, active# dbl1 s X -> dbl1# X) (active# sel(X1, X2) -> active# X2, active# dbl1 X -> dbl1# active X) (active# sel(X1, X2) -> active# X2, active# dbl1 X -> active# X) (active# sel(X1, X2) -> active# X2, active# from X -> from# s X) (active# sel(X1, X2) -> active# X2, active# from X -> cons#(X, from s X)) (active# sel(X1, X2) -> active# X2, active# from X -> s# X) (active# sel(X1, X2) -> active# X2, active# indx(cons(X, Y), Z) -> indx#(Y, Z)) (active# sel(X1, X2) -> active# X2, active# indx(cons(X, Y), Z) -> sel#(X, Z)) (active# sel(X1, X2) -> active# X2, active# indx(cons(X, Y), Z) -> cons#(sel(X, Z), indx(Y, Z))) (active# sel(X1, X2) -> active# X2, active# indx(X1, X2) -> indx#(active X1, X2)) (active# sel(X1, X2) -> active# X2, active# indx(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X2, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (active# sel(X1, X2) -> active# X2, active# sel(X1, X2) -> sel#(active X1, 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) -> active# X2) (active# sel(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X2, active# dbls cons(X, Y) -> cons#(dbl X, dbls Y)) (active# sel(X1, X2) -> active# X2, active# dbls cons(X, Y) -> dbls# Y) (active# sel(X1, X2) -> active# X2, active# dbls cons(X, Y) -> dbl# X) (active# sel(X1, X2) -> active# X2, active# dbls X -> dbls# active X) (active# sel(X1, X2) -> active# X2, active# dbls X -> active# X) (active# sel(X1, X2) -> active# X2, active# dbl s X -> s# s dbl X) (active# sel(X1, X2) -> active# X2, active# dbl s X -> s# dbl X) (active# sel(X1, X2) -> active# X2, active# dbl s X -> dbl# X) (active# sel(X1, X2) -> active# X2, active# dbl X -> dbl# active X) (active# sel(X1, X2) -> active# X2, active# dbl X -> active# X) (proper# cons(X1, X2) -> proper# X2, proper# quote X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# quote X -> quote# proper X) (proper# cons(X1, X2) -> proper# X2, proper# sel1(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# sel1(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# sel1(X1, X2) -> sel1#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# s1 X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# s1 X -> s1# proper X) (proper# cons(X1, X2) -> proper# X2, proper# dbl1 X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# dbl1 X -> dbl1# proper X) (proper# cons(X1, X2) -> proper# X2, proper# from X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# from X -> from# proper X) (proper# cons(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# indx(X1, X2) -> indx#(proper X1, proper 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# cons(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# dbls X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# dbls X -> dbls# proper X) (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# dbl X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# dbl X -> dbl# proper X) (proper# indx(X1, X2) -> proper# X2, proper# quote X -> proper# X) (proper# indx(X1, X2) -> proper# X2, proper# quote X -> quote# proper X) (proper# indx(X1, X2) -> proper# X2, proper# sel1(X1, X2) -> proper# X2) (proper# indx(X1, X2) -> proper# X2, proper# sel1(X1, X2) -> proper# X1) (proper# indx(X1, X2) -> proper# X2, proper# sel1(X1, X2) -> sel1#(proper X1, proper X2)) (proper# indx(X1, X2) -> proper# X2, proper# s1 X -> proper# X) (proper# indx(X1, X2) -> proper# X2, proper# s1 X -> s1# proper X) (proper# indx(X1, X2) -> proper# X2, proper# dbl1 X -> proper# X) (proper# indx(X1, X2) -> proper# X2, proper# dbl1 X -> dbl1# proper X) (proper# indx(X1, X2) -> proper# X2, proper# from X -> proper# X) (proper# indx(X1, X2) -> proper# X2, proper# from X -> from# proper X) (proper# indx(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X2) (proper# indx(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1) (proper# indx(X1, X2) -> proper# X2, proper# indx(X1, X2) -> indx#(proper X1, proper X2)) (proper# indx(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X2) (proper# indx(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1) (proper# indx(X1, X2) -> proper# X2, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# indx(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# indx(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# indx(X1, X2) -> proper# 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(active# quote X -> active# X, active# dbls cons(X, Y) -> dbls# Y) (active# quote X -> active# X, active# dbls cons(X, Y) -> dbl# X) (active# quote X -> active# X, active# dbls X -> dbls# active X) (active# quote X -> active# X, active# dbls X -> active# X) (active# quote X -> active# X, active# dbl s X -> s# s dbl X) (active# quote X -> active# X, active# dbl s X -> s# dbl X) (active# quote X -> active# X, active# dbl s X -> dbl# X) (active# quote X -> active# X, active# dbl X -> dbl# active X) (active# quote X -> active# X, active# dbl X -> active# X) (active# quote s X -> quote# X, quote# ok X -> quote# X) (active# quote s X -> quote# X, quote# mark X -> quote# X) (dbl# ok X -> dbl# X, dbl# ok X -> dbl# X) (dbl# ok X -> dbl# X, dbl# mark X -> dbl# X) (dbls# mark X -> dbls# X, dbls# ok X -> dbls# X) (dbls# mark X -> dbls# X, dbls# mark X -> dbls# X) (from# ok X -> from# X, from# ok X -> from# X) (dbl1# ok X -> dbl1# X, dbl1# ok X -> dbl1# X) (dbl1# ok X -> dbl1# X, dbl1# mark X -> dbl1# X) (s1# ok X -> s1# X, s1# ok X -> s1# X) (s1# ok X -> s1# X, s1# mark X -> s1# X) (quote# ok X -> quote# X, quote# ok X -> quote# X) (quote# ok X -> quote# X, quote# mark X -> quote# X) (proper# s X -> proper# X, proper# quote X -> proper# X) (proper# s X -> proper# X, proper# quote X -> quote# proper X) (proper# s X -> proper# X, proper# sel1(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# sel1(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# sel1(X1, X2) -> sel1#(proper X1, proper X2)) (proper# s X -> proper# X, proper# s1 X -> proper# X) (proper# s X -> proper# X, proper# s1 X -> s1# proper X) (proper# s X -> proper# X, proper# dbl1 X -> proper# X) (proper# s X -> proper# X, proper# dbl1 X -> dbl1# proper X) (proper# s X -> proper# X, proper# from X -> proper# X) (proper# s X -> proper# X, proper# from X -> from# proper X) (proper# s X -> proper# X, proper# indx(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# indx(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# indx(X1, X2) -> indx#(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# 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)) (proper# s X -> proper# X, proper# dbls X -> proper# X) (proper# s X -> proper# X, proper# dbls X -> dbls# proper X) (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# dbl X -> proper# X) (proper# s X -> proper# X, proper# dbl X -> dbl# proper X) (proper# from X -> proper# X, proper# quote X -> proper# X) (proper# from X -> proper# X, proper# quote X -> quote# proper X) (proper# from X -> proper# X, proper# sel1(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# sel1(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# sel1(X1, X2) -> sel1#(proper X1, proper X2)) (proper# from X -> proper# X, proper# s1 X -> proper# X) (proper# from X -> proper# X, proper# s1 X -> s1# proper X) (proper# from X -> proper# X, proper# dbl1 X -> proper# X) (proper# from X -> proper# X, proper# dbl1 X -> dbl1# proper X) (proper# from X -> proper# X, proper# from X -> proper# X) (proper# from X -> proper# X, proper# from X -> from# proper X) (proper# from X -> proper# X, proper# indx(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# indx(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# indx(X1, X2) -> indx#(proper X1, proper X2)) (proper# from X -> proper# X, proper# sel(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# sel(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# from X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# from X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# from X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# from X -> proper# X, proper# dbls X -> proper# X) (proper# from X -> proper# X, proper# dbls X -> dbls# proper X) (proper# from X -> proper# X, proper# s X -> proper# X) (proper# from X -> proper# X, proper# s X -> s# proper X) (proper# from X -> proper# X, proper# dbl X -> proper# X) (proper# from X -> proper# X, proper# dbl X -> dbl# proper X) (proper# s1 X -> proper# X, proper# quote X -> proper# X) (proper# s1 X -> proper# X, proper# quote X -> quote# proper X) (proper# s1 X -> proper# X, proper# sel1(X1, X2) -> proper# X2) (proper# s1 X -> proper# X, proper# sel1(X1, X2) -> proper# X1) (proper# s1 X -> proper# X, proper# sel1(X1, X2) -> sel1#(proper X1, proper X2)) (proper# s1 X -> proper# X, proper# s1 X -> proper# X) (proper# s1 X -> proper# X, proper# s1 X -> s1# proper X) (proper# s1 X -> proper# X, proper# dbl1 X -> proper# X) (proper# s1 X -> proper# X, proper# dbl1 X -> dbl1# proper X) (proper# s1 X -> proper# X, proper# from X -> proper# X) (proper# s1 X -> proper# X, proper# from X -> from# proper X) (proper# s1 X -> proper# X, proper# indx(X1, X2) -> proper# X2) (proper# s1 X -> proper# X, proper# indx(X1, X2) -> proper# X1) (proper# s1 X -> proper# X, proper# indx(X1, X2) -> indx#(proper X1, proper X2)) (proper# s1 X -> proper# X, proper# sel(X1, X2) -> proper# X2) (proper# s1 X -> proper# X, proper# sel(X1, X2) -> proper# X1) (proper# s1 X -> proper# X, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# s1 X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# s1 X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# s1 X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# s1 X -> proper# X, proper# dbls X -> proper# X) (proper# s1 X -> proper# X, proper# dbls X -> dbls# proper X) (proper# s1 X -> proper# X, proper# s X -> proper# X) (proper# s1 X -> proper# X, proper# s X -> s# proper X) (proper# s1 X -> proper# X, proper# dbl X -> proper# X) (proper# s1 X -> proper# X, proper# dbl X -> dbl# proper X) (top# mark X -> proper# X, proper# quote X -> proper# X) (top# mark X -> proper# X, proper# quote X -> quote# proper X) (top# mark X -> proper# X, proper# sel1(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# sel1(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# sel1(X1, X2) -> sel1#(proper X1, proper X2)) (top# mark X -> proper# X, proper# s1 X -> proper# X) (top# mark X -> proper# X, proper# s1 X -> s1# proper X) (top# mark X -> proper# X, proper# dbl1 X -> proper# X) (top# mark X -> proper# X, proper# dbl1 X -> dbl1# proper X) (top# mark X -> proper# X, proper# from X -> proper# X) (top# mark X -> proper# X, proper# from X -> from# proper X) (top# mark X -> proper# X, proper# indx(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# indx(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# indx(X1, X2) -> indx#(proper X1, proper X2)) (top# mark X -> proper# X, proper# sel(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# sel(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (top# mark X -> proper# X, proper# dbls X -> proper# X) (top# mark X -> proper# X, proper# dbls X -> dbls# proper X) (top# mark X -> proper# X, proper# s X -> proper# X) (top# mark X -> proper# X, proper# s X -> s# proper X) (top# mark X -> proper# X, proper# dbl X -> proper# X) (top# mark X -> proper# X, proper# dbl X -> dbl# proper X) (active# from X -> cons#(X, from s X), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# dbl1 s X -> s1# s1 dbl1 X, s1# ok X -> s1# X) (active# dbl1 s X -> s1# s1 dbl1 X, s1# mark X -> s1# X) (active# sel(X1, X2) -> sel#(active X1, X2), sel#(ok X1, ok X2) -> sel#(X1, X2)) (active# sel(X1, X2) -> sel#(active X1, X2), sel#(mark X1, X2) -> sel#(X1, X2)) (active# sel(X1, X2) -> sel#(active X1, X2), sel#(X1, mark X2) -> sel#(X1, X2)) (active# sel1(X1, X2) -> sel1#(active X1, X2), sel1#(ok X1, ok X2) -> sel1#(X1, X2)) (active# sel1(X1, X2) -> sel1#(active X1, X2), sel1#(mark X1, X2) -> sel1#(X1, X2)) (active# sel1(X1, X2) -> sel1#(active X1, X2), sel1#(X1, mark X2) -> sel1#(X1, X2)) (active# indx(cons(X, Y), Z) -> sel#(X, Z), sel#(ok X1, ok X2) -> sel#(X1, X2)) (active# indx(cons(X, Y), Z) -> sel#(X, Z), sel#(mark X1, X2) -> sel#(X1, X2)) (active# indx(cons(X, Y), Z) -> sel#(X, Z), sel#(X1, mark X2) -> sel#(X1, X2)) (active# sel1(s X, cons(Y, Z)) -> sel1#(X, Z), sel1#(ok X1, ok X2) -> sel1#(X1, X2)) (active# sel1(s X, cons(Y, Z)) -> sel1#(X, Z), sel1#(mark X1, X2) -> sel1#(X1, X2)) (active# sel1(s X, cons(Y, Z)) -> sel1#(X, Z), sel1#(X1, mark X2) -> sel1#(X1, X2)) (active# indx(cons(X, Y), Z) -> indx#(Y, Z), indx#(mark X1, X2) -> indx#(X1, X2)) (active# indx(cons(X, Y), Z) -> indx#(Y, Z), indx#(ok X1, ok X2) -> indx#(X1, X2)) (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)) (active# indx(X1, X2) -> indx#(active X1, X2), indx#(mark X1, X2) -> indx#(X1, X2)) (active# indx(X1, X2) -> indx#(active X1, X2), indx#(ok X1, ok X2) -> indx#(X1, X2)) (active# quote sel(X, Y) -> sel1#(X, Y), sel1#(X1, mark X2) -> sel1#(X1, X2)) (active# quote sel(X, Y) -> sel1#(X, Y), sel1#(mark X1, X2) -> sel1#(X1, X2)) (active# quote sel(X, Y) -> sel1#(X, Y), sel1#(ok X1, ok X2) -> sel1#(X1, X2)) (active# dbl s X -> s# s dbl X, s# ok X -> s# X) (top# ok X -> active# X, active# dbl X -> active# X) (top# ok X -> active# X, active# dbl X -> dbl# active X) (top# ok X -> active# X, active# dbl s X -> dbl# X) (top# ok X -> active# X, active# dbl s X -> s# dbl X) (top# ok X -> active# X, active# dbl s X -> s# s dbl X) (top# ok X -> active# X, active# dbls X -> active# X) (top# ok X -> active# X, active# dbls X -> dbls# active X) (top# ok X -> active# X, active# dbls cons(X, Y) -> dbl# X) (top# ok X -> active# X, active# dbls cons(X, Y) -> dbls# Y) (top# ok X -> active# X, active# dbls cons(X, Y) -> cons#(dbl X, dbls Y)) (top# ok X -> active# X, active# sel(X1, X2) -> active# X1) (top# ok X -> active# X, active# sel(X1, X2) -> active# X2) (top# ok X -> active# X, active# sel(X1, X2) -> sel#(X1, active X2)) (top# ok X -> active# X, active# sel(X1, X2) -> sel#(active X1, X2)) (top# ok X -> active# X, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (top# ok X -> active# X, active# indx(X1, X2) -> active# X1) (top# ok X -> active# X, active# indx(X1, X2) -> indx#(active X1, X2)) (top# ok X -> active# X, active# indx(cons(X, Y), Z) -> cons#(sel(X, Z), indx(Y, Z))) (top# ok X -> active# X, active# indx(cons(X, Y), Z) -> sel#(X, Z)) (top# ok X -> active# X, active# indx(cons(X, Y), Z) -> indx#(Y, Z)) (top# ok X -> active# X, active# from X -> s# X) (top# ok X -> active# X, active# from X -> cons#(X, from s X)) (top# ok X -> active# X, active# from X -> from# s X) (top# ok X -> active# X, active# dbl1 X -> active# X) (top# ok X -> active# X, active# dbl1 X -> dbl1# active X) (top# ok X -> active# X, active# dbl1 s X -> dbl1# X) (top# ok X -> active# X, active# dbl1 s X -> s1# dbl1 X) (top# ok X -> active# X, active# dbl1 s X -> s1# s1 dbl1 X) (top# ok X -> active# X, active# s1 X -> active# X) (top# ok X -> active# X, active# s1 X -> s1# active X) (top# ok X -> active# X, active# sel1(X1, X2) -> active# X1) (top# ok X -> active# X, active# sel1(X1, X2) -> active# X2) (top# ok X -> active# X, active# sel1(X1, X2) -> sel1#(X1, active X2)) (top# ok X -> active# X, active# sel1(X1, X2) -> sel1#(active X1, X2)) (top# ok X -> active# X, active# sel1(s X, cons(Y, Z)) -> sel1#(X, Z)) (top# ok X -> active# X, active# quote X -> active# X) (top# ok X -> active# X, active# quote X -> quote# active X) (top# ok X -> active# X, active# quote dbl X -> dbl1# X) (top# ok X -> active# X, active# quote s X -> s1# quote X) (top# ok X -> active# X, active# quote s X -> quote# X) (top# ok X -> active# X, active# quote sel(X, Y) -> sel1#(X, Y)) (proper# quote X -> proper# X, proper# dbl X -> dbl# proper X) (proper# quote X -> proper# X, proper# dbl X -> proper# X) (proper# quote X -> proper# X, proper# s X -> s# proper X) (proper# quote X -> proper# X, proper# s X -> proper# X) (proper# quote X -> proper# X, proper# dbls X -> dbls# proper X) (proper# quote X -> proper# X, proper# dbls X -> proper# X) (proper# quote X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# quote X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# quote X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# quote X -> proper# X, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# quote X -> proper# X, proper# sel(X1, X2) -> proper# X1) (proper# quote X -> proper# X, proper# sel(X1, X2) -> proper# X2) (proper# quote X -> proper# X, proper# indx(X1, X2) -> indx#(proper X1, proper