MAYBE Time: 0.399237 TRS: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s proper X, top mark X -> top proper X, top ok X -> top active X} DP: DP: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2), active# cons(X1, X2) -> cons#(active X1, X2), active# cons(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros()), active# and(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2), active# length X -> active# X, active# length X -> length# active X, active# length cons(N, L) -> length# L, active# length cons(N, L) -> s# length L, active# s X -> active# X, active# s X -> s# active X, and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2), length# mark X -> length# X, length# ok X -> length# X, s# mark X -> s# X, s# ok X -> s# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2), proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2), proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2, proper# length X -> length# proper X, proper# length X -> proper# X, proper# s X -> s# proper X, proper# s 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: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s proper X, top mark X -> top proper X, top ok X -> top active X} UR: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s proper X} EDG: { (active# s X -> active# X, active# s X -> s# active X) (active# s X -> active# X, active# s X -> active# X) (active# s X -> active# X, active# length cons(N, L) -> s# length L) (active# s X -> active# X, active# length cons(N, L) -> length# L) (active# s X -> active# X, active# length X -> length# active X) (active# s X -> active# X, active# length X -> active# X) (active# s X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (active# s X -> active# X, active# and(X1, X2) -> active# X1) (active# s X -> active# X, active# zeros() -> cons#(0(), zeros())) (active# s X -> active# X, active# cons(X1, X2) -> active# X1) (active# s X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (length# ok X -> length# X, length# ok X -> length# X) (length# ok X -> length# X, length# mark X -> length# X) (s# ok X -> s# X, s# ok X -> s# X) (s# ok X -> s# X, s# mark X -> s# 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# length X -> proper# X) (proper# s X -> proper# X, proper# length X -> length# proper X) (proper# s X -> proper# X, proper# and(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# and(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# and(X1, X2) -> and#(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)) (top# ok X -> active# X, active# s X -> s# active X) (top# ok X -> active# X, active# s X -> active# X) (top# ok X -> active# X, active# length cons(N, L) -> s# length L) (top# ok X -> active# X, active# length cons(N, L) -> length# L) (top# ok X -> active# X, active# length X -> length# active X) (top# ok X -> active# X, active# length X -> active# X) (top# ok X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (top# ok X -> active# X, active# and(X1, X2) -> active# X1) (top# ok X -> active# X, active# zeros() -> cons#(0(), zeros())) (top# ok X -> active# X, active# cons(X1, X2) -> active# X1) (top# ok X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# and(X1, X2) -> active# X1, active# s X -> s# active X) (active# and(X1, X2) -> active# X1, active# s X -> active# X) (active# and(X1, X2) -> active# X1, active# length cons(N, L) -> s# length L) (active# and(X1, X2) -> active# X1, active# length cons(N, L) -> length# L) (active# and(X1, X2) -> active# X1, active# length X -> length# active X) (active# and(X1, X2) -> active# X1, active# length X -> active# X) (active# and(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# and(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros())) (active# and(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (proper# and(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# and(X1, X2) -> proper# X1, proper# length X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# length X -> length# proper X) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# and(X1, X2) -> and#(active X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# and(X1, X2) -> and#(active X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (proper# and(X1, X2) -> and#(proper X1, proper X2), and#(ok X1, ok X2) -> and#(X1, X2)) (proper# and(X1, X2) -> and#(proper