MAYBE Time: 0.178989 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# cons(X1, X2) -> active# X1) (active# s X -> active# X, active# cons(X1, X2) -> cons#(active X1, 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# 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# cons(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active 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)) (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) (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) (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# 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) -> 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) -> 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# 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) (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# 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: 0.935721 SCCS (2): Scc: {top# mark X -> top# proper X, top# ok X -> top# active 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 (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 (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