X2)) (proper# quote X -> proper# X, proper# indx(X1, X2) -> proper# X1) (proper# quote X -> proper# X, proper# indx(X1, X2) -> proper# X2) (proper# quote X -> proper# X, proper# from X -> from# proper X) (proper# quote X -> proper# X, proper# from X -> proper# X) (proper# quote X -> proper# X, proper# dbl1 X -> dbl1# proper X) (proper# quote X -> proper# X, proper# dbl1 X -> proper# X) (proper# quote X -> proper# X, proper# s1 X -> s1# proper X) (proper# quote X -> proper# X, proper# s1 X -> proper# X) (proper# quote X -> proper# X, proper# sel1(X1, X2) -> sel1#(proper X1, proper X2)) (proper# quote X -> proper# X, proper# sel1(X1, X2) -> proper# X1) (proper# quote X -> proper# X, proper# sel1(X1, X2) -> proper# X2) (proper# quote X -> proper# X, proper# quote X -> quote# proper X) (proper# quote X -> proper# X, proper# quote X -> proper# X) (proper# dbl1 X -> proper# X, proper# dbl X -> dbl# proper X) (proper# dbl1 X -> proper# X, proper# dbl X -> proper# X) (proper# dbl1 X -> proper# X, proper# s X -> s# proper X) (proper# dbl1 X -> proper# X, proper# s X -> proper# X) (proper# dbl1 X -> proper# X, proper# dbls X -> dbls# proper X) (proper# dbl1 X -> proper# X, proper# dbls X -> proper# X) (proper# dbl1 X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# dbl1 X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# dbl1 X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# dbl1 X -> proper# X, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# dbl1 X -> proper# X, proper# sel(X1, X2) -> proper# X1) (proper# dbl1 X -> proper# X, proper# sel(X1, X2) -> proper# X2) (proper# dbl1 X -> proper# X, proper# indx(X1, X2) -> indx#(proper X1, proper X2)) (proper# dbl1 X -> proper# X, proper# indx(X1, X2) -> 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X -> proper# X) (proper# dbls X -> proper# X, proper# dbls X -> dbls# proper X) (proper# dbls X -> proper# X, proper# dbls X -> proper# X) (proper# dbls X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# dbls X -> proper# X, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# dbls X -> proper# X, proper# sel(X1, X2) -> proper# X1) (proper# dbls X -> proper# X, proper# sel(X1, X2) -> proper# X2) (proper# dbls X -> proper# X, proper# indx(X1, X2) -> indx#(proper X1, proper X2)) (proper# dbls X -> proper# X, proper# indx(X1, X2) -> proper# X1) (proper# dbls X -> proper# X, proper# indx(X1, X2) -> proper# X2) (proper# dbls X -> proper# X, proper# from X -> from# proper X) (proper# dbls X -> proper# X, proper# from X -> proper# X) (proper# dbls X -> proper# X, proper# dbl1 X -> dbl1# proper X) (proper# dbls X -> proper# X, 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-> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# dbl X -> proper# X, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# dbl X -> proper# X, proper# sel(X1, X2) -> proper# X1) (proper# dbl X -> proper# X, proper# sel(X1, X2) -> proper# X2) (proper# dbl X -> proper# X, proper# indx(X1, X2) -> indx#(proper X1, proper X2)) (proper# dbl X -> proper# X, proper# indx(X1, X2) -> proper# X1) (proper# dbl X -> proper# X, proper# indx(X1, X2) -> proper# X2) (proper# dbl X -> proper# X, proper# from X -> from# proper X) (proper# dbl X -> proper# X, proper# from X -> proper# X) (proper# dbl X -> proper# X, proper# dbl1 X -> dbl1# proper X) (proper# dbl X -> proper# X, proper# dbl1 X -> proper# X) (proper# dbl X -> proper# X, proper# s1 X -> s1# proper X) (proper# dbl X -> proper# X, proper# s1 X -> proper# X) (proper# dbl X -> proper# X, proper# sel1(X1, X2) -> sel1#(proper X1, proper X2)) (proper# dbl X -> proper# X, proper# sel1(X1, X2) -> proper# X1) (proper# dbl X -> proper# 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X1) (proper# sel1(X1, X2) -> proper# X1, proper# indx(X1, X2) -> proper# X2) (proper# sel1(X1, X2) -> proper# X1, proper# from X -> from# proper X) (proper# sel1(X1, X2) -> proper# X1, proper# from X -> proper# X) (proper# sel1(X1, X2) -> proper# X1, proper# dbl1 X -> dbl1# proper X) (proper# sel1(X1, X2) -> proper# X1, proper# dbl1 X -> proper# X) (proper# sel1(X1, X2) -> proper# X1, proper# s1 X -> s1# proper X) (proper# sel1(X1, X2) -> proper# X1, proper# s1 X -> proper# X) (proper# sel1(X1, X2) -> proper# X1, proper# sel1(X1, X2) -> sel1#(proper X1, proper X2)) (proper# sel1(X1, X2) -> proper# X1, proper# sel1(X1, X2) -> proper# X1) (proper# sel1(X1, X2) -> proper# X1, proper# sel1(X1, X2) -> proper# X2) (proper# sel1(X1, X2) -> proper# X1, proper# quote X -> quote# proper X) (proper# sel1(X1, X2) -> proper# X1, proper# quote X -> proper# X) (proper# sel(X1, X2) -> proper# X1, proper# dbl X -> dbl# proper X) (proper# sel(X1, X2) -> proper# X1, proper# dbl X -> proper# X) (proper# 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X2) -> active# X1, active# dbl s X -> s# s dbl X) (active# sel1(X1, X2) -> active# X1, active# dbls X -> active# X) (active# sel1(X1, X2) -> active# X1, active# dbls X -> dbls# active X) (active# sel1(X1, X2) -> active# X1, active# dbls cons(X, Y) -> dbl# X) (active# sel1(X1, X2) -> active# X1, active# dbls cons(X, Y) -> dbls# Y) (active# sel1(X1, X2) -> active# X1, active# dbls cons(X, Y) -> cons#(dbl X, dbls Y)) (active# sel1(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X1) (active# sel1(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2) (active# sel1(X1, X2) -> active# X1, active# sel(X1, X2) -> sel#(X1, active X2)) (active# sel1(X1, X2) -> active# X1, active# sel(X1, X2) -> sel#(active X1, X2)) (active# sel1(X1, X2) -> active# X1, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (active# sel1(X1, X2) -> active# X1, active# indx(X1, X2) -> active# X1) (active# sel1(X1, X2) -> active# X1, active# indx(X1, X2) -> indx#(active X1, X2)) (active# sel1(X1, X2) -> active# X1, active# indx(cons(X, Y), Z) -> cons#(sel(X, Z), indx(Y, Z))) (active# sel1(X1, X2) -> active# X1, active# indx(cons(X, Y), Z) -> sel#(X, Z)) (active# sel1(X1, X2) -> active# X1, active# indx(cons(X, Y), Z) -> indx#(Y, Z)) (active# sel1(X1, X2) -> active# X1, active# from X -> s# X) (active# sel1(X1, X2) -> active# X1, active# from X -> cons#(X, from s X)) (active# sel1(X1, X2) -> active# X1, active# from X -> from# s X) (active# sel1(X1, X2) -> active# X1, active# dbl1 X -> active# X) (active# sel1(X1, X2) -> active# X1, active# dbl1 X -> dbl1# active X) (active# sel1(X1, X2) -> active# X1, active# dbl1 s X -> dbl1# X) (active# sel1(X1, X2) -> active# X1, active# dbl1 s X -> s1# dbl1 X) (active# sel1(X1, X2) -> active# X1, active# dbl1 s X -> s1# s1 dbl1 X) (active# sel1(X1, X2) -> active# X1, active# s1 X -> active# X) (active# sel1(X1, X2) -> active# X1, active# s1 X -> s1# active X) (active# sel1(X1, X2) -> active# X1, active# sel1(X1, X2) -> active# X1) (active# sel1(X1, X2) -> active# X1, active# sel1(X1, X2) -> active# X2) (active# sel1(X1, X2) -> active# X1, active# sel1(X1, X2) -> sel1#(X1, active X2)) (active# sel1(X1, X2) -> active# X1, active# sel1(X1, X2) -> sel1#(active X1, X2)) (active# sel1(X1, X2) -> active# X1, active# sel1(s X, cons(Y, Z)) -> sel1#(X, Z)) (active# sel1(X1, X2) -> active# X1, active# quote X -> active# X) (active# sel1(X1, X2) -> active# X1, active# quote X -> quote# active X) (active# sel1(X1, X2) -> active# X1, active# quote dbl X -> dbl1# X) (active# sel1(X1, X2) -> active# X1, active# quote s X -> s1# quote X) (active# sel1(X1, X2) -> active# X1, active# quote s X -> quote# X) (active# sel1(X1, X2) -> active# X1, active# quote sel(X, Y) -> sel1#(X, Y)) (active# sel(X1, X2) -> active# X1, active# dbl X -> active# X) (active# sel(X1, X2) -> active# X1, active# dbl X -> dbl# active X) (active# sel(X1, X2) -> active# X1, active# dbl s X -> dbl# X) (active# sel(X1, X2) -> active# X1, active# dbl s X -> s# dbl X) (active# sel(X1, X2) -> active# X1, active# dbl s X -> s# s dbl X) (active# sel(X1, X2) -> active# X1, active# dbls X -> active# X) (active# sel(X1, X2) -> active# X1, active# dbls X -> dbls# active X) (active# sel(X1, X2) -> active# X1, active# dbls cons(X, Y) -> dbl# X) (active# sel(X1, X2) -> active# X1, active# dbls cons(X, Y) -> dbls# Y) (active# sel(X1, X2) -> active# X1, active# dbls cons(X, Y) -> cons#(dbl X, dbls Y)) (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)) (active# sel(X1, X2) -> active# X1, active# indx(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X1, active# indx(X1, X2) -> indx#(active X1, X2)) (active# sel(X1, X2) -> active# X1, active# indx(cons(X, Y), Z) -> cons#(sel(X, Z), indx(Y, Z))) (active# sel(X1, X2) -> active# X1, active# indx(cons(X, Y), Z) -> sel#(X, Z)) (active# sel(X1, X2) -> active# X1, active# indx(cons(X, Y), Z) -> indx#(Y, Z)) (active# sel(X1, X2) -> active# X1, active# from X -> s# X) (active# sel(X1, X2) -> active# X1, active# from X -> cons#(X, from s X)) (active# sel(X1, X2) -> active# X1, active# from X -> from# s X) (active# sel(X1, X2) -> active# X1, active# dbl1 X -> active# X) (active# sel(X1, X2) -> active# X1, active# dbl1 X -> dbl1# active X) (active# sel(X1, X2) -> active# X1, active# dbl1 s X -> dbl1# X) (active# sel(X1, X2) -> active# X1, active# dbl1 s X -> s1# dbl1 X) (active# sel(X1, X2) -> active# X1, active# dbl1 s X -> s1# s1 dbl1 X) (active# sel(X1, X2) -> active# X1, active# s1 X -> active# X) (active# sel(X1, X2) -> active# X1, active# s1 X -> s1# active X) (active# sel(X1, X2) -> active# X1, active# sel1(X1, X2) -> active# X1) (active# sel(X1, X2) -> active# X1, active# sel1(X1, X2) -> active# X2) (active# sel(X1, X2) -> active# X1, active# sel1(X1, X2) -> sel1#(X1, active X2)) (active# sel(X1, X2) -> active# X1, active# sel1(X1, X2) -> sel1#(active X1, X2)) (active# sel(X1, X2) -> active# X1, active# sel1(s X, cons(Y, Z)) -> sel1#(X, Z)) (active# sel(X1, X2) -> active# X1, active# quote X -> active# X) (active# sel(X1, X2) -> active# X1, active# quote X -> quote# active X) (active# sel(X1, X2) -> active# X1, active# quote dbl X -> dbl1# X) (active# sel(X1, X2) -> active# X1, active# quote s X -> s1# quote X) (active# sel(X1, X2) -> active# X1, active# quote s X -> quote# X) (active# sel(X1, X2) -> active# X1, active# quote sel(X, Y) -> sel1#(X, Y)) (proper# sel1(X1, X2) -> proper# X2, proper# dbl X -> dbl# proper X) (proper# sel1(X1, X2) -> proper# X2, proper# dbl X -> proper# X) (proper# sel1(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# sel1(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# sel1(X1, X2) -> proper# X2, proper# dbls X -> dbls# proper X) (proper# sel1(X1, X2) -> proper# X2, proper# dbls X -> proper# X) (proper# sel1(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# sel1(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# sel1(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# sel1(X1, X2) -> proper# X2, proper# sel(X1, X2) -> sel#(proper X1, proper X2)) (proper# sel1(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1) (proper# sel1(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X2) (proper# sel1(X1, X2) -> proper# X2, proper# indx(X1, X2) -> indx#(proper X1, proper X2)) (proper# sel1(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1) (proper# sel1(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X2) (proper# sel1(X1, X2) -> proper# X2, proper# from X -> from# proper X) (proper# sel1(X1, X2) -> proper# X2, proper# from X -> proper# X) (proper# sel1(X1, X2) -> proper# X2, proper# dbl1 X -> dbl1# proper X) (proper# sel1(X1, X2) -> proper# X2, proper# dbl1 X -> proper# X) (proper# sel1(X1, X2) -> proper# X2, proper# s1 X -> s1# proper X) (proper# sel1(X1, X2) -> proper# X2, proper# s1 X -> proper# X) (proper# sel1(X1, X2) -> proper# X2, proper# sel1(X1, X2) -> sel1#(proper X1, proper X2)) (proper# sel1(X1, X2) -> proper# X2, proper# sel1(X1, X2) -> proper# X1) (proper# sel1(X1, X2) -> proper# X2, proper# sel1(X1, X2) -> proper# X2) (proper# sel1(X1, X2) -> proper# X2, proper# quote X -> quote# proper X) (proper# sel1(X1, X2) -> proper# X2, proper# quote X -> proper# X) (proper# sel(X1, X2) -> proper# X2, proper# dbl X -> dbl# proper X) (proper# sel(X1, X2) -> proper# X2, proper# dbl 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# dbls X -> dbls# proper X) (proper# sel(X1, X2) -> proper# X2, proper# dbls X -> proper# X) (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# 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) (proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> indx#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X2) (proper# sel(X1, X2) -> proper# X2, proper# from X -> from# proper X) (proper# sel(X1, X2) -> proper# X2, proper# from X -> proper# X) (proper# sel(X1, X2) -> proper# X2, proper# dbl1 X -> dbl1# proper X) (proper# sel(X1, X2) -> proper# X2, proper# dbl1 X -> proper# X) (proper# sel(X1, X2) -> proper# X2, proper# s1 X -> s1# proper X) (proper# sel(X1, X2) -> proper# X2, proper# s1 X -> proper# X) (proper# sel(X1, X2) -> proper# X2, proper# sel1(X1, X2) -> sel1#(proper X1, proper X2)) (proper# sel(X1, X2) -> proper# X2, proper# sel1(X1, X2) -> proper# X1) (proper# sel(X1, X2) -> proper# X2, proper# sel1(X1, X2) -> proper# X2) (proper# sel(X1, X2) -> proper# X2, proper# quote X -> quote# proper X) (proper# sel(X1, X2) -> proper# X2, proper# quote X -> proper# X) (active# sel1(X1, X2) -> active# X2, active# dbl X -> active# X) (active# sel1(X1, X2) -> active# X2, active# dbl X -> dbl# active X) (active# sel1(X1, X2) -> active# X2, active# dbl s X -> dbl# X) (active# sel1(X1, X2) -> active# X2, active# dbl s X -> s# dbl X) (active# sel1(X1, X2) -> active# X2, active# dbl s X -> s# s dbl X) (active# sel1(X1, X2) -> active# X2, active# dbls X -> active# X) (active# sel1(X1, X2) -> active# X2, active# dbls X -> dbls# active X) (active# sel1(X1, X2) -> active# X2, active# dbls cons(X, Y) -> dbl# X) (active# sel1(X1, X2) -> active# X2, active# dbls cons(X, Y) -> dbls# Y) (active# sel1(X1, X2) -> active# X2, active# dbls cons(X, Y) -> cons#(dbl X, dbls Y)) (active# sel1(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X1) (active# sel1(X1, X2) -> active# X2, active# sel(X1, X2) -> active# X2) (active# sel1(X1, X2) -> active# X2, active# sel(X1, X2) -> sel#(X1, active X2)) (active# sel1(X1, X2) -> active# X2, active# sel(X1, X2) -> sel#(active X1, X2)) (active# sel1(X1, X2) -> active# X2, active# sel(s X, cons(Y, Z)) -> sel#(X, Z)) (active# sel1(X1, X2) -> active# X2, active# indx(X1, X2) -> active# X1) (active# sel1(X1, X2) -> active# X2, active# indx(X1, X2) -> indx#(active X1, X2)) (active# sel1(X1, X2) -> active# X2, active# indx(cons(X, Y), Z) -> cons#(sel(X, Z), indx(Y, Z))) (active# sel1(X1, X2) -> active# X2, active# indx(cons(X, Y), Z) -> sel#(X, Z)) (active# sel1(X1, X2) -> active# X2, active# indx(cons(X, Y), Z) -> indx#(Y, Z)) (active# sel1(X1, X2) -> active# X2, active# from X -> s# X) (active# sel1(X1, X2) -> active# X2, active# from X -> cons#(X, from s X)) (active# sel1(X1, X2) -> active# X2, active# from X -> from# s X) (active# sel1(X1, X2) -> active# X2, active# dbl1 X -> active# X) (active# sel1(X1, X2) -> active# X2, active# dbl1 X -> dbl1# active X) (active# sel1(X1, X2) -> active# X2, active# dbl1 s X -> dbl1# X) (active# sel1(X1, X2) -> active# X2, active# dbl1 s X -> s1# dbl1 X) (active# sel1(X1, X2) -> active# X2, active# dbl1 s X -> s1# s1 dbl1 X) (active# sel1(X1, X2) -> active# X2, active# s1 X -> active# X) (active# sel1(X1, X2) -> active# X2, active# s1 X -> s1# active X) (active# sel1(X1, X2) -> active# X2, active# sel1(X1, X2) -> active# X1) (active# sel1(X1, X2) -> active# X2, active# sel1(X1, X2) -> active# X2) (active# sel1(X1, X2) -> active# X2, active# sel1(X1, X2) -> sel1#(X1, active X2)) (active# sel1(X1, X2) -> active# X2, active# sel1(X1, X2) -> sel1#(active X1, X2)) (active# sel1(X1, X2) -> active# X2, active# sel1(s X, cons(Y, Z)) -> sel1#(X, Z)) (active# sel1(X1, X2) -> active# X2, active# quote X -> active# X) (active# sel1(X1, X2) -> active# X2, active# quote X -> quote# active X) (active# sel1(X1, X2) -> active# X2, active# quote dbl X -> dbl1# X) (active# sel1(X1, X2) -> active# X2, active# quote s X -> s1# quote X) (active# sel1(X1, X2) -> active# X2, active# quote s X -> quote# X) (active# sel1(X1, X2) -> active# X2, active# quote sel(X, Y) -> sel1#(X, Y)) (sel1#(ok X1, ok X2) -> sel1#(X1, X2), sel1#(X1, mark X2) -> sel1#(X1, X2)) (sel1#(ok X1, ok X2) -> sel1#(X1, X2), sel1#(mark X1, X2) -> sel1#(X1, X2)) (sel1#(ok X1, ok X2) -> sel1#(X1, X2), sel1#(ok X1, ok X2) -> sel1#(X1, X2)) (sel1#(X1, mark X2) -> sel1#(X1, X2), sel1#(X1, mark X2) -> sel1#(X1, X2)) (sel1#(X1, mark