X1, proper X2), and#(mark X1, X2) -> and#(X1, X2)) (proper# and(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# and(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# and(X1, X2) -> proper# X2, proper# length X -> proper# X) (proper# and(X1, X2) -> proper# X2, proper# length X -> length# proper X) (proper# and(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# length X -> length# active X, length# ok X -> length# X) (active# length X -> length# active X, length# mark X -> length# X) (proper# length X -> length# proper X, length# ok X -> length# X) (proper# length X -> length# proper X, length# mark X -> length# X) (top# mark X -> top# proper X, top# ok X -> top# active X) (top# mark X -> top# proper X, top# ok X -> active# X) (top# mark X -> top# proper X, top# mark X -> top# proper X) (top# mark X -> top# proper X, top# mark X -> proper# X) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (and#(ok X1, ok X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (and#(ok X1, ok X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (top# ok X -> top# active X, top# mark X -> proper# X) (top# ok X -> top# active X, top# mark X -> top# proper X) (top# ok X -> top# active X, top# ok X -> active# X) (top# ok X -> top# active X, top# ok X -> top# active X) (proper# s X -> s# proper X, s# mark X -> s# X) (proper# s X -> s# proper X, s# ok X -> s# X) (active# s X -> s# active X, s# mark X -> s# X) (active# s X -> s# active X, s# ok X -> s# X) (active# length cons(N, L) -> s# length L, s# mark X -> s# X) (active# length cons(N, L) -> s# length L, s# ok X -> s# X) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# length X -> length# proper X) (proper# cons(X1, X2) -> proper# X2, proper# length X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# cons(X1, X2) -> proper# X2, proper# s X -> proper# X) (active# length cons(N, L) -> length# L, length# mark X -> length# X) (active# length cons(N, L) -> length# L, length# ok X -> length# X) (proper# cons(X1, X2) -> cons#(proper X1, proper X2), cons#(mark X1, X2) -> cons#(X1, X2)) (proper# cons(X1, X2) -> cons#(proper X1, proper X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# cons(X1, X2) -> cons#(active X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (active# cons(X1, X2) -> cons#(active X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# length X -> length# proper X) (proper# cons(X1, X2) -> proper# X1, proper# length X -> proper# X) (proper# cons(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# cons(X1, X2) -> proper# X1, proper# s X -> proper# X) (active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros())) (active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# cons(X1, X2) -> active# X1, active# length X -> active# X) (active# cons(X1, X2) -> active# X1, active# length X -> length# active X) (active# cons(X1, X2) -> active# X1, active# length cons(N, L) -> length# L) (active# cons(X1, X2) -> active# X1, active# length cons(N, L) -> s# length L) (active# cons(X1, X2) -> active# X1, active# s X -> active# X) (active# cons(X1, X2) -> active# X1, active# s X -> s# active X) (top# mark X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2)) (top# mark X -> proper# X, proper# and(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# and(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# length X -> length# proper X) (top# mark X -> proper# X, proper# length X -> proper# X) (top# mark X -> proper# X, proper# s X -> s# proper X) (top# mark X -> proper# X, proper# s X -> proper# X) (proper# length X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# length X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# length X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# length X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# length X -> proper# X, proper# and(X1, X2) -> proper# X1) (proper# length X -> proper# X, proper# and(X1, X2) -> proper# X2) (proper# length X -> proper# X, proper# length X -> length# proper X) (proper# length X -> proper# X, proper# length X -> proper# X) (proper# length X -> proper# X, proper# s X -> s# proper X) (proper# length X -> proper# X, proper# s X -> proper# X) (s# mark X -> s# X, s# mark X -> s# X) (s# mark X -> s# X, s# ok X -> s# X) (length# mark X -> length# X, length# mark X -> length# X) (length# mark X -> length# X, length# ok