X2) -> sel1#(X1, X2), sel1#(mark X1, X2) -> sel1#(X1, X2)) (sel1#(X1, mark X2) -> sel1#(X1, X2), sel1#(ok X1, ok X2) -> sel1#(X1, X2)) (indx#(mark X1, X2) -> indx#(X1, X2), indx#(mark X1, X2) -> indx#(X1, X2)) (indx#(mark X1, X2) -> indx#(X1, X2), indx#(ok X1, ok X2) -> indx#(X1, X2)) (sel#(mark X1, X2) -> sel#(X1, X2), sel#(X1, mark 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#(ok X1, ok X2) -> sel#(X1, X2)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (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# s1 X -> s1# proper X, s1# mark X -> s1# X) (proper# s1 X -> s1# proper X, s1# ok X -> s1# X) (proper# from X -> from# proper X, from# ok X -> from# X) (proper# s X -> s# proper X, s# ok X -> s# X) (active# quote s X -> s1# quote X, s1# mark X -> s1# X) (active# quote s X -> s1# quote X, s1# ok X -> s1# X) (active# s1 X -> s1# active X, s1# mark X -> s1# X) (active# s1 X -> s1# active X, s1# ok X -> s1# X) (active# dbl1 X -> dbl1# active X, dbl1# mark X -> dbl1# X) (active# dbl1 X -> dbl1# active X, dbl1# ok X -> dbl1# X) (active# dbls X -> dbls# active X, dbls# mark X -> dbls# X) (active# dbls X -> dbls# active X, dbls# ok X -> dbls# X) (active# dbl X -> dbl# active X, dbl# mark X -> dbl# X) (active# dbl X -> dbl# active X, dbl# ok X -> dbl# X) } STATUS: arrows: 0.881380 SCCS (14): Scc: {top# mark X -> top# proper X, top# ok X -> top# active X} Scc: { active# dbl X -> active# X, active# dbls X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2, active# indx(X1, X2) -> active# X1, active# dbl1 X -> active# X, active# s1 X -> active# X, active# sel1(X1, X2) -> active# X1, active# sel1(X1, X2) -> active# X2, active# quote X -> active# X} Scc: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1, proper# indx(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# dbl1 X -> proper# X, proper# s1 X -> proper# X, proper# sel1(X1, X2) -> proper# X1, proper# sel1(X1, X2) -> proper# X2, proper# quote X -> proper# X} Scc: { sel1#(X1, mark X2) -> sel1#(X1, X2), sel1#(mark X1, X2) -> sel1#(X1, X2), sel1#(ok X1, ok X2) -> sel1#(X1, X2)} Scc: { indx#(mark X1, X2) -> indx#(X1, X2), indx#(ok X1, ok X2) -> indx#(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#(ok X1, ok X2) -> cons#(X1, X2)} Scc: {quote# mark X -> quote# X, quote# ok X -> quote# X} Scc: {s1# mark X -> s1# X, s1# ok X -> s1# X} Scc: {dbl1# mark X -> dbl1# X, dbl1# ok X -> dbl1# X} Scc: {from# ok X -> from# X} Scc: {dbls# mark X -> dbls# X, dbls# ok X -> dbls# X} Scc: {s# ok X -> s# X} Scc: {dbl# mark X -> dbl# X, dbl# ok X -> dbl# X} SCC (2): Strict: {top# mark X -> top# proper X, top# ok X -> top# active X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} Fail SCC (10): Strict: { active# dbl X -> active# X, active# dbls X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2, active# indx(X1, X2) -> active# X1, active# dbl1 X -> active# X, active# s1 X -> active# X, active# sel1(X1, X2) -> active# X1, active# sel1(X1, X2) -> active# X2, active# quote X -> active# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = 0, [sel](x0, x1) = x0 + x1, [indx](x0, x1) = x0, [sel1](x0, x1) = x0 + x1, [mark](x0) = x0, [active](x0) = 0, [dbl](x0) = x0, [s](x0) = x0 + 1, [dbls](x0) = x0, [from](x0) = x0 + 1, [dbl1](x0) = x0, [s1](x0) = x0, [quote](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = 0, [top](x0) = 0, [0] = 0, [nil] = 0, [01] = 0, [active#](x0) = x0 Strict: active# quote X -> active# X 1 + 1X >= 0 + 1X active# sel1(X1, X2) -> active# X2 0 + 1X1 + 1X2 >= 0 + 1X2 active# sel1(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 active# s1 X -> active# X 0 + 1X >= 0 + 1X active# dbl1 X -> active# X 0 + 1X >= 0 + 1X active# indx(X1, X2) -> active# X1 0 + 1X1 + 0X2 >= 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# dbls X -> active# X 0 + 1X >= 0 + 1X active# dbl X -> active# 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 quote X -> quote proper X 0 + 0X >= 1 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 0 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 0 + 0X proper nil() -> ok nil() 0 >= 0 proper s X -> s proper X 0 + 0X >= 1 + 0X proper dbl X -> dbl proper X 0 + 0X >= 0 + 0X proper 0() -> ok 0() 0 >= 0 quote ok X -> ok quote X 1 + 0X >= 0 + 0X quote mark X -> mark quote X 1 + 1X >= 1 + 1X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s1 ok X -> ok s1 X 0 + 0X >= 0 + 0X s1 mark X -> mark s1 X 0 + 1X >= 0 + 1X dbl1 ok X -> ok dbl1 X 0 + 0X >= 0 + 0X dbl1 mark X -> mark dbl1 X 0 + 1X >= 0 + 1X from ok X -> ok from X 1 + 0X >= 0 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 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 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 dbls ok X -> ok dbls X 0 + 0X >= 0 + 0X dbls mark X -> mark dbls X 0 + 1X >= 0 + 1X s ok X -> ok s X 1 + 0X >= 0 + 0X dbl ok X -> ok dbl X 0 + 0X >= 0 + 0X dbl mark X -> mark dbl X 0 + 1X >= 0 + 1X active quote sel(X, Y) -> mark sel1(X, Y) 0 + 0X + 0Y >= 0 + 1X + 1Y active quote s X -> mark s1 quote X 0 + 0X >= 1 + 1X active quote dbl X -> mark dbl1 X 0 + 0X >= 0 + 1X active quote 0() -> mark 01() 0 >= 0 active quote X -> quote active X 0 + 0X >= 1 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 active s1 X -> s1 active X 0 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 0 + 0X >= 0 + 1X active dbl1 0() -> mark 01() 0 >= 0 active dbl1 X -> dbl1 active X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 0 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 1X + 1Z active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 1X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active dbls nil() -> mark nil() 0 >= 0 active dbls X -> dbls active X 0 + 0X >= 0 + 0X active dbl s X -> mark s s dbl X 0 + 0X >= 2 + 1X active dbl 0() -> mark 0() 0 >= 0 active dbl X -> dbl active X 0 + 0X >= 0 + 0X SCCS (1): Scc: { active# dbl X -> active# X, active# dbls X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2, active# indx(X1, X2) -> active# X1, active# dbl1 X -> active# X, active# s1 X -> active# X, active# sel1(X1, X2) -> active# X1, active# sel1(X1, X2) -> active# X2} SCC (9): Strict: { active# dbl X -> active# X, active# dbls X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2, active# indx(X1, X2) -> active# X1, active# dbl1 X -> active# X, active# s1 X -> active# X, active# sel1(X1, X2) -> active# X1, active# sel1(X1, X2) -> active# X2} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = 0, [sel](x0, x1) = x0 + x1, [indx](x0, x1) = x0, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [active](x0) = 0, [dbl](x0) = x0, [s](x0) = x0 + 1, [dbls](x0) = x0, [from](x0) = x0 + 1, [dbl1](x0) = x0, [s1](x0) = x0, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = 0, [top](x0) = 0, [0] = 0, [nil] = 0, [01] = 0, [active#](x0) = x0 Strict: active# sel1(X1, X2) -> active# X2 1 + 1X1 + 1X2 >= 0 + 1X2 active# sel1(X1, X2) -> active# X1 1 + 1X1 + 1X2 >= 0 + 1X1 active# s1 X -> active# X 0 + 1X >= 0 + 1X active# dbl1 X -> active# X 0 + 1X >= 0 + 1X active# indx(X1, X2) -> active# X1 0 + 1X1 + 0X2 >= 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# dbls X -> active# X 0 + 1X >= 0 + 1X active# dbl X -> active# 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 quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 0 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 0 + 0X proper nil() -> ok nil() 0 >= 0 proper s X -> s proper X 0 + 0X >= 1 + 0X proper dbl X -> dbl proper X 0 + 0X >= 0 + 0X proper 0() -> ok 0() 0 >= 0 quote ok X -> ok quote X 0 + 0X >= 0 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 s1 ok X -> ok s1 X 0 + 0X >= 0 + 0X s1 mark X -> mark s1 X 0 + 1X >= 0 + 1X dbl1 ok X -> ok dbl1 X 0 + 0X >= 0 + 0X dbl1 mark X -> mark dbl1 X 0 + 1X >= 0 + 1X from ok X -> ok from X 1 + 0X >= 0 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 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 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 dbls ok X -> ok dbls X 0 + 0X >= 0 + 0X dbls mark X -> mark dbls X 0 + 1X >= 0 + 1X s ok X -> ok s X 1 + 0X >= 0 + 0X dbl ok X -> ok dbl X 0 + 0X >= 0 + 0X dbl mark X -> mark dbl X 0 + 1X >= 0 + 1X active quote sel(X, Y) -> mark sel1(X, Y) 0 + 0X + 0Y >= 1 + 1X + 1Y active quote s X -> mark s1 quote X 0 + 0X >= 0 + 0X active quote dbl X -> mark dbl1 X 0 + 0X >= 0 + 1X active quote 0() -> mark 01() 0 >= 0 active quote X -> quote active X 0 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 0 + 0X + 0Y + 0Z >= 1 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active s1 X -> s1 active X 0 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 0 + 0X >= 0 + 1X active dbl1 0() -> mark 01() 0 >= 0 active dbl1 X -> dbl1 active X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 0 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 1X + 1Z active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 1X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active dbls nil() -> mark nil() 0 >= 0 active dbls X -> dbls active X 0 + 0X >= 0 + 0X active dbl s X -> mark s s dbl X 0 + 0X >= 2 + 1X active dbl 0() -> mark 0() 0 >= 0 active dbl X -> dbl active X 0 + 0X >= 0 + 0X SCCS (1): Scc: { active# dbl X -> active# X, active# dbls X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2, active# indx(X1, X2) -> active# X1, active# dbl1 X -> active# X, active# s1 X -> active# X} SCC (7): Strict: { active# dbl X -> active# X, active# dbls X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2, active# indx(X1, X2) -> active# X1, active# dbl1 X -> active# X, active# s1 X -> active# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = 0, [sel](x0, x1) = x0 + x1, [indx](x0, x1) = x0, [sel1](x0, x1) = 0, [mark](x0) = x0, [active](x0) = 0, [dbl](x0) = x0, [s](x0) = x0 + 1, [dbls](x0) = x0, [from](x0) = x0 + 1, [dbl1](x0) = x0, [s1](x0) = x0 + 1, [quote](x0) = x0, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [nil] = 0, [01] = 0, [active#](x0) = x0 Strict: active# s1 X -> active# X 1 + 1X >= 0 + 1X active# dbl1 X -> active# X 0 + 1X >= 0 + 1X active# indx(X1, X2) -> active# X1 0 + 1X1 + 0X2 >= 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# dbls X -> active# X 0 + 1X >= 0 + 1X active# dbl X -> active# 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 quote X -> quote proper X 1 + 1X >= 1 + 1X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper s1 X -> s1 proper X 2 + 1X >= 2 + 1X proper dbl1 X -> dbl1 proper X 1 + 1X >= 1 + 1X proper 01() -> ok 01() 1 >= 1 proper from X -> from proper X 2 + 1X >= 2 + 1X proper indx(X1, X2) -> indx(proper X1, proper X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper dbls X -> dbls proper X 1 + 1X >= 1 + 1X proper nil() -> ok nil() 1 >= 1 proper s X -> s proper X 2 + 1X >= 2 + 1X proper dbl X -> dbl proper X 1 + 1X >= 1 + 1X proper 0() -> ok 0() 1 >= 1 quote ok X -> ok quote X 1 + 1X >= 1 + 1X quote mark X -> mark quote X 0 + 1X >= 0 + 1X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s1 ok X -> ok s1 X 2 + 1X >= 2 + 1X s1 mark X -> mark s1 X 1 + 1X >= 1 + 1X dbl1 ok X -> ok dbl1 X 1 + 1X >= 1 + 1X dbl1 mark X -> mark dbl1 X 0 + 1X >= 0 + 1X from ok X -> ok from X 2 + 1X >= 2 + 1X indx(ok X1, ok X2) -> ok indx(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 dbls ok X -> ok dbls X 1 + 1X >= 1 + 1X dbls mark X -> mark dbls X 0 + 1X >= 0 + 1X s ok X -> ok s X 2 + 1X >= 2 + 1X dbl ok X -> ok dbl X 1 + 1X >= 1 + 1X dbl mark X -> mark dbl X 0 + 1X >= 0 + 1X active quote sel(X, Y) -> mark sel1(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active quote s X -> mark s1 quote X 0 + 0X >= 1 + 1X active quote dbl X -> mark dbl1 X 0 + 0X >= 0 + 1X active quote 0() -> mark 01() 0 >= 0 active quote X -> quote active X 0 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel1(X1, X2) -> sel1(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s1 X -> s1 active X 0 + 0X >= 1 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 0 + 0X >= 2 + 1X active dbl1 0() -> mark 01() 0 >= 0 active dbl1 X -> dbl1 active X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 0 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 1X + 1Z active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 1X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active dbls nil() -> mark nil() 0 >= 0 active dbls X -> dbls active X 0 + 0X >= 0 + 0X active dbl s X -> mark s s dbl X 0 + 0X >= 2 + 1X active dbl 0() -> mark 0() 0 >= 0 active dbl X -> dbl active X 0 + 0X >= 0 + 0X SCCS (1): Scc: { active# dbl X -> active# X, active# dbls X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2, active# indx(X1, X2) -> active# X1, active# dbl1 X -> active# X} SCC (6): Strict: { active# dbl X -> active# X, active# dbls X -> active# X, active# sel(X1, X2) -> active# X1, active# sel(X1, X2) -> active# X2, active# indx(X1, X2) -> active# X1, active# dbl1 X -> active# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1 + 1, [sel](x0, x1) = x0 + x1 + 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [dbl](x0) = x0 + 1, [s](x0) = x0 + 1, [dbls](x0) = x0 + 1, [from](x0) = x0 + 1, [dbl1](x0) = x0 + 1, [s1](x0) = 0, [quote](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 1, [01] = 1, [active#](x0) = x0 + 1 Strict: active# dbl1 X -> active# X 2 + 1X >= 1 + 1X active# indx(X1, X2) -> active# X1 2 + 1X1 + 0X2 >= 1 + 1X1 active# sel(X1, X2) -> active# X2 2 + 1X1 + 1X2 >= 1 + 1X2 active# sel(X1, X2) -> active# X1 2 + 1X1 + 1X2 >= 1 + 1X1 active# dbls X -> active# X 2 + 1X >= 1 + 1X active# dbl X -> active# X 2 + 1X >= 1 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper quote X -> quote proper X 0 + 0X >= 1 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 1 + 0X proper 01() -> ok 01() 0 >= 2 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 2 proper s X -> s proper X 0 + 0X >= 1 + 0X proper dbl X -> dbl proper X 0 + 0X >= 1 + 0X proper 0() -> ok 0() 0 >= 2 quote ok X -> ok quote X 2 + 1X >= 2 + 1X quote mark X -> mark quote X 2 + 1X >= 2 + 1X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 s1 ok X -> ok s1 X 0 + 0X >= 1 + 0X s1 mark X -> mark s1 X 0 + 0X >= 1 + 0X dbl1 ok X -> ok dbl1 X 2 + 1X >= 2 + 1X dbl1 mark X -> mark dbl1 X 2 + 1X >= 2 + 1X from ok X -> ok from X 2 + 1X >= 2 + 1X indx(ok X1, ok X2) -> ok indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 2 + 1X >= 2 + 1X s ok X -> ok s X 2 + 1X >= 2 + 1X dbl ok X -> ok dbl X 2 + 1X >= 2 + 1X dbl mark X -> mark dbl X 2 + 1X >= 2 + 1X active quote sel(X, Y) -> mark sel1(X, Y) 3 + 1X + 1Y >= 2 + 1X + 1Y active quote s X -> mark s1 quote X 3 + 1X >= 1 + 0X active quote dbl X -> mark dbl1 X 3 + 1X >= 2 + 1X active quote 0() -> mark 01() 3 >= 2 active quote X -> quote active X 2 + 1X >= 2 + 1X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 4 + 1X + 1Y + 1Z >= 2 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 4 + 1X + 1Y >= 1 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s1 X -> s1 active X 1 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 3 + 1X >= 1 + 0X active dbl1 0() -> mark 01() 3 >= 2 active dbl1 X -> dbl1 active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 4 + 2X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 1Y + 0Z >= 4 + 1X + 1Y + 1Z active indx(nil(), X) -> mark nil() 3 + 0X >= 2 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 4 + 1X + 1Y + 1Z >= 2 + 1X + 1Z active sel(0(), cons(X, Y)) -> mark X 4 + 1X + 1Y >= 1 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 1Y >= 4 + 1X + 1Y active dbls nil() -> mark nil() 3 >= 2 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 3 + 1X >= 4 + 1X active dbl 0() -> mark 0() 3 >= 2 active dbl X -> dbl active X 2 + 1X >= 2 + 1X Qed SCC (15): Strict: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1, proper# indx(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# dbl1 X -> proper# X, proper# s1 X -> proper# X, proper# sel1(X1, X2) -> proper# X1, proper# sel1(X1, X2) -> proper# X2, proper# quote X -> proper# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = x0 + x1, [indx](x0, x1) = x0 + x1, [sel1](x0, x1) = x0 + x1, [mark](x0) = 0, [active](x0) = 0, [dbl](x0) = x0, [s](x0) = x0, [dbls](x0) = x0, [from](x0) = x0, [dbl1](x0) = x0, [s1](x0) = x0, [quote](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = 0, [top](x0) = 0, [0] = 0, [nil] = 0, [01] = 0, [proper#](x0) = x0 Strict: proper# quote X -> proper# X 1 + 1X >= 0 + 1X proper# sel1(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# sel1(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 proper# s1 X -> proper# X 0 + 1X >= 0 + 1X proper# dbl1 X -> proper# X 0 + 1X >= 0 + 1X proper# from X -> proper# X 0 + 1X >= 0 + 1X proper# indx(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# indx(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# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 proper# dbls X -> proper# X 0 + 1X >= 0 + 1X proper# s X -> proper# X 0 + 1X >= 0 + 1X proper# dbl X -> proper# 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 quote X -> quote proper X 0 + 0X >= 1 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 0 proper from X -> from proper X 0 + 0X >= 0 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 0 + 0X proper nil() -> ok nil() 0 >= 0 proper s X -> s proper X 0 + 0X >= 0 + 0X proper dbl X -> dbl proper X 0 + 0X >= 0 + 0X proper 0() -> ok 0() 0 >= 0 quote ok X -> ok quote X 1 + 0X >= 0 + 0X quote mark X -> mark quote X 1 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 s1 ok X -> ok s1 X 0 + 0X >= 0 + 0X s1 mark X -> mark s1 X 0 + 0X >= 0 + 0X dbl1 ok X -> ok dbl1 X 0 + 0X >= 0 + 0X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 0 + 0X >= 0 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 0 + 0X1 + 1X2 >= 0 + 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 + 1X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 dbls ok X -> ok dbls X 0 + 0X >= 0 + 0X dbls mark X -> mark dbls X 0 + 0X >= 0 + 0X s ok X -> ok s X 0 + 0X >= 0 + 0X dbl ok X -> ok dbl X 0 + 0X >= 0 + 0X dbl mark X -> mark dbl X 0 + 0X >= 0 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active quote s X -> mark s1 quote X 0 + 0X >= 0 + 0X active quote dbl X -> mark dbl1 X 0 + 0X >= 0 + 0X active quote 0() -> mark 01() 0 >= 0 active quote X -> quote active X 0 + 0X >= 1 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel1(X1, X2) -> sel1(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 active s1 X -> s1 active X 0 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 0 + 0X >= 0 + 0X active dbl1 0() -> mark 01() 0 >= 0 active dbl1 X -> dbl1 active X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 0 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active dbls nil() -> mark nil() 0 >= 0 active dbls X -> dbls active X 0 + 0X >= 0 + 0X active dbl s X -> mark s s dbl X 0 + 0X >= 0 + 0X active dbl 0() -> mark 0() 0 >= 0 active dbl X -> dbl active X 0 + 0X >= 0 + 0X SCCS (1): Scc: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1, proper# indx(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# dbl1 X -> proper# X, proper# s1 X -> proper# X, proper# sel1(X1, X2) -> proper# X1, proper# sel1(X1, X2) -> proper# X2} SCC (14): Strict: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1, proper# indx(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# dbl1 X -> proper# X, proper# s1 X -> proper# X, proper# sel1(X1, X2) -> proper# X1, proper# sel1(X1, X2) -> proper# X2} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = x0 + x1, [indx](x0, x1) = x0 + x1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = 0, [active](x0) = 0, [dbl](x0) = x0, [s](x0) = x0, [dbls](x0) = x0, [from](x0) = x0, [dbl1](x0) = x0, [s1](x0) = x0, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = 0, [top](x0) = 0, [0] = 0, [nil] = 0, [01] = 0, [proper#](x0) = x0 Strict: proper# sel1(X1, X2) -> proper# X2 1 + 1X1 + 1X2 >= 0 + 1X2 proper# sel1(X1, X2) -> proper# X1 1 + 1X1 + 1X2 >= 0 + 1X1 proper# s1 X -> proper# X 0 + 1X >= 0 + 1X proper# dbl1 X -> proper# X 0 + 1X >= 0 + 1X proper# from X -> proper# X 0 + 1X >= 0 + 1X proper# indx(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# indx(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# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 proper# dbls X -> proper# X 0 + 1X >= 0 + 1X proper# s X -> proper# X 0 + 1X >= 0 + 1X proper# dbl X -> proper# 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 quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 0 proper from X -> from proper X 0 + 0X >= 0 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 0 + 0X proper nil() -> ok nil() 0 >= 0 proper s X -> s proper X 0 + 0X >= 0 + 0X proper dbl X -> dbl proper X 0 + 0X >= 0 + 0X proper 0() -> ok 0() 0 >= 0 quote ok X -> ok quote X 0 + 0X >= 0 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 1 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 s1 ok X -> ok s1 X 0 + 0X >= 0 + 0X s1 mark X -> mark s1 X 0 + 0X >= 0 + 0X dbl1 ok X -> ok dbl1 X 0 + 0X >= 0 + 0X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 0 + 0X >= 0 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 0 + 0X1 + 1X2 >= 0 + 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 + 1X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 dbls ok X -> ok dbls X 0 + 0X >= 0 + 0X dbls mark X -> mark dbls X 0 + 0X >= 0 + 0X s ok X -> ok s X 0 + 0X >= 0 + 0X dbl ok X -> ok dbl X 0 + 0X >= 0 + 0X dbl mark X -> mark dbl X 0 + 0X >= 0 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active quote s X -> mark s1 quote X 0 + 0X >= 0 + 0X active quote dbl X -> mark dbl1 X 0 + 0X >= 0 + 0X active quote 0() -> mark 01() 0 >= 0 active quote X -> quote active X 0 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel1(X1, X2) -> sel1(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 active s1 X -> s1 active X 0 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 0 + 0X >= 0 + 0X active dbl1 0() -> mark 01() 0 >= 0 active dbl1 X -> dbl1 active X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 0 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active dbls nil() -> mark nil() 0 >= 0 active dbls X -> dbls active X 0 + 0X >= 0 + 0X active dbl s X -> mark s s dbl X 0 + 0X >= 0 + 0X active dbl 0() -> mark 0() 0 >= 0 active dbl X -> dbl active X 0 + 0X >= 0 + 0X SCCS (1): Scc: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1, proper# indx(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# dbl1 X -> proper# X, proper# s1 X -> proper# X} SCC (12): Strict: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1, proper# indx(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# dbl1 X -> proper# X, proper# s1 X -> proper# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = x0 + x1, [indx](x0, x1) = x0 + x1, [sel1](x0, x1) = x0 + 1, [mark](x0) = 0, [active](x0) = 0, [dbl](x0) = x0, [s](x0) = x0, [dbls](x0) = x0, [from](x0) = x0, [dbl1](x0) = x0, [s1](x0) = x0 + 1, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [nil] = 0, [01] = 1, [proper#](x0) = x0 Strict: proper# s1 X -> proper# X 1 + 1X >= 0 + 1X proper# dbl1 X -> proper# X 0 + 1X >= 0 + 1X proper# from X -> proper# X 0 + 1X >= 0 + 1X proper# indx(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# indx(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# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 proper# dbls X -> proper# X 0 + 1X >= 0 + 1X proper# s X -> proper# X 0 + 1X >= 0 + 1X proper# dbl X -> proper# 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 quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 1 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 2 proper from X -> from proper X 0 + 0X >= 0 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 0 + 0X proper nil() -> ok nil() 0 >= 1 proper s X -> s proper X 0 + 0X >= 0 + 0X proper dbl X -> dbl proper X 0 + 0X >= 0 + 0X proper 0() -> ok 0() 0 >= 1 quote ok X -> ok quote X 0 + 0X >= 1 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s1 ok X -> ok s1 X 2 + 1X >= 2 + 1X s1 mark X -> mark s1 X 1 + 0X >= 0 + 0X dbl1 ok X -> ok dbl1 X 1 + 1X >= 1 + 1X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 1X >= 1 + 1X indx(ok X1, ok X2) -> ok indx(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 indx(mark X1, X2) -> mark indx(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 dbls ok X -> ok dbls X 1 + 1X >= 1 + 1X dbls mark X -> mark dbls X 0 + 0X >= 0 + 0X s ok X -> ok s X 1 + 1X >= 1 + 1X dbl ok X -> ok dbl X 1 + 1X >= 1 + 1X dbl mark X -> mark dbl X 0 + 0X >= 0 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active quote s X -> mark s1 quote X 0 + 0X >= 0 + 0X active quote dbl X -> mark dbl1 X 0 + 0X >= 0 + 0X active quote 0() -> mark 01() 0 >= 0 active quote X -> quote active X 0 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel1(X1, X2) -> sel1(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active s1 X -> s1 active X 0 + 0X >= 1 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 0 + 0X >= 0 + 0X active dbl1 0() -> mark 01() 0 >= 0 active dbl1 X -> dbl1 active X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 0 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active dbls nil() -> mark nil() 0 >= 0 active dbls X -> dbls active X 0 + 0X >= 0 + 0X active dbl s X -> mark s s dbl X 0 + 0X >= 0 + 0X active dbl 0() -> mark 0() 0 >= 0 active dbl X -> dbl active X 0 + 0X >= 0 + 0X SCCS (1): Scc: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1, proper# indx(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# dbl1 X -> proper# X} SCC (11): Strict: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1, proper# indx(X1, X2) -> proper# X2, proper# from X -> proper# X, proper# dbl1 X -> proper# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = x0 + x1, [indx](x0, x1) = x0 + x1, [sel1](x0, x1) = x0, [mark](x0) = 0, [active](x0) = 0, [dbl](x0) = x0, [s](x0) = x0, [dbls](x0) = x0, [from](x0) = x0, [dbl1](x0) = x0 + 1, [s1](x0) = 0, [quote](x0) = 0, [proper](x0) = x0 + 1, [ok](x0) = 0, [top](x0) = 0, [0] = 0, [nil] = 0, [01] = 1, [proper#](x0) = x0 Strict: proper# dbl1 X -> proper# X 1 + 1X >= 0 + 1X proper# from X -> proper# X 0 + 1X >= 0 + 1X proper# indx(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# indx(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# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 proper# dbls X -> proper# X 0 + 1X >= 0 + 1X proper# s X -> proper# X 0 + 1X >= 0 + 1X proper# dbl X -> proper# 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 quote X -> quote proper X 1 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 proper s1 X -> s1 proper X 1 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 2 + 1X >= 2 + 1X proper 01() -> ok 01() 2 >= 0 proper from X -> from proper X 1 + 1X >= 1 + 1X proper indx(X1, X2) -> indx(proper X1, proper X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 proper dbls X -> dbls proper X 1 + 1X >= 1 + 1X proper nil() -> ok nil() 1 >= 0 proper s X -> s proper X 1 + 1X >= 1 + 1X proper dbl X -> dbl proper X 1 + 1X >= 1 + 1X proper 0() -> ok 0() 1 >= 0 quote ok X -> ok quote X 0 + 0X >= 0 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 s1 ok X -> ok s1 X 0 + 0X >= 0 + 0X s1 mark X -> mark s1 X 0 + 0X >= 0 + 0X dbl1 ok X -> ok dbl1 X 1 + 0X >= 0 + 0X dbl1 mark X -> mark dbl1 X 1 + 0X >= 0 + 0X from ok X -> ok from X 0 + 0X >= 0 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 0 + 0X1 + 1X2 >= 0 + 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 + 1X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 dbls ok X -> ok dbls X 0 + 0X >= 0 + 0X dbls mark X -> mark dbls X 0 + 0X >= 0 + 0X s ok X -> ok s X 0 + 0X >= 0 + 0X dbl ok X -> ok dbl X 0 + 0X >= 0 + 0X dbl mark X -> mark dbl X 0 + 0X >= 0 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active quote s X -> mark s1 quote X 0 + 0X >= 0 + 0X active quote dbl X -> mark dbl1 X 0 + 0X >= 0 + 0X active quote 0() -> mark 01() 0 >= 0 active quote X -> quote active X 0 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel1(X1, X2) -> sel1(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel1(X1, X2) -> sel1(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 active s1 X -> s1 active X 0 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 0 + 0X >= 0 + 0X active dbl1 0() -> mark 01() 0 >= 0 active dbl1 X -> dbl1 active X 0 + 0X >= 1 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 0 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active dbls nil() -> mark nil() 0 >= 0 active dbls X -> dbls active X 0 + 0X >= 0 + 0X active dbl s X -> mark s s dbl X 0 + 0X >= 0 + 0X active dbl 0() -> mark 0() 0 >= 0 active dbl X -> dbl active X 0 + 0X >= 0 + 0X SCCS (1): Scc: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1, proper# indx(X1, X2) -> proper# X2, proper# from X -> proper# X} SCC (10): Strict: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1, proper# indx(X1, X2) -> proper# X2, proper# from X -> proper# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = x0 + x1, [indx](x0, x1) = x0 + x1, [sel1](x0, x1) = 0, [mark](x0) = 0, [active](x0) = 0, [dbl](x0) = x0, [s](x0) = x0, [dbls](x0) = x0, [from](x0) = x0 + 1, [dbl1](x0) = 0, [s1](x0) = 0, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = 0, [top](x0) = 0, [0] = 0, [nil] = 0, [01] = 0, [proper#](x0) = x0 Strict: proper# from X -> proper# X 1 + 1X >= 0 + 1X proper# indx(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# indx(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# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 proper# dbls X -> proper# X 0 + 1X >= 0 + 1X proper# s X -> proper# X 0 + 1X >= 0 + 1X proper# dbl X -> proper# 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 quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 0 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 0 + 0X proper nil() -> ok nil() 0 >= 0 proper s X -> s proper X 0 + 0X >= 0 + 0X proper dbl X -> dbl proper X 0 + 0X >= 0 + 0X proper 0() -> ok 0() 0 >= 0 quote ok X -> ok quote X 0 + 0X >= 0 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s1 ok X -> ok s1 X 0 + 0X >= 0 + 0X s1 mark X -> mark s1 X 0 + 0X >= 0 + 0X dbl1 ok X -> ok dbl1 X 0 + 0X >= 0 + 0X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 0X >= 0 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 0 + 0X1 + 1X2 >= 0 + 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 + 1X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 dbls ok X -> ok dbls X 0 + 0X >= 0 + 0X dbls mark X -> mark dbls X 0 + 0X >= 0 + 0X s ok X -> ok s X 0 + 0X >= 0 + 0X dbl ok X -> ok dbl X 0 + 0X >= 0 + 0X dbl mark X -> mark dbl X 0 + 0X >= 0 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active quote s X -> mark s1 quote X 0 + 0X >= 0 + 0X active quote dbl X -> mark dbl1 X 0 + 0X >= 0 + 0X active quote 0() -> mark 01() 0 >= 0 active quote X -> quote active X 0 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel1(X1, X2) -> sel1(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel1(X1, X2) -> sel1(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s1 X -> s1 active X 0 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 0 + 0X >= 0 + 0X active dbl1 0() -> mark 01() 0 >= 0 active dbl1 X -> dbl1 active X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 0 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active dbls nil() -> mark nil() 0 >= 0 active dbls X -> dbls active X 0 + 0X >= 0 + 0X active dbl s X -> mark s s dbl X 0 + 0X >= 0 + 0X active dbl 0() -> mark 0() 0 >= 0 active dbl X -> dbl active X 0 + 0X >= 0 + 0X SCCS (1): Scc: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1, proper# indx(X1, X2) -> proper# X2} SCC (9): Strict: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2, proper# indx(X1, X2) -> proper# X1, proper# indx(X1, X2) -> proper# X2} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = x0 + x1, [indx](x0, x1) = x0 + x1 + 1, [sel1](x0, x1) = 0, [mark](x0) = 0, [active](x0) = 0, [dbl](x0) = x0, [s](x0) = x0, [dbls](x0) = x0, [from](x0) = x0, [dbl1](x0) = 0, [s1](x0) = 0, [quote](x0) = 0, [proper](x0) = x0 + 1, [ok](x0) = 0, [top](x0) = 0, [0] = 0, [nil] = 0, [01] = 1, [proper#](x0) = x0 Strict: proper# indx(X1, X2) -> proper# X2 1 + 1X1 + 1X2 >= 0 + 1X2 proper# indx(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# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 proper# dbls X -> proper# X 0 + 1X >= 0 + 1X proper# s X -> proper# X 0 + 1X >= 0 + 1X proper# dbl X -> proper# 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 quote X -> quote proper X 1 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper s1 X -> s1 proper X 1 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 1 + 0X >= 0 + 0X proper 01() -> ok 01() 2 >= 0 proper from X -> from proper X 1 + 1X >= 1 + 1X proper indx(X1, X2) -> indx(proper X1, proper X2) 2 + 1X1 + 1X2 >= 3 + 1X1 + 1X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 proper dbls X -> dbls proper X 1 + 1X >= 1 + 1X proper nil() -> ok nil() 1 >= 0 proper s X -> s proper X 1 + 1X >= 1 + 1X proper dbl X -> dbl proper X 1 + 1X >= 1 + 1X proper 0() -> ok 0() 1 >= 0 quote ok X -> ok quote X 0 + 0X >= 0 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s1 ok X -> ok s1 X 0 + 0X >= 0 + 0X s1 mark X -> mark s1 X 0 + 0X >= 0 + 0X dbl1 ok X -> ok dbl1 X 0 + 0X >= 0 + 0X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 0 + 0X >= 0 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 1 + 0X1 + 1X2 >= 0 + 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 + 1X2 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 dbls ok X -> ok dbls X 0 + 0X >= 0 + 0X dbls mark X -> mark dbls X 0 + 0X >= 0 + 0X s ok X -> ok s X 0 + 0X >= 0 + 0X dbl ok X -> ok dbl X 0 + 0X >= 0 + 0X dbl mark X -> mark dbl X 0 + 0X >= 0 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active quote s X -> mark s1 quote X 0 + 0X >= 0 + 0X active quote dbl X -> mark dbl1 X 0 + 0X >= 0 + 0X active quote 0() -> mark 01() 0 >= 0 active quote X -> quote active X 0 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel1(X1, X2) -> sel1(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel1(X1, X2) -> sel1(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s1 X -> s1 active X 0 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 0 + 0X >= 0 + 0X active dbl1 0() -> mark 01() 0 >= 0 active dbl1 X -> dbl1 active X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 0 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active dbls nil() -> mark nil() 0 >= 0 active dbls X -> dbls active X 0 + 0X >= 0 + 0X active dbl s X -> mark s s dbl X 0 + 0X >= 0 + 0X active dbl 0() -> mark 0() 0 >= 0 active dbl X -> dbl active X 0 + 0X >= 0 + 0X SCCS (1): Scc: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2} SCC (7): Strict: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# sel(X1, X2) -> proper# X1, proper# sel(X1, X2) -> proper# X2} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = x0 + x1 + 1, [indx](x0, x1) = x0, [sel1](x0, x1) = 0, [mark](x0) = 0, [active](x0) = 0, [dbl](x0) = x0, [s](x0) = x0, [dbls](x0) = x0, [from](x0) = x0, [dbl1](x0) = 0, [s1](x0) = 0, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = 0, [top](x0) = 0, [0] = 0, [nil] = 0, [01] = 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# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 proper# dbls X -> proper# X 0 + 1X >= 0 + 1X proper# s X -> proper# X 0 + 1X >= 0 + 1X proper# dbl X -> proper# 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 quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 0 proper from X -> from proper X 0 + 0X >= 0 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 0 + 0X proper nil() -> ok nil() 0 >= 0 proper s X -> s proper X 0 + 0X >= 0 + 0X proper dbl X -> dbl proper X 0 + 0X >= 0 + 0X proper 0() -> ok 0() 0 >= 0 quote ok X -> ok quote X 0 + 0X >= 0 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s1 ok X -> ok s1 X 0 + 0X >= 0 + 0X s1 mark X -> mark s1 X 0 + 0X >= 0 + 0X dbl1 ok X -> ok dbl1 X 0 + 0X >= 0 + 0X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 0 + 0X >= 0 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 0 + 0X1 + 1X2 >= 0 + 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 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 dbls ok X -> ok dbls X 0 + 0X >= 0 + 0X dbls mark X -> mark dbls X 0 + 0X >= 0 + 0X s ok X -> ok s X 0 + 0X >= 0 + 0X dbl ok X -> ok dbl X 0 + 0X >= 0 + 0X dbl mark X -> mark dbl X 0 + 0X >= 0 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active quote s X -> mark s1 quote X 0 + 0X >= 0 + 0X active quote dbl X -> mark dbl1 X 0 + 0X >= 0 + 0X active quote 0() -> mark 01() 0 >= 0 active quote X -> quote active X 0 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel1(X1, X2) -> sel1(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel1(X1, X2) -> sel1(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s1 X -> s1 active X 0 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 0 + 0X >= 0 + 0X active dbl1 0() -> mark 01() 0 >= 0 active dbl1 X -> dbl1 active X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 0 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active dbls nil() -> mark nil() 0 >= 0 active dbls X -> dbls active X 0 + 0X >= 0 + 0X active dbl s X -> mark s s dbl X 0 + 0X >= 0 + 0X active dbl 0() -> mark 0() 0 >= 0 active dbl X -> dbl active X 0 + 0X >= 0 + 0X SCCS (1): Scc: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2} SCC (5): Strict: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X, proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1 + 1, [sel](x0, x1) = 0, [indx](x0, x1) = 0, [sel1](x0, x1) = 0, [mark](x0) = 0, [active](x0) = 0, [dbl](x0) = x0, [s](x0) = x0, [dbls](x0) = x0, [from](x0) = x0 + 1, [dbl1](x0) = 0, [s1](x0) = 0, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = 0, [top](x0) = 0, [0] = 0, [nil] = 0, [01] = 0, [proper#](x0) = x0 Strict: proper# cons(X1, X2) -> proper# X2 1 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 1 + 1X1 + 1X2 >= 0 + 1X1 proper# dbls X -> proper# X 0 + 1X >= 0 + 1X proper# s X -> proper# X 0 + 1X >= 0 + 1X proper# dbl X -> proper# 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 quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 0 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 0 + 0X proper nil() -> ok nil() 0 >= 0 proper s X -> s proper X 0 + 0X >= 0 + 0X proper dbl X -> dbl proper X 0 + 0X >= 0 + 0X proper 0() -> ok 0() 0 >= 0 quote ok X -> ok quote X 0 + 0X >= 0 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s1 ok X -> ok s1 X 0 + 0X >= 0 + 0X s1 mark X -> mark s1 X 0 + 0X >= 0 + 0X dbl1 ok X -> ok dbl1 X 0 + 0X >= 0 + 0X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 0X >= 0 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 0 + 0X1 + 0X2 >= 0 + 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 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 dbls ok X -> ok dbls X 0 + 0X >= 0 + 0X dbls mark X -> mark dbls X 0 + 0X >= 0 + 0X s ok X -> ok s X 0 + 0X >= 0 + 0X dbl ok X -> ok dbl X 0 + 0X >= 0 + 0X dbl mark X -> mark dbl X 0 + 0X >= 0 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active quote s X -> mark s1 quote X 0 + 0X >= 0 + 0X active quote dbl X -> mark dbl1 X 0 + 0X >= 0 + 0X active quote 0() -> mark 01() 0 >= 0 active quote X -> quote active X 0 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel1(X1, X2) -> sel1(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel1(X1, X2) -> sel1(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s1 X -> s1 active X 0 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 0 + 0X >= 0 + 0X active dbl1 0() -> mark 01() 0 >= 0 active dbl1 X -> dbl1 active X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 0 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active dbls nil() -> mark nil() 0 >= 0 active dbls X -> dbls active X 0 + 0X >= 0 + 0X active dbl s X -> mark s s dbl X 0 + 0X >= 0 + 0X active dbl 0() -> mark 0() 0 >= 0 active dbl X -> dbl active X 0 + 0X >= 0 + 0X SCCS (1): Scc: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X} SCC (3): Strict: { proper# dbl X -> proper# X, proper# s X -> proper# X, proper# dbls X -> proper# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 0, [indx](x0, x1) = 0, [sel1](x0, x1) = 0, [mark](x0) = 0, [active](x0) = 0, [dbl](x0) = x0, [s](x0) = x0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = 0, [s1](x0) = 0, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = 0, [top](x0) = 0, [0] = 0, [nil] = 1, [01] = 0, [proper#](x0) = x0 Strict: proper# dbls X -> proper# X 1 + 1X >= 0 + 1X proper# s X -> proper# X 0 + 1X >= 0 + 1X proper# dbl X -> proper# 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 quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 0 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 0 proper s X -> s proper X 0 + 0X >= 0 + 0X proper dbl X -> dbl proper X 0 + 0X >= 0 + 0X proper 0() -> ok 0() 0 >= 0 quote ok X -> ok quote X 0 + 0X >= 0 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s1 ok X -> ok s1 X 0 + 0X >= 0 + 0X s1 mark X -> mark s1 X 0 + 0X >= 0 + 0X dbl1 ok X -> ok dbl1 X 0 + 0X >= 0 + 0X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 0X >= 0 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 0 + 0X1 + 0X2 >= 0 + 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 >= 0 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 dbls ok X -> ok dbls X 1 + 0X >= 0 + 0X dbls mark X -> mark dbls X 1 + 0X >= 0 + 0X s ok X -> ok s X 0 + 0X >= 0 + 0X dbl ok X -> ok dbl X 0 + 0X >= 0 + 0X dbl mark X -> mark dbl X 0 + 0X >= 0 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active quote s X -> mark s1 quote X 0 + 0X >= 0 + 0X active quote dbl X -> mark dbl1 X 0 + 0X >= 0 + 0X active quote 0() -> mark 01() 0 >= 0 active quote X -> quote active X 0 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X active sel1(X1, X2) -> sel1(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel1(X1, X2) -> sel1(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s1 X -> s1 active X 0 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 0 + 0X >= 0 + 0X active dbl1 0() -> mark 01() 0 >= 0 active dbl1 X -> dbl1 active X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 0 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 0X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active dbls nil() -> mark nil() 0 >= 0 active dbls X -> dbls active X 0 + 0X >= 1 + 0X active dbl s X -> mark s s dbl X 0 + 0X >= 0 + 0X active dbl 0() -> mark 0() 0 >= 0 active dbl X -> dbl active X 0 + 0X >= 0 + 0X SCCS (1): Scc: {proper# dbl X -> proper# X, proper# s X -> proper# X} SCC (2): Strict: {proper# dbl X -> proper# X, proper# s X -> proper# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0, [sel](x0, x1) = 0, [indx](x0, x1) = 0, [sel1](x0, x1) = 0, [mark](x0) = x0, [active](x0) = 0, [dbl](x0) = x0, [s](x0) = x0 + 1, [dbls](x0) = 0, [from](x0) = x0 + 1, [dbl1](x0) = 0, [s1](x0) = x0 + 1, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [nil] = 0, [01] = 0, [proper#](x0) = x0 Strict: proper# s X -> proper# X 1 + 1X >= 0 + 1X proper# dbl X -> proper# 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 quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 1 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 1 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 0 + 0X proper nil() -> ok nil() 0 >= 1 proper s X -> s proper X 0 + 0X >= 1 + 0X proper dbl X -> dbl proper X 0 + 0X >= 0 + 0X proper 0() -> ok 0() 0 >= 1 quote ok X -> ok quote X 0 + 0X >= 1 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s1 ok X -> ok s1 X 2 + 1X >= 2 + 1X s1 mark X -> mark s1 X 1 + 1X >= 1 + 1X dbl1 ok X -> ok dbl1 X 0 + 0X >= 1 + 0X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 2 + 1X >= 2 + 1X indx(ok X1, ok X2) -> ok indx(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, 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 cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 dbls ok X -> ok dbls X 0 + 0X >= 1 + 0X dbls mark X -> mark dbls X 0 + 0X >= 0 + 0X s ok X -> ok s X 2 + 1X >= 2 + 1X dbl ok X -> ok dbl X 1 + 1X >= 1 + 1X dbl mark X -> mark dbl X 0 + 1X >= 0 + 1X active quote sel(X, Y) -> mark sel1(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active quote s X -> mark s1 quote X 0 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 0 + 0X >= 0 + 0X active quote 0() -> mark 01() 0 >= 0 active quote X -> quote active X 0 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel1(X1, X2) -> sel1(X1, active X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s1 X -> s1 active X 0 + 0X >= 1 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 0 + 0X >= 2 + 0X active dbl1 0() -> mark 01() 0 >= 0 active dbl1 X -> dbl1 active X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 2 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 0 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 0 + 0X + 0Y >= 0 + 1X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active dbls nil() -> mark nil() 0 >= 0 active dbls X -> dbls active X 0 + 0X >= 0 + 0X active dbl s X -> mark s s dbl X 0 + 0X >= 2 + 1X active dbl 0() -> mark 0() 0 >= 0 active dbl X -> dbl active X 0 + 0X >= 0 + 0X SCCS (1): Scc: {proper# dbl X -> proper# X} SCC (1): Strict: {proper# dbl X -> proper# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [active](x0) = x0 + 1, [dbl](x0) = x0 + 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = x0 + 1, [dbl1](x0) = x0 + 1, [s1](x0) = x0 + 1, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [nil] = 0, [01] = 0, [proper#](x0) = x0 + 1 Strict: proper# dbl X -> proper# X 2 + 1X >= 1 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 1 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 1 + 0X proper 01() -> ok 01() 0 >= 1 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 1 proper s X -> s proper X 0 + 0X >= 0 + 0X proper dbl X -> dbl proper X 0 + 0X >= 1 + 0X proper 0() -> ok 0() 0 >= 1 quote ok X -> ok quote X 0 + 0X >= 1 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 s1 ok X -> ok s1 X 2 + 1X >= 2 + 1X s1 mark X -> mark s1 X 1 + 1X >= 1 + 1X dbl1 ok X -> ok dbl1 X 2 + 1X >= 2 + 1X dbl1 mark X -> mark dbl1 X 1 + 1X >= 1 + 1X from ok X -> ok from X 2 + 1X >= 2 + 1X indx(ok X1, ok X2) -> ok indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 1 + 1X >= 1 + 1X s ok X -> ok s X 0 + 0X >= 1 + 0X dbl ok X -> ok dbl X 2 + 1X >= 2 + 1X dbl mark X -> mark dbl X 1 + 1X >= 1 + 1X active quote sel(X, Y) -> mark sel1(X, Y) 1 + 0X + 0Y >= 1 + 1X + 1Y active quote s X -> mark s1 quote X 1 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 1 + 0X >= 1 + 1X active quote 0() -> mark 01() 1 >= 0 active quote X -> quote active X 1 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 3 + 0X + 1Y + 0Z >= 1 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 3 + 1X + 0Y >= 0 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s1 X -> s1 active X 2 + 1X >= 2 + 1X active dbl1 s X -> mark s1 s1 dbl1 X 2 + 0X >= 3 + 1X active dbl1 0() -> mark 01() 2 >= 0 active dbl1 X -> dbl1 active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 1 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 0Z >= 2 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 1 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 0 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 2 + 1X + 0Y active dbls nil() -> mark nil() 2 >= 0 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 0 + 0X active dbl 0() -> mark 0() 2 >= 0 active dbl X -> dbl active X 2 + 1X >= 2 + 1X Qed SCC (3): Strict: { sel1#(X1, mark X2) -> sel1#(X1, X2), sel1#(mark X1, X2) -> sel1#(X1, X2), sel1#(ok X1, ok X2) -> sel1#(X1, X2)} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = x0 + 1, [dbls](x0) = x0 + 1, [from](x0) = 0, [dbl1](x0) = 1, [s1](x0) = 0, [quote](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 1, [sel1#](x0, x1) = x0 + 1 Strict: sel1#(ok X1, ok X2) -> sel1#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel1#(mark X1, X2) -> sel1#(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel1#(X1, mark X2) -> sel1#(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 quote X -> quote proper X 0 + 0X >= 1 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 1 + 0X proper 01() -> ok 01() 0 >= 2 proper from X -> from proper X 0 + 0X >= 0 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 1 proper s X -> s proper X 0 + 0X >= 1 + 0X proper dbl X -> dbl proper X 0 + 0X >= 1 + 0X proper 0() -> ok 0() 0 >= 2 quote ok X -> ok quote X 2 + 1X >= 2 + 1X quote mark X -> mark quote X 2 + 1X >= 2 + 1X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 s1 ok X -> ok s1 X 0 + 0X >= 1 + 0X s1 mark X -> mark s1 X 0 + 0X >= 1 + 0X dbl1 ok X -> ok dbl1 X 1 + 0X >= 2 + 0X dbl1 mark X -> mark dbl1 X 1 + 0X >= 2 + 0X from ok X -> ok from X 0 + 0X >= 1 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 2 + 1X >= 2 + 1X s ok X -> ok s X 2 + 1X >= 2 + 1X dbl ok X -> ok dbl X 1 + 0X >= 2 + 0X dbl mark X -> mark dbl X 1 + 0X >= 2 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 3 + 0X + 1Y >= 2 + 1X + 1Y active quote s X -> mark s1 quote X 3 + 1X >= 1 + 0X active quote dbl X -> mark dbl1 X 3 + 0X >= 2 + 0X active quote 0() -> mark 01() 3 >= 2 active quote X -> quote active X 2 + 1X >= 2 + 1X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 4 + 1X + 0Y + 1Z >= 2 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 4 + 0X + 1Y >= 1 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s1 X -> s1 active X 1 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 2 + 0X >= 1 + 0X active dbl1 0() -> mark 01() 2 >= 2 active dbl1 X -> dbl1 active X 2 + 0X >= 1 + 0X active from X -> mark cons(X, from s X) 1 + 0X >= 2 + 