X -> length# X) (active# length X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# length X -> active# X, active# cons(X1, X2) -> active# X1) (active# length X -> active# X, active# zeros() -> cons#(0(), zeros())) (active# length X -> active# X, active# and(X1, X2) -> active# X1) (active# length X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (active# length X -> active# X, active# length X -> active# X) (active# length X -> active# X, active# length X -> length# active X) (active# length X -> active# X, active# length cons(N, L) -> length# L) (active# length X -> active# X, active# length cons(N, L) -> s# length L) (active# length X -> active# X, active# s X -> active# X) (active# length X -> active# X, active# s X -> s# active X) } STATUS: arrows: 0.844812 SCCS (7): Scc: {top# mark X -> top# proper X, top# ok X -> top# active X} Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2, proper# length X -> proper# X, proper# s X -> proper# X} Scc: {active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1, active# length X -> active# X, active# s X -> active# X} Scc: {s# mark X -> s# X, s# ok X -> s# X} Scc: {length# mark X -> length# X, length# ok X -> length# X} Scc: { and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)} Scc: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)} SCC (2): Strict: {top# mark X -> top# proper X, top# ok X -> top# active X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s proper X, top mark X -> top proper X, top ok X -> top active X} Fail SCC (6): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2, proper# length X -> proper# X, proper# s X -> proper# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = x0 + x1, [mark](x0) = 0, [active](x0) = 0, [length](x0) = x0, [s](x0) = x0 + 1, [ok](x0) = x0 + 1, [proper](x0) = 0, [top](x0) = 0, [0] = 0, [zeros] = 0, [tt] = 0, [nil] = 0, [proper#](x0) = x0 Strict: proper# s X -> proper# X 1 + 1X >= 0 + 1X proper# length X -> proper# X 0 + 1X >= 0 + 1X proper# and(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# and(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 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper s X -> s proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 1 proper length X -> length proper X 0 + 0X >= 0 + 0X proper tt() -> ok tt() 0 >= 1 proper and(X1, X2) -> and(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper zeros() -> ok zeros() 0 >= 1 proper 0() -> ok 0() 0 >= 1 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 1 + 0X >= 0 + 0X length ok X -> ok length X 1 + 1X >= 1 + 1X length mark X -> mark length X 0 + 0X >= 0 + 0X and(ok X1, ok X2) -> ok and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> mark and(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 1 + 0X active length nil() -> mark 0() 0 >= 0 active length cons(N, L) -> mark s length L 0 + 0L + 0N >= 0 + 0L active length X -> length active X 0 + 0X >= 0 + 0X active and(tt(), X) -> mark X 0 + 0X >= 0 + 0X active and(X1, X2) -> and(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active zeros() -> mark cons(0(), zeros()) 0 >= 0 active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2, proper# length X -> proper# X} SCC (5): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2, proper# length X -> proper# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = x0 + x1, [mark](x0) = 0, [active](x0) = 0, [length](x0) = x0 + 1, [s](x0) = x0 + 1, [ok](x0) = x0 + 1, [proper](x0) = 0, [top](x0) = 0, [0] = 1, [zeros] = 1, [tt] = 0, [nil] = 1, [proper#](x0) = x0 Strict: proper# length X -> proper# X 1 + 1X >= 0 + 1X proper# and(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# and(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 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper s X -> s proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 2 proper length X -> length proper X 0 + 0X >= 1 + 0X proper tt() -> ok tt() 0 >= 1 proper and(X1, X2) -> and(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper zeros() -> ok zeros() 0 >= 2 proper 0() -> ok 0() 0 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 1 + 0X >= 0 + 0X length ok X -> ok length X 2 + 1X >= 2 + 1X length mark X -> mark length X 1 + 0X >= 0 + 0X and(ok X1, ok X2) -> ok and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> mark and(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 