0X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 0X + 1Y + 0Z >= 3 + 0X + 1Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 1 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 0Y + 1Z >= 2 + 0X + 1Z active sel(0(), cons(X, Y)) -> mark X 3 + 0X + 1Y >= 1 + 1X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 0X + 1Y >= 3 + 0X + 1Y active dbls nil() -> mark nil() 2 >= 1 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 4 + 0X active dbl 0() -> mark 0() 2 >= 2 active dbl X -> dbl active X 2 + 0X >= 1 + 0X SCCS (1): Scc: {sel1#(X1, mark X2) -> sel1#(X1, X2)} SCC (1): Strict: {sel1#(X1, mark X2) -> sel1#(X1, X2)} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + x1 + 1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = 1, [s1](x0) = 0, [quote](x0) = x0 + 1, [proper](x0) = 1, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [nil] = 0, [01] = 1, [sel1#](x0, x1) = x0 Strict: sel1#(X1, mark X2) -> sel1#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 0X proper quote X -> quote proper X 1 + 0X >= 2 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 1 + 0X1 + 0X2 >= 3 + 0X1 + 0X2 proper s1 X -> s1 proper X 1 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 1 + 0X >= 1 + 0X proper 01() -> ok 01() 1 >= 2 proper from X -> from proper X 1 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 1 + 0X1 + 0X2 >= 3 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 proper dbls X -> dbls proper X 1 + 0X >= 2 + 0X proper nil() -> ok nil() 1 >= 1 proper s X -> s proper X 1 + 0X >= 0 + 0X proper dbl X -> dbl proper X 1 + 0X >= 1 + 0X proper 0() -> ok 0() 1 >= 2 quote ok X -> ok quote X 2 + 1X >= 2 + 1X quote mark X -> mark quote X 2 + 1X >= 2 + 1X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 s1 ok X -> ok s1 X 0 + 0X >= 1 + 0X s1 mark X -> mark s1 X 0 + 0X >= 1 + 0X dbl1 ok X -> ok dbl1 X 1 + 0X >= 2 + 0X dbl1 mark X -> mark dbl1 X 1 + 0X >= 2 + 0X from ok X -> ok from X 1 + 0X >= 2 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 indx(mark X1, X2) -> mark indx(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 2 + 1X >= 2 + 1X s ok X -> ok s X 0 + 0X >= 1 + 0X dbl ok X -> ok dbl X 1 + 0X >= 2 + 0X dbl mark X -> mark dbl X 1 + 0X >= 2 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 3 + 0X + 0Y >= 2 + 1X + 1Y active quote s X -> mark s1 quote X 2 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 3 + 0X >= 2 + 0X active quote 0() -> mark 01() 3 >= 2 active quote X -> quote active X 2 + 1X >= 2 + 1X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 3 + 0X + 1Y + 0Z >= 2 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 4 + 1X + 0Y >= 1 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s1 X -> s1 active X 1 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 2 + 0X >= 1 + 0X active dbl1 0() -> mark 01() 2 >= 2 active dbl1 X -> dbl1 active X 2 + 0X >= 1 + 0X active from X -> mark cons(X, from s X) 2 + 0X >= 2 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 1Z >= 3 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 1X >= 1 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 2 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 1 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 3 + 0X + 0Y active dbls nil() -> mark nil() 2 >= 1 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 1 + 0X active dbl 0() -> mark 0() 2 >= 2 active dbl X -> dbl active X 2 + 0X >= 1 + 0X Qed SCC (2): Strict: { indx#(mark X1, X2) -> indx#(X1, X2), indx#(ok X1, ok X2) -> indx#(X1, X2)} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = x0 + 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = x0 + 1, [dbls](x0) = x0 + 1, [from](x0) = x0 + 1, [dbl1](x0) = 1, [s1](x0) = x0 + 1, [quote](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 1, [indx#](x0, x1) = x0 Strict: indx#(ok X1, ok X2) -> indx#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 indx#(mark X1, X2) -> indx#(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 quote X -> quote proper X 0 + 0X >= 1 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 1 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 1 + 0X proper 01() -> ok 01() 0 >= 2 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 1 proper s X -> s proper X 0 + 0X >= 1 + 0X proper dbl X -> dbl proper X 0 + 0X >= 1 + 0X proper 0() -> ok 0() 0 >= 2 quote ok X -> ok quote X 2 + 1X >= 2 + 1X quote mark X -> mark quote X 2 + 1X >= 2 + 1X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s1 ok X -> ok s1 X 2 + 1X >= 2 + 1X s1 mark X -> mark s1 X 2 + 1X >= 2 + 1X dbl1 ok X -> ok dbl1 X 1 + 0X >= 2 + 0X dbl1 mark X -> mark dbl1 X 1 + 0X >= 2 + 0X from ok X -> ok from X 2 + 1X >= 2 + 1X indx(ok X1, ok X2) -> ok indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 2 + 1X >= 2 + 1X s ok X -> ok s X 2 + 1X >= 2 + 1X dbl ok X -> ok dbl X 1 + 0X >= 2 + 0X dbl mark X -> mark dbl X 1 + 0X >= 2 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 3 + 0X + 1Y >= 1 + 0X + 0Y active quote s X -> mark s1 quote X 3 + 1X >= 3 + 1X active quote dbl X -> mark dbl1 X 3 + 0X >= 2 + 0X active quote 0() -> mark 01() 3 >= 2 active quote X -> quote active X 2 + 1X >= 2 + 1X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 1 + 0X + 0Y + 0Z >= 1 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 1 + 0X + 0Y >= 1 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel1(X1, X2) -> sel1(X1, active X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s1 X -> s1 active X 2 + 1X >= 2 + 1X active dbl1 s X -> mark s1 s1 dbl1 X 2 + 0X >= 4 + 0X active dbl1 0() -> mark 01() 2 >= 2 active dbl1 X -> dbl1 active X 2 + 0X >= 1 + 0X active from X -> mark cons(X, from s X) 2 + 1X >= 3 + 2X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 2 + 1X + 1Y + 0Z >= 3 + 0X + 1Y + 1Z active indx(nil(), X) -> mark nil() 2 + 0X >= 1 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 1Y + 1Z >= 2 + 0X + 1Z active sel(0(), cons(X, Y)) -> mark X 2 + 1X + 1Y >= 1 + 1X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 2 + 1X + 1Y >= 3 + 0X + 1Y active dbls nil() -> mark nil() 2 >= 1 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 4 + 0X active dbl 0() -> mark 0() 2 >= 2 active dbl X -> dbl active X 2 + 0X >= 1 + 0X SCCS (1): Scc: {indx#(mark X1, X2) -> indx#(X1, X2)} SCC (1): Strict: {indx#(mark X1, X2) -> indx#(X1, X2)} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + x1 + 1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = 1, [s1](x0) = 0, [quote](x0) = x0 + 1, [proper](x0) = 1, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [nil] = 0, [01] = 1, [indx#](x0, x1) = x0 Strict: indx#(mark X1, X2) -> indx#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 0X proper quote X -> quote proper X 1 + 0X >= 2 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 1 + 0X1 + 0X2 >= 3 + 0X1 + 0X2 proper s1 X -> s1 proper X 1 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 1 + 0X >= 1 + 0X proper 01() -> ok 01() 1 >= 2 proper from X -> from proper X 1 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 1 + 0X1 + 0X2 >= 3 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 proper dbls X -> dbls proper X 1 + 0X >= 2 + 0X proper nil() -> ok nil() 1 >= 1 proper s X -> s proper X 1 + 0X >= 0 + 0X proper dbl X -> dbl proper X 1 + 0X >= 1 + 0X proper 0() -> ok 0() 1 >= 2 quote ok X -> ok quote X 2 + 1X >= 2 + 1X quote mark X -> mark quote X 2 + 1X >= 2 + 1X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 s1 ok X -> ok s1 X 0 + 0X >= 1 + 0X s1 mark X -> mark s1 X 0 + 0X >= 1 + 0X dbl1 ok X -> ok dbl1 X 1 + 0X >= 2 + 0X dbl1 mark X -> mark dbl1 X 1 + 0X >= 2 + 0X from ok X -> ok from X 1 + 0X >= 2 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 indx(mark X1, X2) -> mark indx(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 2 + 1X >= 2 + 1X s ok X -> ok s X 0 + 0X >= 1 + 0X dbl ok X -> ok dbl X 1 + 0X >= 2 + 0X dbl mark X -> mark dbl X 1 + 0X >= 2 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 3 + 0X + 0Y >= 2 + 1X + 1Y active quote s X -> mark s1 quote X 2 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 3 + 0X >= 2 + 0X active quote 0() -> mark 01() 3 >= 2 active quote X -> quote active X 2 + 1X >= 2 + 1X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 3 + 0X + 1Y + 0Z >= 2 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 4 + 1X + 0Y >= 1 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s1 X -> s1 active X 1 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 2 + 0X >= 1 + 0X active dbl1 0() -> mark 01() 2 >= 2 active dbl1 X -> dbl1 active X 2 + 0X >= 1 + 0X active from X -> mark cons(X, from s X) 2 + 0X >= 2 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 1Z >= 3 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 1X >= 1 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 2 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 1 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 3 + 0X + 0Y active dbls nil() -> mark nil() 2 >= 1 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 1 + 0X active dbl 0() -> mark 0() 2 >= 2 active dbl X -> dbl active X 2 + 0X >= 1 + 0X 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: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = x0 + 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = x0 + 1, [dbls](x0) = x0 + 1, [from](x0) = 0, [dbl1](x0) = 1, [s1](x0) = 0, [quote](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 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 quote X -> quote proper X 0 + 0X >= 1 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 1 + 0X proper 01() -> ok 01() 0 >= 2 proper from X -> from proper X 0 + 0X >= 0 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 1 proper s X -> s proper X 0 + 0X >= 1 + 0X proper dbl X -> dbl proper X 0 + 0X >= 1 + 0X proper 0() -> ok 0() 0 >= 2 quote ok X -> ok quote X 2 + 1X >= 2 + 1X quote mark X -> mark quote X 2 + 1X >= 2 + 1X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 s1 ok X -> ok s1 X 0 + 0X >= 1 + 0X s1 mark X -> mark s1 X 0 + 0X >= 1 + 0X dbl1 ok X -> ok dbl1 X 1 + 0X >= 2 + 0X dbl1 mark X -> mark dbl1 X 1 + 0X >= 2 + 0X from ok X -> ok from X 0 + 0X >= 1 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 sel(X1, mark X2) -> mark sel(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 2 + 1X >= 2 + 1X s ok X -> ok s X 2 + 1X >= 2 + 1X dbl ok X -> ok dbl X 1 + 0X >= 2 + 0X dbl mark X -> mark dbl X 1 + 0X >= 2 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 3 + 0X + 1Y >= 2 + 1X + 1Y active quote s X -> mark s1 quote X 3 + 1X >= 1 + 0X active quote dbl X -> mark dbl1 X 3 + 0X >= 2 + 0X active quote 0() -> mark 01() 3 >= 2 active quote X -> quote active X 2 + 1X >= 2 + 1X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 4 + 1X + 0Y + 1Z >= 2 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 4 + 0X + 1Y >= 1 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s1 X -> s1 active X 1 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 2 + 0X >= 1 + 0X active dbl1 0() -> mark 01() 2 >= 2 active dbl1 X -> dbl1 active X 2 + 0X >= 1 + 0X active from X -> mark cons(X, from s X) 1 + 0X >= 2 + 0X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 0X + 1Y + 0Z >= 3 + 0X + 1Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 1 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 3 + 0X + 0Y + 1Z >= 2 + 0X + 1Z active sel(0(), cons(X, Y)) -> mark X 3 + 0X + 1Y >= 1 + 1X 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 dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 0X + 1Y >= 3 + 0X + 1Y active dbls nil() -> mark nil() 2 >= 1 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 4 + 0X active dbl 0() -> mark 0() 2 >= 2 active dbl X -> dbl active X 2 + 0X >= 1 + 0X SCCS (1): Scc: {sel#(X1, mark X2) -> sel#(X1, X2)} SCC (1): Strict: {sel#(X1, mark X2) -> sel#(X1, X2)} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + x1 + 1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = 1, [s1](x0) = 0, [quote](x0) = x0 + 1, [proper](x0) = 1, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [nil] = 0, [01] = 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 >= 2 + 0X proper quote X -> quote proper X 1 + 0X >= 2 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 1 + 0X1 + 0X2 >= 3 + 0X1 + 0X2 proper s1 X -> s1 proper X 1 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 1 + 0X >= 1 + 0X proper 01() -> ok 01() 1 >= 2 proper from X -> from proper X 1 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 1 + 0X1 + 0X2 >= 3 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 proper dbls X -> dbls proper X 1 + 0X >= 2 + 0X proper nil() -> ok nil() 1 >= 1 proper s X -> s proper X 1 + 0X >= 0 + 0X proper dbl X -> dbl proper X 1 + 0X >= 1 + 0X proper 0() -> ok 0() 1 >= 2 quote ok X -> ok quote X 2 + 1X >= 2 + 1X quote mark X -> mark quote X 2 + 1X >= 2 + 1X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 s1 ok X -> ok s1 X 0 + 0X >= 1 + 0X s1 mark X -> mark s1 X 0 + 0X >= 1 + 0X dbl1 ok X -> ok dbl1 X 1 + 0X >= 2 + 0X dbl1 mark X -> mark dbl1 X 1 + 0X >= 2 + 0X from ok X -> ok from X 1 + 0X >= 2 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 indx(mark X1, X2) -> mark indx(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 2 + 1X >= 2 + 1X s ok X -> ok s X 0 + 0X >= 1 + 0X dbl ok X -> ok dbl X 1 + 0X >= 2 + 0X dbl mark X -> mark dbl X 1 + 0X >= 2 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 3 + 0X + 0Y >= 2 + 1X + 1Y active quote s X -> mark s1 quote X 2 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 3 + 0X >= 2 + 0X active quote 0() -> mark 01() 3 >= 2 active quote X -> quote active X 2 + 1X >= 2 + 1X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 3 + 0X + 1Y + 0Z >= 2 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 4 + 1X + 0Y >= 1 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s1 X -> s1 active X 1 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 2 + 0X >= 1 + 0X active dbl1 0() -> mark 01() 2 >= 2 active dbl1 X -> dbl1 active X 2 + 0X >= 1 + 0X active from X -> mark cons(X, from s X) 2 + 0X >= 2 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 1Z >= 3 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 1X >= 1 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 2 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 1 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 3 + 0X + 0Y active dbls nil() -> mark nil() 2 >= 1 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 1 + 0X active dbl 0() -> mark 0() 2 >= 2 active dbl X -> dbl active X 2 + 0X >= 1 + 0X Qed SCC (1): Strict: {cons#(ok X1, ok X2) -> cons#(X1, X2)} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + x1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = x0 + 1, [dbls](x0) = x0 + 1, [from](x0) = x0 + 1, [dbl1](x0) = 1, [s1](x0) = x0 + 1, [quote](x0) = x0 + 1, [proper](x0) = 1, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 1, [cons#](x0, x1) = x0 Strict: cons#(ok X1, ok X2) -> cons#(X1, X2) 1 + 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 quote X -> quote proper X 1 + 0X >= 2 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 1 + 0X1 + 0X2 >= 3 + 0X1 + 0X2 proper s1 X -> s1 proper X 1 + 0X >= 2 + 0X proper dbl1 X -> dbl1 proper X 1 + 0X >= 1 + 0X proper 01() -> ok 01() 1 >= 2 proper from X -> from proper X 1 + 0X >= 2 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 proper dbls X -> dbls proper X 1 + 0X >= 2 + 0X proper nil() -> ok nil() 1 >= 1 proper s X -> s proper X 1 + 0X >= 2 + 0X proper dbl X -> dbl proper X 1 + 0X >= 1 + 0X proper 0() -> ok 0() 1 >= 2 quote ok X -> ok quote X 2 + 1X >= 2 + 1X quote mark X -> mark quote X 2 + 1X >= 2 + 1X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 s1 ok X -> ok s1 X 2 + 1X >= 2 + 1X s1 mark X -> mark s1 X 2 + 1X >= 2 + 1X dbl1 ok X -> ok dbl1 X 1 + 0X >= 2 + 0X dbl1 mark X -> mark dbl1 X 1 + 0X >= 2 + 0X from ok X -> ok from X 2 + 1X >= 2 + 1X indx(ok X1, ok X2) -> ok indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 2 + 1X >= 2 + 1X s ok X -> ok s X 2 + 1X >= 2 + 1X dbl ok X -> ok dbl X 1 + 0X >= 2 + 0X dbl mark X -> mark dbl X 1 + 0X >= 2 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 3 + 0X + 0Y >= 2 + 1X + 1Y active quote s X -> mark s1 quote X 3 + 1X >= 3 + 1X active quote dbl X -> mark dbl1 X 3 + 0X >= 2 + 0X active quote 0() -> mark 01() 3 >= 2 active quote X -> quote active X 2 + 1X >= 2 + 1X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 3 + 1X + 1Y + 1Z >= 2 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 3 + 1X + 1Y >= 1 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s1 X -> s1 