1 + 0X active length nil() -> mark 0() 0 >= 0 active length cons(N, L) -> mark s length L 0 + 0L + 0N >= 0 + 0L active length X -> length active X 0 + 0X >= 1 + 0X active and(tt(), X) -> mark X 0 + 0X >= 0 + 0X active and(X1, X2) -> and(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active zeros() -> mark cons(0(), zeros()) 0 >= 0 active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2} SCC (4): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = x0 + x1 + 1, [mark](x0) = 0, [active](x0) = 0, [length](x0) = 0, [s](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0, [top](x0) = 0, [0] = 1, [zeros] = 1, [tt] = 1, [nil] = 0, [proper#](x0) = x0 Strict: proper# and(X1, X2) -> proper# X2 1 + 1X1 + 1X2 >= 0 + 1X2 proper# and(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 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper s X -> s proper X 0 + 0X >= 0 + 0X proper nil() -> ok nil() 0 >= 1 proper length X -> length proper X 0 + 0X >= 0 + 0X proper tt() -> ok tt() 1 >= 2 proper and(X1, X2) -> and(proper X1, proper X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 proper zeros() -> ok zeros() 1 >= 2 proper 0() -> ok 0() 1 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 0 + 0X length ok X -> ok length X 0 + 0X >= 1 + 0X length mark X -> mark length X 0 + 0X >= 0 + 0X and(ok X1, ok X2) -> ok and(X1, X2) 3 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 and(mark X1, X2) -> mark and(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 0 + 0X active length nil() -> mark 0() 0 >= 0 active length cons(N, L) -> mark s length L 0 + 0L + 0N >= 0 + 0L active length X -> length active X 0 + 0X >= 0 + 0X active and(tt(), X) -> mark X 0 + 0X >= 0 + 0X active and(X1, X2) -> and(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 active zeros() -> mark cons(0(), zeros()) 0 >= 0 active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2} SCC (2): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [length](x0) = 0, [s](x0) = 0, [ok](x0) = 0, [proper](x0) = 0, [top](x0) = 0, [0] = 0, [zeros] = 1, [tt] = 0, [nil] = 0, [proper#](x0) = x0 + 1 Strict: proper# cons(X1, X2) -> proper# X2 2 + 1X1 + 1X2 >= 1 + 1X2 proper# cons(X1, X2) -> proper# X1 2 + 1X1 + 1X2 >= 1 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper s X -> s proper X 0 + 0X >= 0 + 0X proper nil() -> ok nil() 0 >= 0 proper length X -> length proper X 0 + 0X >= 0 + 0X proper tt() -> ok tt() 0 >= 0 proper and(X1, X2) -> and(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper zeros() -> ok zeros() 0 >= 0 proper 0() -> ok 0() 0 >= 0 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s ok X -> ok s X 0 + 0X >= 0 + 0X s mark X -> mark s X 0 + 0X >= 1 + 0X length ok X -> ok length X 0 + 0X >= 0 + 0X length mark X -> mark length X 0 + 0X >= 1 + 0X and(ok X1, ok X2) -> ok and(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(mark X1, X2) -> mark and(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active s X -> s active X 1 + 0X >= 0 + 0X active length nil() -> mark 0() 1 >= 1 active length cons(N, L) -> mark s length L 1 + 0L + 0N >= 1 + 0L active length X -> length active X 1 + 0X >= 0 + 0X active and(tt(), X) -> mark X 2 + 0X >= 1 + 1X active and(X1, X2) -> and(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active zeros() -> mark cons(0(), zeros()) 2 >= 3 active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 Qed SCC (4): Strict: {active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1, active# length X -> active# X, active# s X -> active# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = x0 + x1, [mark](x0) = 0, [active](x0) = 0, [length](x0) = x0, [s](x0) = x0 + 1, [ok](x0) = x0 + 1, [proper](x0) = 0, [top](x0) = 0, [0] = 0, [zeros] = 0, [tt] = 0, [nil] = 0, [active#](x0) = x0 Strict: active# s X -> active# X 1 + 1X >= 0 + 1X active# length X -> active# X 0 + 1X >= 0 + 1X active# and(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper s X -> s proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 1 proper length X -> length proper X 0 + 0X >= 0 + 0X proper tt() -> ok tt() 0 >= 1 proper and(X1, X2) -> and(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper zeros() -> ok zeros() 0 >= 1 proper 0() -> ok 0() 0 >= 1 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 1 + 0X >= 0 + 0X length ok X -> ok length X 1 + 1X >= 1 + 1X length mark X -> mark length X 0 + 0X >= 0 + 0X and(ok X1, ok X2) -> ok and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> mark and(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 1 + 0X active length nil() -> mark 0() 0 >= 0 active length cons(N, L) -> mark s length L 0 + 0L + 0N >= 0 + 0L active length X -> length active X 0 + 0X >= 0 + 0X active and(tt(), X) -> mark X 0 + 0X >= 0 + 0X active and(X1, X2) -> and(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active zeros() -> mark cons(0(), zeros()) 0 >= 0 active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1, active# length X -> active# X} SCC (3): Strict: {active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1, active# length X -> active# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = x0 + x1, [mark](x0) = 0, [active](x0) = 0, [length](x0) = x0 + 1, [s](x0) = x0 + 1, [ok](x0) = x0 + 1, [proper](x0) = 0, [top](x0) = 0, [0] = 1, [zeros] = 1, [tt] = 0, [nil] = 1, [active#](x0) = x0 Strict: active# length X -> active# X 1 + 1X >= 0 + 1X active# and(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper s X -> s proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 2 proper length X -> length proper X 0 + 0X >= 1 + 0X proper tt() -> ok tt() 0 >= 1 proper and(X1, X2) -> and(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper zeros() -> ok zeros() 0 >= 2 proper 0() -> ok 0() 0 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 1 + 0X >= 0 + 0X length ok X -> ok length X 2 + 1X >= 2 + 1X length mark X -> mark length X 1 + 0X >= 0 + 0X and(ok X1, ok X2) -> ok and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> mark and(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 1 + 0X active length nil() -> mark 0() 0 >= 0 active length cons(N, L) -> mark s length L 0 + 0L + 0N >= 0 + 0L active length X -> length active X 0 + 0X >= 1 + 0X active and(tt(), X) -> mark X 0 + 0X >= 0 + 0X active and(X1, X2) -> and(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 active zeros() -> mark cons(0(), zeros()) 0 >= 0 active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1} SCC (2): Strict: {active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = x0 + 1, [mark](x0) = 0, [active](x0) = 0, [length](x0) = 0, [s](x0) = 0, [ok](x0) = 1, [proper](x0) = 0, [top](x0) = 0, [0] = 1, [zeros] = 1, [tt] = 1, [nil] = 0, [active#](x0) = x0 Strict: active# and(X1, X2) -> active# X1 1 + 1X1 + 0X2 >= 0 + 1X1 active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper s X -> s proper X 0 + 0X >= 0 + 0X proper nil() -> ok nil() 0 >= 1 proper length X -> length proper X 0 + 0X >= 0 + 0X proper tt() -> ok tt() 0 >= 1 proper and(X1, X2) -> and(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper zeros() -> ok zeros() 0 >= 1 proper 0() -> ok 0() 0 >= 1 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 0 + 0X length ok X -> ok length X 0 + 0X >= 1 + 0X length mark X -> mark length X 0 + 0X >= 0 + 0X and(ok X1, ok X2) -> ok and(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(mark X1, X2) -> mark and(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 0 + 0X active length nil() -> mark 0() 0 >= 0 active length cons(N, L) -> mark s length L 0 + 0L + 0N >= 0 + 0L active length X -> length active X 0 + 0X >= 0 + 0X active and(tt(), X) -> mark X 0 + 0X >= 0 + 0X active and(X1, X2) -> and(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zeros() -> mark cons(0(), zeros()) 0 >= 0 active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1} SCC (1): Strict: {active# cons(X1, X2) -> active# X1} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [length](x0) = x0 + 1, [s](x0) = x0 + 1, [ok](x0) = 1, [proper](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [zeros] = 1, [tt] = 0, [nil] = 0, [active#](x0) = x0 Strict: active# cons(X1, X2) -> active# X1 1 + 1X1 + 0X2 >= 0 + 1X1 Weak: top ok X -> top active X 2 + 0X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper nil() -> ok nil() 1 >= 1 proper length X -> length proper X 2 + 1X >= 2 + 1X proper tt() -> ok tt() 1 >= 1 proper and(X1, X2) -> and(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper zeros() -> ok zeros() 2 >= 1 proper 0() -> ok 0() 2 >= 1 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 0X >= 1 + 0X s mark X -> mark s X 2 + 1X >= 2 + 1X length ok X -> ok length X 2 + 0X >= 1 + 0X