active X 2 + 1X >= 2 + 1X active dbl1 s X -> mark s1 s1 dbl1 X 2 + 0X >= 4 + 0X active dbl1 0() -> mark 01() 2 >= 2 active dbl1 X -> dbl1 active X 2 + 0X >= 1 + 0X active from X -> mark cons(X, from s X) 2 + 1X >= 3 + 2X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 2 + 1X + 1Y + 0Z >= 3 + 0X + 1Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 1 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 2 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 1 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 2 + 1X + 1Y >= 3 + 0X + 1Y active dbls nil() -> mark nil() 2 >= 1 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 4 + 0X active dbl 0() -> mark 0() 2 >= 2 active dbl X -> dbl active X 2 + 0X >= 1 + 0X Qed SCC (2): Strict: {quote# mark X -> quote# X, quote# ok X -> quote# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = x0 + 1, [s1](x0) = 0, [quote](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 1, [quote#](x0) = x0 Strict: quote# ok X -> quote# X 0 + 1X >= 0 + 1X quote# mark X -> quote# X 1 + 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 quote X -> quote proper X 2 + 1X >= 2 + 1X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper s1 X -> s1 proper X 1 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 2 + 1X >= 2 + 1X proper 01() -> ok 01() 2 >= 1 proper from X -> from proper X 2 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper dbls X -> dbls proper X 2 + 1X >= 2 + 1X proper nil() -> ok nil() 1 >= 0 proper s X -> s proper X 1 + 0X >= 0 + 0X proper dbl X -> dbl proper X 2 + 0X >= 1 + 0X proper 0() -> ok 0() 2 >= 1 quote ok X -> ok quote X 1 + 1X >= 1 + 1X quote mark X -> mark quote X 2 + 1X >= 2 + 1X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s1 ok X -> ok s1 X 0 + 0X >= 0 + 0X s1 mark X -> mark s1 X 0 + 0X >= 1 + 0X dbl1 ok X -> ok dbl1 X 1 + 1X >= 1 + 1X dbl1 mark X -> mark dbl1 X 2 + 1X >= 2 + 1X from ok X -> ok from X 1 + 0X >= 1 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 dbls ok X -> ok dbls X 1 + 1X >= 1 + 1X dbls mark X -> mark dbls X 2 + 1X >= 2 + 1X s ok X -> ok s X 0 + 0X >= 0 + 0X dbl ok X -> ok dbl X 1 + 0X >= 1 + 0X dbl mark X -> mark dbl X 1 + 0X >= 2 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 3 + 0X + 0Y >= 1 + 0X + 0Y active quote s X -> mark s1 quote X 2 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 3 + 0X >= 2 + 1X active quote 0() -> mark 01() 3 >= 2 active quote X -> quote active X 2 + 1X >= 2 + 1X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 1 + 0X + 0Y + 0Z >= 1 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 1 + 0X + 0Y >= 1 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel1(X1, X2) -> sel1(X1, active X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s1 X -> s1 active X 1 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 2 + 0X >= 1 + 0X active dbl1 0() -> mark 01() 3 >= 2 active dbl1 X -> dbl1 active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 0X >= 2 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 0Z >= 3 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 1 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 2 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 1 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 3 + 0X + 0Y active dbls nil() -> mark nil() 2 >= 1 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 1 + 0X active dbl 0() -> mark 0() 2 >= 2 active dbl X -> dbl active X 2 + 0X >= 1 + 0X SCCS (1): Scc: {quote# ok X -> quote# X} SCC (1): Strict: {quote# ok X -> quote# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = 0, [s1](x0) = x0 + 1, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 0, [quote#](x0) = x0 + 1 Strict: quote# ok X -> quote# X 2 + 1X >= 1 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 1 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 1 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 1 proper s X -> s proper X 0 + 0X >= 0 + 0X proper dbl X -> dbl proper X 0 + 0X >= 1 + 0X proper 0() -> ok 0() 0 >= 2 quote ok X -> ok quote X 0 + 0X >= 1 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 s1 ok X -> ok s1 X 2 + 1X >= 2 + 1X s1 mark X -> mark s1 X 1 + 1X >= 1 + 1X dbl1 ok X -> ok dbl1 X 0 + 0X >= 1 + 0X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 0X >= 2 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 1 + 1X >= 1 + 1X s ok X -> ok s X 0 + 0X >= 1 + 0X dbl ok X -> ok dbl X 1 + 0X >= 2 + 0X dbl mark X -> mark dbl X 1 + 0X >= 1 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 1 + 0X + 0Y >= 1 + 1X + 1Y active quote s X -> mark s1 quote X 1 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 1 + 0X >= 0 + 0X active quote 0() -> mark 01() 1 >= 0 active quote X -> quote active X 1 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 3 + 0X + 1Y + 0Z >= 1 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 4 + 1X + 0Y >= 0 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s1 X -> s1 active X 2 + 1X >= 2 + 1X active dbl1 s X -> mark s1 s1 dbl1 X 1 + 0X >= 2 + 0X active dbl1 0() -> mark 01() 1 >= 0 active dbl1 X -> dbl1 active X 1 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 2 + 0X >= 1 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 0Z >= 2 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 1 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 0 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 2 + 0X + 0Y active dbls nil() -> mark nil() 2 >= 0 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 0 + 0X active dbl 0() -> mark 0() 2 >= 1 active dbl X -> dbl active X 2 + 0X >= 1 + 0X Qed SCC (2): Strict: {s1# mark X -> s1# X, s1# ok X -> s1# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = x0 + 1, [s1](x0) = 0, [quote](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 1, [s1#](x0) = x0 Strict: s1# ok X -> s1# X 0 + 1X >= 0 + 1X s1# mark X -> s1# X 1 + 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 quote X -> quote proper X 2 + 1X >= 2 + 1X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper s1 X -> s1 proper X 1 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 2 + 1X >= 2 + 1X proper 01() -> ok 01() 2 >= 1 proper from X -> from proper X 2 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper dbls X -> dbls proper X 2 + 1X >= 2 + 1X proper nil() -> ok nil() 1 >= 0 proper s X -> s proper X 1 + 0X >= 0 + 0X proper dbl X -> dbl proper X 2 + 0X >= 1 + 0X proper 0() -> ok 0() 2 >= 1 quote ok X -> ok quote X 1 + 1X >= 1 + 1X quote mark X -> mark quote X 2 + 1X >= 2 + 1X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s1 ok X -> ok s1 X 0 + 0X >= 0 + 0X s1 mark X -> mark s1 X 0 + 0X >= 1 + 0X dbl1 ok X -> ok dbl1 X 1 + 1X >= 1 + 1X dbl1 mark X -> mark dbl1 X 2 + 1X >= 2 + 1X from ok X -> ok from X 1 + 0X >= 1 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 dbls ok X -> ok dbls X 1 + 1X >= 1 + 1X dbls mark X -> mark dbls X 2 + 1X >= 2 + 1X s ok X -> ok s X 0 + 0X >= 0 + 0X dbl ok X -> ok dbl X 1 + 0X >= 1 + 0X dbl mark X -> mark dbl X 1 + 0X >= 2 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 3 + 0X + 0Y >= 1 + 0X + 0Y active quote s X -> mark s1 quote X 2 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 3 + 0X >= 2 + 1X active quote 0() -> mark 01() 3 >= 2 active quote X -> quote active X 2 + 1X >= 2 + 1X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 1 + 0X + 0Y + 0Z >= 1 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 1 + 0X + 0Y >= 1 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel1(X1, X2) -> sel1(X1, active X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s1 X -> s1 active X 1 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 2 + 0X >= 1 + 0X active dbl1 0() -> mark 01() 3 >= 2 active dbl1 X -> dbl1 active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 0X >= 2 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 0Z >= 3 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 1 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 2 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 1 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 3 + 0X + 0Y active dbls nil() -> mark nil() 2 >= 1 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 1 + 0X active dbl 0() -> mark 0() 2 >= 2 active dbl X -> dbl active X 2 + 0X >= 1 + 0X SCCS (1): Scc: {s1# ok X -> s1# X} SCC (1): Strict: {s1# ok X -> s1# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = 0, [s1](x0) = x0 + 1, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 0, [s1#](x0) = x0 + 1 Strict: s1# ok X -> s1# X 2 + 1X >= 1 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 1 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 1 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 1 proper s X -> s proper X 0 + 0X >= 0 + 0X proper dbl X -> dbl proper X 0 + 0X >= 1 + 0X proper 0() -> ok 0() 0 >= 2 quote ok X -> ok quote X 0 + 0X >= 1 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 s1 ok X -> ok s1 X 2 + 1X >= 2 + 1X s1 mark X -> mark s1 X 1 + 1X >= 1 + 1X dbl1 ok X -> ok dbl1 X 0 + 0X >= 1 + 0X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 0X >= 2 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 1 + 1X >= 1 + 1X s ok X -> ok s X 0 + 0X >= 1 + 0X dbl ok X -> ok dbl X 1 + 0X >= 2 + 0X dbl mark X -> mark dbl X 1 + 0X >= 1 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 1 + 0X + 0Y >= 1 + 1X + 1Y active quote s X -> mark s1 quote X 1 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 1 + 0X >= 0 + 0X active quote 0() -> mark 01() 1 >= 0 active quote X -> quote active X 1 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 3 + 0X + 1Y + 0Z >= 1 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 4 + 1X + 0Y >= 0 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s1 X -> s1 active X 2 + 1X >= 2 + 1X active dbl1 s X -> mark s1 s1 dbl1 X 1 + 0X >= 2 + 0X active dbl1 0() -> mark 01() 1 >= 0 active dbl1 X -> dbl1 active X 1 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 2 + 0X >= 1 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 0Z >= 2 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 1 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 0 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 2 + 0X + 0Y active dbls nil() -> mark nil() 2 >= 0 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 0 + 0X active dbl 0() -> mark 0() 2 >= 1 active dbl X -> dbl active X 2 + 0X >= 1 + 0X Qed SCC (2): Strict: {dbl1# mark X -> dbl1# X, dbl1# ok X -> dbl1# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = x0 + 1, [s1](x0) = 0, [quote](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 1, [dbl1#](x0) = x0 Strict: dbl1# ok X -> dbl1# X 0 + 1X >= 0 + 1X dbl1# mark X -> dbl1# X 1 + 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 quote X -> quote proper X 2 + 1X >= 2 + 1X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper s1 X -> s1 proper X 1 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 2 + 1X >= 2 + 1X proper 01() -> ok 01() 2 >= 1 proper from X -> from proper X 2 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper dbls X -> dbls proper X 2 + 1X >= 2 + 1X proper nil() -> ok nil() 1 >= 0 proper s X -> s proper X 1 + 0X >= 0 + 0X proper dbl X -> dbl proper X 2 + 0X >= 1 + 0X proper 0() -> ok 0() 2 >= 1 quote ok X -> ok quote X 1 + 1X >= 1 + 1X quote mark X -> mark quote X 2 + 1X >= 2 + 1X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s1 ok X -> ok s1 X 0 + 0X >= 0 + 0X s1 mark X -> mark s1 X 0 + 0X >= 1 + 0X dbl1 ok X -> ok dbl1 X 1 + 1X >= 1 + 1X dbl1 mark X -> mark dbl1 X 2 + 1X >= 2 + 1X from ok X -> ok from X 1 + 0X >= 1 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 dbls ok X -> ok dbls X 1 + 1X >= 1 + 1X dbls mark X -> mark dbls X 2 + 1X >= 2 + 1X s ok X -> ok s X 0 + 0X >= 0 + 0X dbl ok X -> ok dbl X 1 + 0X >= 1 + 0X dbl mark X -> mark dbl X 1 + 0X >= 2 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 3 + 0X + 0Y >= 1 + 0X + 0Y active quote s X -> mark s1 quote X 2 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 3 + 0X >= 2 + 1X active quote 0() -> mark 01() 3 >= 2 active quote X -> quote active X 2 + 1X >= 2 + 1X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 1 + 0X + 0Y + 0Z >= 1 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 1 + 0X + 0Y >= 1 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel1(X1, X2) -> sel1(X1, active X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s1 X -> s1 active X 1 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 2 + 0X >= 1 + 0X active dbl1 0() -> mark 01() 3 >= 2 active dbl1 X -> dbl1 active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 0X >= 2 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 0Z >= 3 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 1 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 2 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 1 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 3 + 0X + 0Y active dbls nil() -> mark nil() 2 >= 1 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 1 + 0X active dbl 0() -> mark 0() 2 >= 2 active dbl X -> dbl active X 2 + 0X >= 1 + 0X SCCS (1): Scc: {dbl1# ok X -> dbl1# X} SCC (1): Strict: {dbl1# ok X -> dbl1# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = 0, [s1](x0) = x0 + 1, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 0, [dbl1#](x0) = x0 + 1 Strict: dbl1# ok X -> dbl1# X 2 + 1X >= 1 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 1 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 1 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 1 proper s X -> s proper X 0 + 0X >= 0 + 0X proper dbl X -> dbl proper X 0 + 0X >= 1 + 0X proper 0() -> ok 0() 0 >= 2 quote ok X -> ok quote X 0 + 0X >= 1 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 s1 ok X -> ok s1 X 2 + 1X >= 2 + 1X s1 mark X -> mark s1 X 1 + 1X >= 1 + 1X dbl1 ok X -> ok dbl1 X 0 + 0X >= 1 + 0X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 0X >= 2 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 1 + 1X >= 1 + 1X s ok X -> ok s X 0 + 0X >= 1 + 0X dbl ok X -> ok dbl X 1 + 0X >= 2 + 0X dbl mark X -> mark dbl X 1 + 0X >= 1 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 1 + 0X + 0Y >= 1 + 1X + 1Y active quote s X -> mark s1 quote X 1 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 1 + 0X >= 0 + 0X active quote 0() -> mark 01() 1 >= 0 active quote X -> quote active X 1 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 3 + 0X + 1Y + 0Z >= 1 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 4 + 1X + 0Y >= 0 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s1 X -> s1 active X 2 + 1X >= 2 + 1X active dbl1 s X -> mark s1 s1 dbl1 X 1 + 0X >= 2 + 0X active dbl1 0() -> mark 01() 1 >= 0 active dbl1 X -> dbl1 active X 1 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 2 + 0X >= 1 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 0Z >= 2 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 1 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 0 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 2 + 0X + 0Y active dbls nil() -> mark nil() 2 >= 0 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 0 + 0X active dbl 0() -> mark 0() 2 >= 1 active dbl X -> dbl active X 2 + 0X >= 1 + 0X Qed SCC (1): Strict: {from# ok X -> from# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = 0, [s1](x0) = x0 + 1, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 0, [from#](x0) = x0 + 1 Strict: from# ok X -> from# X 2 + 1X >= 1 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 1 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 1 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 1 proper s X -> s proper X 0 + 0X >= 0 + 0X proper dbl X -> dbl proper X 0 + 0X >= 1 + 0X proper 0() -> ok 0() 0 >= 2 quote ok X -> ok quote X 0 + 0X >= 1 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 s1 ok X -> ok s1 X 2 + 1X >= 2 + 1X s1 mark X -> mark s1 X 1 + 1X >= 1 + 1X dbl1 ok X -> ok dbl1 X 0 + 0X >= 1 + 0X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 0X >= 2 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 1 + 1X >= 1 + 1X s ok X -> ok s X 0 + 0X >= 1 + 0X dbl ok X -> ok dbl X 1 + 0X >= 2 + 0X dbl mark X -> mark dbl X 1 + 0X >= 1 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 1 + 0X + 0Y >= 1 + 1X + 1Y active quote s X -> mark s1 quote X 1 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 1 + 0X >= 0 + 0X active quote 0() -> mark 01() 1 >= 0 active quote X -> quote active X 1 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 3 + 0X + 1Y + 0Z >= 1 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 4 + 1X + 0Y >= 