length mark X -> mark length X 2 + 1X >= 2 + 1X and(ok X1, ok X2) -> ok and(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(mark X1, X2) -> mark and(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active s X -> s active X 2 + 1X >= 2 + 1X active length nil() -> mark 0() 2 >= 2 active length cons(N, L) -> mark s length L 3 + 0L + 1N >= 3 + 1L active length X -> length active X 2 + 1X >= 2 + 1X active and(tt(), X) -> mark X 2 + 0X >= 1 + 1X active and(X1, X2) -> and(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active zeros() -> mark cons(0(), zeros()) 2 >= 3 active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed SCC (2): Strict: {s# mark X -> s# X, s# ok X -> s# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = 0, [mark](x0) = x0, [active](x0) = 0, [length](x0) = 0, [s](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = 0, [top](x0) = 0, [0] = 0, [zeros] = 1, [tt] = 1, [nil] = 1, [s#](x0) = x0 Strict: s# ok X -> s# X 1 + 1X >= 0 + 1X s# mark X -> s# X 0 + 1X >= 0 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper s X -> s proper X 0 + 0X >= 0 + 0X proper nil() -> ok nil() 0 >= 2 proper length X -> length proper X 0 + 0X >= 0 + 0X proper tt() -> ok tt() 0 >= 2 proper and(X1, X2) -> and(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper zeros() -> ok zeros() 0 >= 2 proper 0() -> ok 0() 0 >= 1 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 0 + 0X length ok X -> ok length X 0 + 0X >= 1 + 0X length mark X -> mark length X 0 + 0X >= 0 + 0X and(ok X1, ok X2) -> ok and(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(mark X1, X2) -> mark and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 0 + 0X active length nil() -> mark 0() 0 >= 0 active length cons(N, L) -> mark s length L 0 + 0L + 0N >= 0 + 0L active length X -> length active X 0 + 0X >= 0 + 0X active and(tt(), X) -> mark X 0 + 0X >= 0 + 1X active and(X1, X2) -> and(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zeros() -> mark cons(0(), zeros()) 0 >= 0 active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {s# mark X -> s# X} SCC (1): Strict: {s# mark X -> s# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [length](x0) = x0 + 1, [s](x0) = x0 + 1, [ok](x0) = 1, [proper](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [zeros] = 1, [tt] = 0, [nil] = 0, [s#](x0) = x0 Strict: s# mark X -> s# X 1 + 1X >= 0 + 1X Weak: top ok X -> top active X 2 + 0X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper nil() -> ok nil() 1 >= 1 proper length X -> length proper X 2 + 1X >= 2 + 1X proper tt() -> ok tt() 1 >= 1 proper and(X1, X2) -> and(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper zeros() -> ok zeros() 2 >= 1 proper 0() -> ok 0() 2 >= 1 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 0X >= 1 + 0X s mark X -> mark s X 2 + 1X >= 2 + 1X length ok X -> ok length X 2 + 0X >= 1 + 0X length mark X -> mark length X 2 + 1X >= 2 + 1X and(ok X1, ok X2) -> ok and(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(mark X1, X2) -> mark and(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active s X -> s active X 2 + 1X >= 2 + 1X active length nil() -> mark 0() 2 >= 2 active length cons(N, L) -> mark s length L 3 + 0L + 1N >= 3 + 1L active length X -> length active X 2 + 1X >= 2 + 1X active and(tt(), X) -> mark X 2 + 0X >= 1 + 1X active and(X1, X2) -> and(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active zeros() -> mark cons(0(), zeros()) 2 >= 3 active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed SCC (2): Strict: {length# mark X -> length# X, length# ok X -> length# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = 0, [mark](x0) = x0, [active](x0) = 0, [length](x0) = 0, [s](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = 0, [top](x0) = 0, [0] = 0, [zeros] = 1, [tt] = 1, [nil] = 1, [length#](x0) = x0 Strict: length# ok X -> length# X 1 + 1X >= 0 + 1X length# mark X -> length# 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 s X -> s proper X 0 + 0X >= 0 + 0X proper nil() -> ok nil() 0 >= 2 proper length X -> length proper X 0 + 0X >= 0 + 0X proper tt() -> ok tt() 0 >= 2 proper and(X1, X2) -> and(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 proper zeros() -> ok zeros() 0 >= 2 proper 0() -> ok 0() 0 >= 1 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 0 + 0X length ok X -> ok length X 0 + 0X >= 1 + 0X length mark X -> mark length X 0 + 0X >= 0 + 0X and(ok X1, ok X2) -> ok and(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(mark X1, X2) -> mark and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active s X -> s active X 0 + 0X >= 0 + 0X active length nil() -> mark 0() 0 >= 0 active length cons(N, L) -> mark s length L 0 + 0L + 0N >= 0 + 0L active length X -> length active X 0 + 0X >= 0 + 0X active and(tt(), X) -> mark X 0 + 0X >= 0 + 1X active and(X1, X2) -> and(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active zeros() -> mark cons(0(), zeros()) 0 >= 0 active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {length# mark X -> length# X} SCC (1): Strict: {length# mark X -> length# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [length](x0) = x0 + 1, [s](x0) = x0 + 1, [ok](x0) = 1, [proper](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [zeros] = 1, [tt] = 0, [nil] = 0, [length#](x0) = x0 Strict: length# mark X -> length# X 1 + 1X >= 0 + 1X Weak: top ok X -> top active X 2 + 0X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper nil() -> ok nil() 1 >= 1 proper length X -> length proper X 2 + 1X >= 2 + 1X proper tt() -> ok tt() 1 >= 1 proper and(X1, X2) -> and(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper zeros() -> ok zeros() 2 >= 1 proper 0() -> ok 0() 2 >= 1 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 0X >= 1 + 0X s mark X -> mark s X 2 + 1X >= 2 + 1X length ok X -> ok length X 2 + 0X >= 1 + 0X length mark X -> mark length X 2 + 1X >= 2 + 1X and(ok X1, ok X2) -> ok and(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(mark X1, X2) -> mark and(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active s X -> s active X 2 + 1X >= 2 + 1X active length nil() -> mark 0() 2 >= 2 active length cons(N, L) -> mark s length L 3 + 0L + 1N >= 3 + 1L active length X -> length active X 2 + 1X >= 2 + 1X active and(tt(), X) -> mark X 2 + 0X >= 1 + 1X active and(X1, X2) -> and(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active zeros() -> mark cons(0(), zeros()) 2 >= 3 active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed SCC (2): Strict: { and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [length](x0) = x0 + 1, [s](x0) = x0 + 1, [ok](x0) = x0 + 1, [proper](x0) = 0, [top](x0) = 0, [0] = 1, [zeros] = 1, [tt] = 1, [nil] = 0, [and#](x0, x1) = x0 Strict: and#(ok X1, ok X2) -> and#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 and#(mark X1, X2) -> and#(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 s X -> s proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 1 proper length X -> length proper X 0 + 0X >= 1 + 0X proper tt() -> ok tt() 0 >= 2 proper and(X1, X2) -> and(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper zeros() -> ok zeros() 0 >= 2 proper 0() -> ok 0() 0 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X length ok X -> ok length X 2 + 1X >= 2 + 1X length mark X -> mark length X 2 + 1X >= 2 + 1X and(ok X1, ok X2) -> ok and(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 and(mark X1, X2) -> mark and(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 active s X -> s active X 2 + 1X >= 2 + 1X active length nil() -> mark 0() 2 >= 2 active length cons(N, L) -> mark s length L 3 + 0L + 1N >= 3 + 1L active length X -> length active X 2 + 1X >= 2 + 1X active and(tt(), X) -> mark X 2 + 0X >= 1 + 1X active and(X1, X2) -> and(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zeros() -> mark cons(0(), zeros()) 2 >= 3 active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 SCCS (1): Scc: {and#(mark X1, X2) -> and#(X1, X2)} SCC (1): Strict: {and#(mark X1, X2) -> and#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [length](x0) = x0 + 1, [s](x0) = x0 + 1, [ok](x0) = 1, [proper](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [zeros] = 1, [tt] = 0, [nil] = 0, [and#](x0, x1) = x0 Strict: and#(mark X1, X2) -> and#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: top ok X -> top active X 2 + 0X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper nil() -> ok nil() 1 >= 1 proper length X -> length proper X 2 + 1X >= 2 + 1X proper tt() -> ok tt() 1 >= 1 proper and(X1, X2) -> and(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper zeros() -> ok zeros() 2 >= 1 proper 0() -> ok 0() 2 >= 1 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 