0 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s1 X -> s1 active X 2 + 1X >= 2 + 1X active dbl1 s X -> mark s1 s1 dbl1 X 1 + 0X >= 2 + 0X active dbl1 0() -> mark 01() 1 >= 0 active dbl1 X -> dbl1 active X 1 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 2 + 0X >= 1 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 0Z >= 2 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 1 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 0 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 2 + 0X + 0Y active dbls nil() -> mark nil() 2 >= 0 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 0 + 0X active dbl 0() -> mark 0() 2 >= 1 active dbl X -> dbl active X 2 + 0X >= 1 + 0X Qed SCC (2): Strict: {dbls# mark X -> dbls# X, dbls# ok X -> dbls# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = x0 + 1, [s1](x0) = 0, [quote](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 1, [dbls#](x0) = x0 Strict: dbls# ok X -> dbls# X 0 + 1X >= 0 + 1X dbls# mark X -> dbls# X 1 + 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 quote X -> quote proper X 2 + 1X >= 2 + 1X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper s1 X -> s1 proper X 1 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 2 + 1X >= 2 + 1X proper 01() -> ok 01() 2 >= 1 proper from X -> from proper X 2 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper dbls X -> dbls proper X 2 + 1X >= 2 + 1X proper nil() -> ok nil() 1 >= 0 proper s X -> s proper X 1 + 0X >= 0 + 0X proper dbl X -> dbl proper X 2 + 0X >= 1 + 0X proper 0() -> ok 0() 2 >= 1 quote ok X -> ok quote X 1 + 1X >= 1 + 1X quote mark X -> mark quote X 2 + 1X >= 2 + 1X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s1 ok X -> ok s1 X 0 + 0X >= 0 + 0X s1 mark X -> mark s1 X 0 + 0X >= 1 + 0X dbl1 ok X -> ok dbl1 X 1 + 1X >= 1 + 1X dbl1 mark X -> mark dbl1 X 2 + 1X >= 2 + 1X from ok X -> ok from X 1 + 0X >= 1 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 dbls ok X -> ok dbls X 1 + 1X >= 1 + 1X dbls mark X -> mark dbls X 2 + 1X >= 2 + 1X s ok X -> ok s X 0 + 0X >= 0 + 0X dbl ok X -> ok dbl X 1 + 0X >= 1 + 0X dbl mark X -> mark dbl X 1 + 0X >= 2 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 3 + 0X + 0Y >= 1 + 0X + 0Y active quote s X -> mark s1 quote X 2 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 3 + 0X >= 2 + 1X active quote 0() -> mark 01() 3 >= 2 active quote X -> quote active X 2 + 1X >= 2 + 1X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 1 + 0X + 0Y + 0Z >= 1 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 1 + 0X + 0Y >= 1 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel1(X1, X2) -> sel1(X1, active X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s1 X -> s1 active X 1 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 2 + 0X >= 1 + 0X active dbl1 0() -> mark 01() 3 >= 2 active dbl1 X -> dbl1 active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 0X >= 2 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 0Z >= 3 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 1 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 2 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 1 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 3 + 0X + 0Y active dbls nil() -> mark nil() 2 >= 1 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 1 + 0X active dbl 0() -> mark 0() 2 >= 2 active dbl X -> dbl active X 2 + 0X >= 1 + 0X SCCS (1): Scc: {dbls# ok X -> dbls# X} SCC (1): Strict: {dbls# ok X -> dbls# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = 0, [s1](x0) = x0 + 1, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 0, [dbls#](x0) = x0 + 1 Strict: dbls# ok X -> dbls# X 2 + 1X >= 1 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 1 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 1 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 1 proper s X -> s proper X 0 + 0X >= 0 + 0X proper dbl X -> dbl proper X 0 + 0X >= 1 + 0X proper 0() -> ok 0() 0 >= 2 quote ok X -> ok quote X 0 + 0X >= 1 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 s1 ok X -> ok s1 X 2 + 1X >= 2 + 1X s1 mark X -> mark s1 X 1 + 1X >= 1 + 1X dbl1 ok X -> ok dbl1 X 0 + 0X >= 1 + 0X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 0X >= 2 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 1 + 1X >= 1 + 1X s ok X -> ok s X 0 + 0X >= 1 + 0X dbl ok X -> ok dbl X 1 + 0X >= 2 + 0X dbl mark X -> mark dbl X 1 + 0X >= 1 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 1 + 0X + 0Y >= 1 + 1X + 1Y active quote s X -> mark s1 quote X 1 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 1 + 0X >= 0 + 0X active quote 0() -> mark 01() 1 >= 0 active quote X -> quote active X 1 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 3 + 0X + 1Y + 0Z >= 1 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 4 + 1X + 0Y >= 0 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s1 X -> s1 active X 2 + 1X >= 2 + 1X active dbl1 s X -> mark s1 s1 dbl1 X 1 + 0X >= 2 + 0X active dbl1 0() -> mark 01() 1 >= 0 active dbl1 X -> dbl1 active X 1 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 2 + 0X >= 1 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 0Z >= 2 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 1 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 0 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 2 + 0X + 0Y active dbls nil() -> mark nil() 2 >= 0 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 0 + 0X active dbl 0() -> mark 0() 2 >= 1 active dbl X -> dbl active X 2 + 0X >= 1 + 0X Qed SCC (1): Strict: {s# ok X -> s# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = 0, [s1](x0) = x0 + 1, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 0, [s#](x0) = x0 + 1 Strict: s# ok X -> s# X 2 + 1X >= 1 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 1 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 1 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 1 proper s X -> s proper X 0 + 0X >= 0 + 0X proper dbl X -> dbl proper X 0 + 0X >= 1 + 0X proper 0() -> ok 0() 0 >= 2 quote ok X -> ok quote X 0 + 0X >= 1 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 s1 ok X -> ok s1 X 2 + 1X >= 2 + 1X s1 mark X -> mark s1 X 1 + 1X >= 1 + 1X dbl1 ok X -> ok dbl1 X 0 + 0X >= 1 + 0X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 0X >= 2 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 1 + 1X >= 1 + 1X s ok X -> ok s X 0 + 0X >= 1 + 0X dbl ok X -> ok dbl X 1 + 0X >= 2 + 0X dbl mark X -> mark dbl X 1 + 0X >= 1 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 1 + 0X + 0Y >= 1 + 1X + 1Y active quote s X -> mark s1 quote X 1 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 1 + 0X >= 0 + 0X active quote 0() -> mark 01() 1 >= 0 active quote X -> quote active X 1 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 3 + 0X + 1Y + 0Z >= 1 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 4 + 1X + 0Y >= 0 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s1 X -> s1 active X 2 + 1X >= 2 + 1X active dbl1 s X -> mark s1 s1 dbl1 X 1 + 0X >= 2 + 0X active dbl1 0() -> mark 01() 1 >= 0 active dbl1 X -> dbl1 active X 1 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 2 + 0X >= 1 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 0Z >= 2 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 1 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 0 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 2 + 0X + 0Y active dbls nil() -> mark nil() 2 >= 0 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 0 + 0X active dbl 0() -> mark 0() 2 >= 1 active dbl X -> dbl active X 2 + 0X >= 1 + 0X Qed SCC (2): Strict: {dbl# mark X -> dbl# X, dbl# ok X -> dbl# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = x0 + 1, [s1](x0) = 0, [quote](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 1, [dbl#](x0) = x0 Strict: dbl# ok X -> dbl# X 0 + 1X >= 0 + 1X dbl# mark X -> dbl# X 1 + 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 quote X -> quote proper X 2 + 1X >= 2 + 1X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper s1 X -> s1 proper X 1 + 0X >= 0 + 0X proper dbl1 X -> dbl1 proper X 2 + 1X >= 2 + 1X proper 01() -> ok 01() 2 >= 1 proper from X -> from proper X 2 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper dbls X -> dbls proper X 2 + 1X >= 2 + 1X proper nil() -> ok nil() 1 >= 0 proper s X -> s proper X 1 + 0X >= 0 + 0X proper dbl X -> dbl proper X 2 + 0X >= 1 + 0X proper 0() -> ok 0() 2 >= 1 quote ok X -> ok quote X 1 + 1X >= 1 + 1X quote mark X -> mark quote X 2 + 1X >= 2 + 1X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s1 ok X -> ok s1 X 0 + 0X >= 0 + 0X s1 mark X -> mark s1 X 0 + 0X >= 1 + 0X dbl1 ok X -> ok dbl1 X 1 + 1X >= 1 + 1X dbl1 mark X -> mark dbl1 X 2 + 1X >= 2 + 1X from ok X -> ok from X 1 + 0X >= 1 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 dbls ok X -> ok dbls X 1 + 1X >= 1 + 1X dbls mark X -> mark dbls X 2 + 1X >= 2 + 1X s ok X -> ok s X 0 + 0X >= 0 + 0X dbl ok X -> ok dbl X 1 + 0X >= 1 + 0X dbl mark X -> mark dbl X 1 + 0X >= 2 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 3 + 0X + 0Y >= 1 + 0X + 0Y active quote s X -> mark s1 quote X 2 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 3 + 0X >= 2 + 1X active quote 0() -> mark 01() 3 >= 2 active quote X -> quote active X 2 + 1X >= 2 + 1X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 1 + 0X + 0Y + 0Z >= 1 + 0X + 0Z active sel1(0(), cons(X, Y)) -> mark X 1 + 0X + 0Y >= 1 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active sel1(X1, X2) -> sel1(X1, active X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s1 X -> s1 active X 1 + 0X >= 0 + 0X active dbl1 s X -> mark s1 s1 dbl1 X 2 + 0X >= 1 + 0X active dbl1 0() -> mark 01() 3 >= 2 active dbl1 X -> dbl1 active X 2 + 1X >= 2 + 1X active from X -> mark cons(X, from s X) 2 + 0X >= 2 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 0Z >= 3 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 1 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 2 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 1 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 3 + 0X + 0Y active dbls nil() -> mark nil() 2 >= 1 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 1 + 0X active dbl 0() -> mark 0() 2 >= 2 active dbl X -> dbl active X 2 + 0X >= 1 + 0X SCCS (1): Scc: {dbl# ok X -> dbl# X} SCC (1): Strict: {dbl# ok X -> dbl# X} Weak: { active dbl X -> dbl active X, active dbl 0() -> mark 0(), active dbl s X -> mark s s dbl X, active dbls X -> dbls active X, active dbls nil() -> mark nil(), active dbls cons(X, Y) -> mark cons(dbl X, dbls Y), active sel(X1, X2) -> sel(X1, active X2), active sel(X1, X2) -> sel(active X1, X2), active sel(0(), cons(X, Y)) -> mark X, active sel(s X, cons(Y, Z)) -> mark sel(X, Z), active indx(X1, X2) -> indx(active X1, X2), active indx(nil(), X) -> mark nil(), active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)), active from X -> mark cons(X, from s X), active dbl1 X -> dbl1 active X, active dbl1 0() -> mark 01(), active dbl1 s X -> mark s1 s1 dbl1 X, active s1 X -> s1 active X, active sel1(X1, X2) -> sel1(X1, active X2), active sel1(X1, X2) -> sel1(active X1, X2), active sel1(0(), cons(X, Y)) -> mark X, active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z), active quote X -> quote active X, active quote 0() -> mark 01(), active quote dbl X -> mark dbl1 X, active quote s X -> mark s1 quote X, active quote sel(X, Y) -> mark sel1(X, Y), dbl mark X -> mark dbl X, dbl ok X -> ok dbl X, s ok X -> ok s X, dbls mark X -> mark dbls X, dbls ok X -> ok dbls X, cons(ok X1, ok X2) -> ok cons(X1, X2), sel(X1, mark X2) -> mark sel(X1, X2), sel(mark X1, X2) -> mark sel(X1, X2), sel(ok X1, ok X2) -> ok sel(X1, X2), indx(mark X1, X2) -> mark indx(X1, X2), indx(ok X1, ok X2) -> ok indx(X1, X2), from ok X -> ok from X, dbl1 mark X -> mark dbl1 X, dbl1 ok X -> ok dbl1 X, s1 mark X -> mark s1 X, s1 ok X -> ok s1 X, sel1(X1, mark X2) -> mark sel1(X1, X2), sel1(mark X1, X2) -> mark sel1(X1, X2), sel1(ok X1, ok X2) -> ok sel1(X1, X2), quote mark X -> mark quote X, quote ok X -> ok quote X, proper 0() -> ok 0(), proper dbl X -> dbl proper X, proper s X -> s proper X, proper nil() -> ok nil(), proper dbls X -> dbls proper X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper sel(X1, X2) -> sel(proper X1, proper X2), proper indx(X1, X2) -> indx(proper X1, proper X2), proper from X -> from proper X, proper 01() -> ok 01(), proper dbl1 X -> dbl1 proper X, proper s1 X -> s1 proper X, proper sel1(X1, X2) -> sel1(proper X1, proper X2), proper quote X -> quote proper X, top mark X -> top proper X, top ok X -> top active X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cons](x0, x1) = x0 + 1, [sel](x0, x1) = 1, [indx](x0, x1) = x0 + 1, [sel1](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [active](x0) = x0 + 1, [dbl](x0) = 1, [s](x0) = 0, [dbls](x0) = x0 + 1, [from](x0) = 1, [dbl1](x0) = 0, [s1](x0) = x0 + 1, [quote](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [nil] = 0, [01] = 0, [dbl#](x0) = x0 + 1 Strict: dbl# ok X -> dbl# X 2 + 1X >= 1 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper quote X -> quote proper X 0 + 0X >= 0 + 0X proper sel1(X1, X2) -> sel1(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper s1 X -> s1 proper X 0 + 0X >= 1 + 0X proper dbl1 X -> dbl1 proper X 0 + 0X >= 0 + 0X proper 01() -> ok 01() 0 >= 1 proper from X -> from proper X 0 + 0X >= 1 + 0X proper indx(X1, X2) -> indx(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper sel(X1, X2) -> sel(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper dbls X -> dbls proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 1 proper s X -> s proper X 0 + 0X >= 0 + 0X proper dbl X -> dbl proper X 0 + 0X >= 1 + 0X proper 0() -> ok 0() 0 >= 2 quote ok X -> ok quote X 0 + 0X >= 1 + 0X quote mark X -> mark quote X 0 + 0X >= 0 + 0X sel1(ok X1, ok X2) -> ok sel1(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 sel1(mark X1, X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 sel1(X1, mark X2) -> mark sel1(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 s1 ok X -> ok s1 X 2 + 1X >= 2 + 1X s1 mark X -> mark s1 X 1 + 1X >= 1 + 1X dbl1 ok X -> ok dbl1 X 0 + 0X >= 1 + 0X dbl1 mark X -> mark dbl1 X 0 + 0X >= 0 + 0X from ok X -> ok from X 1 + 0X >= 2 + 0X indx(ok X1, ok X2) -> ok indx(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 indx(mark X1, X2) -> mark indx(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 sel(ok X1, ok X2) -> ok sel(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 sel(mark X1, X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 sel(X1, mark X2) -> mark sel(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 dbls ok X -> ok dbls X 2 + 1X >= 2 + 1X dbls mark X -> mark dbls X 1 + 1X >= 1 + 1X s ok X -> ok s X 0 + 0X >= 1 + 0X dbl ok X -> ok dbl X 1 + 0X >= 2 + 0X dbl mark X -> mark dbl X 1 + 0X >= 1 + 0X active quote sel(X, Y) -> mark sel1(X, Y) 1 + 0X + 0Y >= 1 + 1X + 1Y active quote s X -> mark s1 quote X 1 + 0X >= 1 + 0X active quote dbl X -> mark dbl1 X 1 + 0X >= 0 + 0X active quote 0() -> mark 01() 1 >= 0 active quote X -> quote active X 1 + 0X >= 0 + 0X active sel1(s X, cons(Y, Z)) -> mark sel1(X, Z) 3 + 0X + 1Y + 0Z >= 1 + 1X + 1Z active sel1(0(), cons(X, Y)) -> mark X 4 + 1X + 0Y >= 0 + 1X active sel1(X1, X2) -> sel1(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active sel1(X1, X2) -> sel1(X1, active X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 active s1 X -> s1 active X 2 + 1X >= 2 + 1X active dbl1 s X -> mark s1 s1 dbl1 X 1 + 0X >= 2 + 0X active dbl1 0() -> mark 01() 1 >= 0 active dbl1 X -> dbl1 active X 1 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 2 + 0X >= 1 + 1X active indx(cons(X, Y), Z) -> mark cons(sel(X, Z), indx(Y, Z)) 3 + 1X + 0Y + 0Z >= 2 + 0X + 0Y + 0Z active indx(nil(), X) -> mark nil() 2 + 0X >= 0 active indx(X1, X2) -> indx(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active sel(s X, cons(Y, Z)) -> mark sel(X, Z) 2 + 0X + 0Y + 0Z >= 1 + 0X + 0Z active sel(0(), cons(X, Y)) -> mark X 2 + 0X + 0Y >= 0 + 1X active sel(X1, X2) -> sel(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active sel(X1, X2) -> sel(X1, active X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active dbls cons(X, Y) -> mark cons(dbl X, dbls Y) 3 + 1X + 0Y >= 2 + 0X + 0Y active dbls nil() -> mark nil() 2 >= 0 active dbls X -> dbls active X 2 + 1X >= 2 + 1X active dbl s X -> mark s s dbl X 2 + 0X >= 0 + 0X active dbl 0() -> mark 0() 2 >= 1 active dbl X -> dbl active X 2 + 0X >= 1 + 0X Qed