0X >= 1 + 0X s mark X -> mark s X 2 + 1X >= 2 + 1X length ok X -> ok length X 2 + 0X >= 1 + 0X length mark X -> mark length X 2 + 1X >= 2 + 1X and(ok X1, ok X2) -> ok and(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(mark X1, X2) -> mark and(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active s X -> s active X 2 + 1X >= 2 + 1X active length nil() -> mark 0() 2 >= 2 active length cons(N, L) -> mark s length L 3 + 0L + 1N >= 3 + 1L active length X -> length active X 2 + 1X >= 2 + 1X active and(tt(), X) -> mark X 2 + 0X >= 1 + 1X active and(X1, X2) -> and(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active zeros() -> mark cons(0(), zeros()) 2 >= 3 active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed SCC (2): Strict: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [length](x0) = x0 + 1, [s](x0) = x0 + 1, [ok](x0) = x0 + 1, [proper](x0) = 0, [top](x0) = 0, [0] = 1, [zeros] = 1, [tt] = 1, [nil] = 0, [cons#](x0, x1) = x0 Strict: cons#(ok X1, ok X2) -> cons#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons#(mark X1, X2) -> cons#(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper s X -> s proper X 0 + 0X >= 1 + 0X proper nil() -> ok nil() 0 >= 1 proper length X -> length proper X 0 + 0X >= 1 + 0X proper tt() -> ok tt() 0 >= 2 proper and(X1, X2) -> and(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 proper zeros() -> ok zeros() 0 >= 2 proper 0() -> ok 0() 0 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X length ok X -> ok length X 2 + 1X >= 2 + 1X length mark X -> mark length X 2 + 1X >= 2 + 1X and(ok X1, ok X2) -> ok and(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 and(mark X1, X2) -> mark and(X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 active s X -> s active X 2 + 1X >= 2 + 1X active length nil() -> mark 0() 2 >= 2 active length cons(N, L) -> mark s length L 3 + 0L + 1N >= 3 + 1L active length X -> length active X 2 + 1X >= 2 + 1X active and(tt(), X) -> mark X 2 + 0X >= 1 + 1X active and(X1, X2) -> and(active X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active zeros() -> mark cons(0(), zeros()) 2 >= 3 active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 SCCS (1): Scc: {cons#(mark X1, X2) -> cons#(X1, X2)} SCC (1): Strict: {cons#(mark X1, X2) -> cons#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active length X -> length active X, active length cons(N, L) -> mark s length L, active length nil() -> mark 0(), active s X -> s active X, and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), length mark X -> mark length X, length ok X -> ok length X, s mark X -> mark s X, s ok X -> ok s X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper and(X1, X2) -> and(proper X1, proper X2), proper tt() -> ok tt(), proper length X -> length proper X, proper nil() -> ok nil(), proper s X -> s 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, [and](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [length](x0) = x0 + 1, [s](x0) = x0 + 1, [ok](x0) = 1, [proper](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [zeros] = 1, [tt] = 0, [nil] = 0, [cons#](x0, x1) = x0 Strict: cons#(mark X1, X2) -> cons#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: top ok X -> top active X 2 + 0X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper nil() -> ok nil() 1 >= 1 proper length X -> length proper X 2 + 1X >= 2 + 1X proper tt() -> ok tt() 1 >= 1 proper and(X1, X2) -> and(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 proper zeros() -> ok zeros() 2 >= 1 proper 0() -> ok 0() 2 >= 1 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 0X >= 1 + 0X s mark X -> mark s X 2 + 1X >= 2 + 1X length ok X -> ok length X 2 + 0X >= 1 + 0X length mark X -> mark length X 2 + 1X >= 2 + 1X and(ok X1, ok X2) -> ok and(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(mark X1, X2) -> mark and(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active s X -> s active X 2 + 1X >= 2 + 1X active length nil() -> mark 0() 2 >= 2 active length cons(N, L) -> mark s length L 3 + 0L + 1N >= 3 + 1L active length X -> length active X 2 + 1X >= 2 + 1X active and(tt(), X) -> mark X 2 + 0X >= 1 + 1X active and(X1, X2) -> and(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 active zeros() -> mark cons(0(), zeros()) 2 >= 3 active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed