MAYBE Time: 4.027366 TRS: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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), f# mark X -> f# X, f# ok X -> f# X, s# mark X -> s# X, s# ok X -> s# X, active# cons(X1, X2) -> cons#(active X1, X2), active# cons(X1, X2) -> active# X1, active# f X -> f# active X, active# f X -> active# X, active# f 0() -> cons#(0(), f s 0()), active# f 0() -> f# s 0(), active# f 0() -> s# 0(), active# f s 0() -> f# p s 0(), active# f s 0() -> p# s 0(), active# s X -> s# active X, active# s X -> active# X, active# p X -> active# X, active# p X -> p# active X, p# mark X -> p# X, p# ok X -> p# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2), proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> f# proper X, proper# f X -> proper# X, proper# s X -> s# proper X, proper# s X -> proper# X, proper# p X -> p# proper X, proper# p 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), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p proper X} EDG: {(active# f X -> f# active X, f# ok X -> f# X) (active# f X -> f# active X, f# mark X -> f# X) (active# p X -> p# active X, p# ok X -> p# X) (active# p X -> p# active X, p# mark X -> p# X) (proper# s X -> s# proper X, s# ok X -> s# X) (proper# s X -> s# proper X, s# mark X -> s# 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) (proper# cons(X1, X2) -> proper# X2, proper# p X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# p X -> p# 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# f X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# f X -> f# proper X) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (f# ok X -> f# X, f# ok X -> f# X) (f# ok X -> f# X, f# mark X -> f# X) (s# ok X -> s# X, s# ok X -> s# X) (s# ok X -> s# X, s# mark X -> s# X) (active# s X -> active# X, active# p X -> p# active X) (active# s X -> active# X, active# p X -> active# X) (active# s X -> active# X, active# s X -> active# X) (active# s X -> active# X, active# s X -> s# active X) (active# s X -> active# X, active# f s 0() -> p# s 0()) (active# s X -> active# X, active# f s 0() -> f# p s 0()) (active# s X -> active# X, active# f 0() -> s# 0()) (active# s X -> active# X, active# f 0() -> f# s 0()) (active# s X -> active# X, active# f 0() -> cons#(0(), f s 0())) (active# s X -> active# X, active# f X -> active# X) (active# s X -> active# X, active# f X -> f# active X) (active# s X -> active# X, active# cons(X1, X2) -> active# X1) (active# s X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (p# mark X -> p# X, p# ok X -> p# X) (p# mark X -> p# X, p# mark X -> p# X) (proper# f X -> proper# X, proper# p X -> proper# X) (proper# f X -> proper# X, proper# p X -> p# proper X) (proper# f X -> proper# X, proper# s X -> proper# X) (proper# f X -> proper# X, proper# s X -> s# proper X) (proper# f X -> proper# X, proper# f X -> proper# X) (proper# f X -> proper# X, proper# f X -> f# proper X) (proper# f X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# f X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# f X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# p X -> proper# X, proper# p X -> proper# X) (proper# p X -> proper# X, proper# p X -> p# proper X) (proper# p X -> proper# X, proper# s X -> proper# X) (proper# p X -> proper# X, proper# s X -> s# proper X) (proper# p X -> proper# X, proper# f X -> proper# X) (proper# p X -> proper# X, proper# f X -> f# proper X) (proper# p X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# p X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# p X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (top# ok X -> active# X, active# p X -> p# active X) (top# ok X -> active# X, active# p X -> active# X) (top# ok X -> active# X, active# s X -> active# X) (top# ok X -> active# X, active# s X -> s# active X) (top# ok X -> active# X, active# f s 0() -> p# s 0()) (top# ok X -> active# X, active# f s 0() -> f# p s 0()) (top# ok X -> active# X, active# f 0() -> s# 0()) (top# ok X -> active# X, active# f 0() -> f# s 0()) (top# ok X -> active# X, active# f 0() -> cons#(0(), f s 0())) (top# ok X -> active# X, active# f X -> active# X) (top# ok X -> active# X, active# f X -> f# active X) (top# ok X -> active# X, active# cons(X1, X2) -> active# X1) (top# ok X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# cons(X1, X2) -> cons#(active X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# cons(X1, X2) -> cons#(active X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (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)) (active# cons(X1, X2) -> active# X1, active# p X -> p# active X) (active# cons(X1, X2) -> active# X1, active# p X -> active# X) (active# cons(X1, X2) -> active# X1, active# s X -> active# X) (active# cons(X1, X2) -> active# X1, active# s X -> s# active X) (active# cons(X1, X2) -> active# X1, active# f s 0() -> p# s 0()) (active# cons(X1, X2) -> active# X1, active# f s 0() -> f# p s 0()) (active# cons(X1, X2) -> active# X1, active# f 0() -> s# 0()) (active# cons(X1, X2) -> active# X1, active# f 0() -> f# s 0()) (active# cons(X1, X2) -> active# X1, active# f 0() -> cons#(0(), f s 0())) (active# cons(X1, X2) -> active# X1, active# f X -> active# X) (active# cons(X1, X2) -> active# X1, active# f X -> f# active X) (active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (proper# cons(X1, X2) -> proper# X1, proper# 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# f X -> f# proper X) (proper# cons(X1, X2) -> proper# X1, proper# f 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) (proper# cons(X1, X2) -> proper# X1, proper# p X -> p# proper X) (proper# cons(X1, X2) -> proper# X1, proper# p X -> proper# X) (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# mark X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# f X -> f# proper X) (top# mark X -> proper# X, proper# f X -> proper# X) (top# mark X -> proper# X, proper# s X -> s# proper X) (top# mark X -> proper# X, proper# s X -> proper# X) (top# mark X -> proper# X, proper# p X -> p# proper X) (top# mark X -> proper# X, proper# p X -> proper# X) (proper# s X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# f X -> f# proper X) (proper# s X -> proper# X, proper# f X -> proper# X) (proper# s X -> proper# X, proper# s X -> s# proper X) (proper# s X -> proper# X, proper# s X -> proper# X) (proper# s X -> proper# X, proper# p X -> p# proper X) (proper# s X -> proper# X, proper# p X -> proper# X) (p# ok X -> p# X, p# mark X -> p# X) (p# ok X -> p# X, p# ok X -> p# X) (active# p X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# p X -> active# X, active# cons(X1, X2) -> active# X1) (active# p X -> active# X, active# f X -> f# active X) (active# p X -> active# X, active# f X -> active# X) (active# p X -> active# X, active# f 0() -> cons#(0(), f s 0())) (active# p X -> active# X, active# f 0() -> f# s 0()) (active# p X -> active# X, active# f 0() -> s# 0()) (active# p X -> active# X, active# f s 0() -> f# p s 0()) (active# p X -> active# X, active# f s 0() -> p# s 0()) (active# p X -> active# X, active# s X -> s# active X) (active# p X -> active# X, active# s X -> active# X) (active# p X -> active# X, active# p X -> active# X) (active# p X -> active# X, active# p X -> p# active X) (active# f X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# f X -> active# X, active# cons(X1, X2) -> active# X1) (active# f X -> active# X, active# f X -> f# active X) (active# f X -> active# X, active# f X -> active# X) (active# f X -> active# X, active# f 0() -> cons#(0(), f s 0())) (active# f X -> active# X, active# f 0() -> f# s 0()) (active# f X -> active# X, active# f 0() -> s# 0()) (active# f X -> active# X, active# f s 0() -> f# p s 0()) (active# f X -> active# X, active# f s 0() -> p# s 0()) (active# f X -> active# X, active# s X -> s# active X) (active# f X -> active# X, active# s X -> active# X) (active# f X -> active# X, active# p X -> active# X) (active# f X -> active# X, active# p X -> p# active X) (s# mark X -> s# X, s# mark X -> s# X) (s# mark X -> s# X, s# ok X -> s# X) (f# mark X -> f# X, f# mark X -> f# X) (f# mark X -> f# X, f# ok X -> f# 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# p X -> p# proper X, p# mark X -> p# X) (proper# p X -> p# proper X, p# ok X -> p# X) (proper# f X -> f# proper X, f# mark X -> f# X) (proper# f X -> f# proper X, f# ok X -> f# X) (active# s X -> s# active X, s# mark X -> s# X) (active# s X -> s# active X, s# ok X -> s# 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))} STATUS: arrows: 0.862457 SCCS (7): Scc: {top# mark X -> top# proper X, top# ok X -> top# active X} Scc: {active# cons(X1, X2) -> active# X1, active# f X -> active# X, active# s X -> active# X, active# p X -> active# X} Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> proper# X, proper# s X -> proper# X, proper# p X -> proper# X} Scc: {p# mark X -> p# X, p# ok X -> p# X} Scc: {s# mark X -> s# X, s# ok X -> s# X} Scc: {f# mark X -> f# X, f# ok X -> f# X} Scc: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)} SCC (2): Strict: {top# mark X -> top# proper X, top# ok X -> top# active X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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# f X -> active# X, active# s X -> active# X, active# p X -> active# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = 0, [f](x0) = x0, [s](x0) = x0, [active](x0) = 0, [p](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [active#](x0) = x0 Strict: active# p X -> active# X 1 + 1X >= 0 + 1X active# s X -> active# X 0 + 1X >= 0 + 1X active# f X -> active# X 0 + 1X >= 0 + 1X active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper p X -> p proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 1 + 1X >= 1 + 1X proper f X -> f proper X 1 + 1X >= 1 + 1X proper 0() -> ok 0() 1 >= 1 proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 p ok X -> ok p X 2 + 1X >= 2 + 1X p mark X -> mark p X 1 + 0X >= 0 + 0X active p s X -> mark X 0 + 0X >= 0 + 0X active p X -> p active X 0 + 0X >= 1 + 0X active s X -> s active X 0 + 0X >= 0 + 0X active f s 0() -> mark f p s 0() 0 >= 0 active f 0() -> mark cons(0(), f s 0()) 0 >= 0 active f X -> f active X 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 0 + 0X >= 0 + 0X f ok X -> ok f X 1 + 1X >= 1 + 1X f mark X -> mark f X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1, active# f X -> active# X, active# s X -> active# X} SCC (3): Strict: {active# cons(X1, X2) -> active# X1, active# f X -> active# X, active# s X -> active# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = 0, [f](x0) = x0, [s](x0) = x0 + 1, [active](x0) = 0, [p](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [active#](x0) = x0 Strict: active# s X -> active# X 1 + 1X >= 0 + 1X active# f X -> active# X 0 + 1X >= 0 + 1X active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper p X -> p proper X 0 + 0X >= 1 + 0X proper s X -> s proper X 0 + 0X >= 1 + 0X proper f X -> f proper X 0 + 0X >= 0 + 0X proper 0() -> ok 0() 0 >= 1 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 p ok X -> ok p X 2 + 1X >= 2 + 1X p mark X -> mark p X 1 + 0X >= 0 + 0X active p s X -> mark X 0 + 0X >= 0 + 0X active p X -> p active X 0 + 0X >= 1 + 0X active s X -> s active X 0 + 0X >= 1 + 0X active f s 0() -> mark f p s 0() 0 >= 0 active f 0() -> mark cons(0(), f s 0()) 0 >= 0 active f X -> f active X 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 1 + 0X >= 0 + 0X f ok X -> ok f X 1 + 1X >= 1 + 1X f mark X -> mark f X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1, active# f X -> active# X} SCC (2): Strict: {active# cons(X1, X2) -> active# X1, active# f X -> active# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = 0, [f](x0) = x0 + 1, [s](x0) = 0, [active](x0) = 0, [p](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [active#](x0) = x0 Strict: active# f X -> active# X 1 + 1X >= 0 + 1X active# cons(X1, X2) -> active# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper p X -> p proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 1 + 0X >= 0 + 0X proper f X -> f proper X 2 + 1X >= 2 + 1X proper 0() -> ok 0() 2 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 p ok X -> ok p X 2 + 1X >= 2 + 1X p mark X -> mark p X 1 + 0X >= 0 + 0X active p s X -> mark X 0 + 0X >= 0 + 0X active p X -> p active X 0 + 0X >= 1 + 0X active s X -> s active X 0 + 0X >= 0 + 0X active f s 0() -> mark f p s 0() 0 >= 0 active f 0() -> mark cons(0(), f s 0()) 0 >= 0 active f X -> f active X 0 + 0X >= 1 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 0 + 0X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f X 1 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {active# cons(X1, X2) -> active# X1} SCC (1): Strict: {active# cons(X1, X2) -> active# X1} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = x0 + 1, [f](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [p](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [active#](x0) = x0 Strict: active# cons(X1, X2) -> active# X1 1 + 1X1 + 0X2 >= 0 + 1X1 Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper p X -> p proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper f X -> f proper X 2 + 1X >= 2 + 1X proper 0() -> ok 0() 2 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 p ok X -> ok p X 2 + 1X >= 2 + 1X p mark X -> mark p X 2 + 1X >= 2 + 1X active p s X -> mark X 3 + 1X >= 1 + 1X active p X -> p active X 2 + 1X >= 2 + 1X active s X -> s active X 2 + 1X >= 2 + 1X active f s 0() -> mark f p s 0() 4 >= 5 active f 0() -> mark cons(0(), f s 0()) 3 >= 3 active f X -> f active X 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed SCC (5): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> proper# X, proper# s X -> proper# X, proper# p X -> proper# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = 0, [f](x0) = x0, [s](x0) = x0, [active](x0) = 0, [p](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [proper#](x0) = x0 Strict: proper# p X -> proper# X 1 + 1X >= 0 + 1X proper# s X -> proper# X 0 + 1X >= 0 + 1X proper# f X -> proper# X 0 + 1X >= 0 + 1X proper# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper p X -> p proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 1 + 1X >= 1 + 1X proper f X -> f proper X 1 + 1X >= 1 + 1X proper 0() -> ok 0() 1 >= 1 proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 p ok X -> ok p X 2 + 1X >= 2 + 1X p mark X -> mark p X 1 + 0X >= 0 + 0X active p s X -> mark X 0 + 0X >= 0 + 0X active p X -> p active X 0 + 0X >= 1 + 0X active s X -> s active X 0 + 0X >= 0 + 0X active f s 0() -> mark f p s 0() 0 >= 0 active f 0() -> mark cons(0(), f s 0()) 0 >= 0 active f X -> f active X 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 s ok X -> ok s X 1 + 1X >= 1 + 1X s mark X -> mark s X 0 + 0X >= 0 + 0X f ok X -> ok f X 1 + 1X >= 1 + 1X f mark X -> mark f X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> proper# X, proper# s X -> proper# X} SCC (4): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> proper# X, proper# s X -> proper# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = 0, [f](x0) = x0, [s](x0) = x0 + 1, [active](x0) = 0, [p](x0) = x0 + 1, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 0, [proper#](x0) = x0 Strict: proper# s X -> proper# X 1 + 1X >= 0 + 1X proper# f X -> proper# X 0 + 1X >= 0 + 1X proper# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper p X -> p proper X 0 + 0X >= 1 + 0X proper s X -> s proper X 0 + 0X >= 1 + 0X proper f X -> f proper X 0 + 0X >= 0 + 0X proper 0() -> ok 0() 0 >= 1 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 p ok X -> ok p X 2 + 1X >= 2 + 1X p mark X -> mark p X 1 + 0X >= 0 + 0X active p s X -> mark X 0 + 0X >= 0 + 0X active p X -> p active X 0 + 0X >= 1 + 0X active s X -> s active X 0 + 0X >= 1 + 0X active f s 0() -> mark f p s 0() 0 >= 0 active f 0() -> mark cons(0(), f s 0()) 0 >= 0 active f X -> f active X 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 1 + 0X >= 0 + 0X f ok X -> ok f X 1 + 1X >= 1 + 1X f mark X -> mark f X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> proper# X} SCC (3): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# f X -> proper# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = 0, [f](x0) = x0 + 1, [s](x0) = 0, [active](x0) = 0, [p](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [proper#](x0) = x0 Strict: proper# f X -> proper# X 1 + 1X >= 0 + 1X proper# cons(X1, X2) -> proper# X2 0 + 1X1 + 1X2 >= 0 + 1X2 proper# cons(X1, X2) -> proper# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper p X -> p proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 1 + 0X >= 0 + 0X proper f X -> f proper X 2 + 1X >= 2 + 1X proper 0() -> ok 0() 2 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 p ok X -> ok p X 2 + 1X >= 2 + 1X p mark X -> mark p X 1 + 0X >= 0 + 0X active p s X -> mark X 0 + 0X >= 0 + 0X active p X -> p active X 0 + 0X >= 1 + 0X active s X -> s active X 0 + 0X >= 0 + 0X active f s 0() -> mark f p s 0() 0 >= 0 active f 0() -> mark cons(0(), f s 0()) 0 >= 0 active f X -> f active X 0 + 0X >= 1 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 1X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 0 + 0X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f X 1 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2} SCC (2): Strict: {proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = x0 + 1, [f](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = 0, [p](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = 0, [top](x0) = 0, [0] = 1, [proper#](x0) = x0 + 1 Strict: proper# cons(X1, X2) -> proper# X2 2 + 1X1 + 1X2 >= 1 + 1X2 proper# cons(X1, X2) -> proper# X1 2 + 1X1 + 1X2 >= 1 + 1X1 Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper p X -> p proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper f X -> f proper X 2 + 1X >= 2 + 1X proper 0() -> ok 0() 2 >= 0 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 1X2 >= 3 + 1X1 + 1X2 p ok X -> ok p X 1 + 0X >= 0 + 0X p mark X -> mark p X 2 + 1X >= 2 + 1X active p s X -> mark X 0 + 0X >= 1 + 1X active p X -> p active X 0 + 0X >= 1 + 0X active s X -> s active X 0 + 0X >= 1 + 0X active f s 0() -> mark f p s 0() 0 >= 5 active f 0() -> mark cons(0(), f s 0()) 0 >= 6 active f X -> f active X 0 + 0X >= 1 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 s ok X -> ok s X 1 + 0X >= 0 + 0X s mark X -> mark s X 2 + 1X >= 2 + 1X f ok X -> ok f X 1 + 0X >= 0 + 0X f mark X -> mark f X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 Qed SCC (2): Strict: {p# mark X -> p# X, p# ok X -> p# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = x0, [f](x0) = 0, [s](x0) = 0, [active](x0) = 0, [p](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [p#](x0) = x0 Strict: p# ok X -> p# X 1 + 1X >= 0 + 1X p# mark X -> p# 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 p X -> p proper X 0 + 0X >= 0 + 0X proper s X -> s proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 0 + 0X proper 0() -> ok 0() 0 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 p ok X -> ok p X 0 + 0X >= 1 + 0X p mark X -> mark p X 0 + 0X >= 0 + 0X active p s X -> mark X 0 + 0X >= 0 + 1X active p X -> p active X 0 + 0X >= 0 + 0X active s X -> s active X 0 + 0X >= 0 + 0X active f s 0() -> mark f p s 0() 0 >= 0 active f 0() -> mark cons(0(), f s 0()) 0 >= 0 active f X -> f active X 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 0 + 0X f ok X -> ok f X 0 + 0X >= 1 + 0X f mark X -> mark f X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {p# mark X -> p# X} SCC (1): Strict: {p# mark X -> p# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = x0 + 1, [f](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [p](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [p#](x0) = x0 Strict: p# mark X -> p# X 1 + 1X >= 0 + 1X Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper p X -> p proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper f X -> f proper X 2 + 1X >= 2 + 1X proper 0() -> ok 0() 2 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 p ok X -> ok p X 2 + 1X >= 2 + 1X p mark X -> mark p X 2 + 1X >= 2 + 1X active p s X -> mark X 3 + 1X >= 1 + 1X active p X -> p active X 2 + 1X >= 2 + 1X active s X -> s active X 2 + 1X >= 2 + 1X active f s 0() -> mark f p s 0() 4 >= 5 active f 0() -> mark cons(0(), f s 0()) 3 >= 3 active f X -> f active X 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed SCC (2): Strict: {s# mark X -> s# X, s# ok X -> s# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = x0, [f](x0) = 0, [s](x0) = 0, [active](x0) = 0, [p](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [s#](x0) = x0 Strict: s# ok X -> s# X 1 + 1X >= 0 + 1X s# mark X -> s# X 0 + 1X >= 0 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper p X -> p proper X 0 + 0X >= 0 + 0X proper s X -> s proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 0 + 0X proper 0() -> ok 0() 0 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 p ok X -> ok p X 0 + 0X >= 1 + 0X p mark X -> mark p X 0 + 0X >= 0 + 0X active p s X -> mark X 0 + 0X >= 0 + 1X active p X -> p active X 0 + 0X >= 0 + 0X active s X -> s active X 0 + 0X >= 0 + 0X active f s 0() -> mark f p s 0() 0 >= 0 active f 0() -> mark cons(0(), f s 0()) 0 >= 0 active f X -> f active X 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 0 + 0X f ok X -> ok f X 0 + 0X >= 1 + 0X f mark X -> mark f X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {s# mark X -> s# X} SCC (1): Strict: {s# mark X -> s# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = x0 + 1, [f](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [p](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [s#](x0) = x0 Strict: s# mark X -> s# X 1 + 1X >= 0 + 1X Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper p X -> p proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper f X -> f proper X 2 + 1X >= 2 + 1X proper 0() -> ok 0() 2 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 p ok X -> ok p X 2 + 1X >= 2 + 1X p mark X -> mark p X 2 + 1X >= 2 + 1X active p s X -> mark X 3 + 1X >= 1 + 1X active p X -> p active X 2 + 1X >= 2 + 1X active s X -> s active X 2 + 1X >= 2 + 1X active f s 0() -> mark f p s 0() 4 >= 5 active f 0() -> mark cons(0(), f s 0()) 3 >= 3 active f X -> f active X 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed SCC (2): Strict: {f# mark X -> f# X, f# ok X -> f# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = x0, [f](x0) = 0, [s](x0) = 0, [active](x0) = 0, [p](x0) = 0, [proper](x0) = 0, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [f#](x0) = x0 Strict: f# ok X -> f# X 1 + 1X >= 0 + 1X f# mark X -> f# X 0 + 1X >= 0 + 1X Weak: top ok X -> top active X 0 + 0X >= 0 + 0X top mark X -> top proper X 0 + 0X >= 0 + 0X proper p X -> p proper X 0 + 0X >= 0 + 0X proper s X -> s proper X 0 + 0X >= 0 + 0X proper f X -> f proper X 0 + 0X >= 0 + 0X proper 0() -> ok 0() 0 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 p ok X -> ok p X 0 + 0X >= 1 + 0X p mark X -> mark p X 0 + 0X >= 0 + 0X active p s X -> mark X 0 + 0X >= 0 + 1X active p X -> p active X 0 + 0X >= 0 + 0X active s X -> s active X 0 + 0X >= 0 + 0X active f s 0() -> mark f p s 0() 0 >= 0 active f 0() -> mark cons(0(), f s 0()) 0 >= 0 active f X -> f active X 0 + 0X >= 0 + 0X active cons(X1, X2) -> cons(active X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s ok X -> ok s X 0 + 0X >= 1 + 0X s mark X -> mark s X 0 + 0X >= 0 + 0X f ok X -> ok f X 0 + 0X >= 1 + 0X f mark X -> mark f X 0 + 0X >= 0 + 0X cons(ok X1, ok X2) -> ok cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: {f# mark X -> f# X} SCC (1): Strict: {f# mark X -> f# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = x0 + 1, [f](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [p](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [f#](x0) = x0 Strict: f# mark X -> f# X 1 + 1X >= 0 + 1X Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper p X -> p proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper f X -> f proper X 2 + 1X >= 2 + 1X proper 0() -> ok 0() 2 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 p ok X -> ok p X 2 + 1X >= 2 + 1X p mark X -> mark p X 2 + 1X >= 2 + 1X active p s X -> mark X 3 + 1X >= 1 + 1X active p X -> p active X 2 + 1X >= 2 + 1X active s X -> s active X 2 + 1X >= 2 + 1X active f s 0() -> mark f p s 0() 4 >= 5 active f 0() -> mark cons(0(), f s 0()) 3 >= 3 active f X -> f active X 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed SCC (2): Strict: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = x0 + 1, [f](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [p](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = 0, [0] = 1, [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 p X -> p proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper f X -> f proper X 2 + 1X >= 2 + 1X proper 0() -> ok 0() 2 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 p ok X -> ok p X 2 + 1X >= 2 + 1X p mark X -> mark p X 2 + 1X >= 2 + 1X active p s X -> mark X 3 + 1X >= 1 + 1X active p X -> p active X 2 + 1X >= 2 + 1X active s X -> s active X 2 + 1X >= 2 + 1X active f s 0() -> mark f p s 0() 4 >= 5 active f 0() -> mark cons(0(), f s 0()) 3 >= 3 active f X -> f active X 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 SCCS (1): Scc: {cons#(mark X1, X2) -> cons#(X1, X2)} SCC (1): Strict: {cons#(mark X1, X2) -> cons#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), f mark X -> mark f X, f ok X -> ok f X, s mark X -> mark s X, s ok X -> ok s X, active cons(X1, X2) -> cons(active X1, X2), active f X -> f active X, active f 0() -> mark cons(0(), f s 0()), active f s 0() -> mark f p s 0(), active s X -> s active X, active p X -> p active X, active p s X -> mark X, p mark X -> mark p X, p ok X -> ok p X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper f X -> f proper X, proper s X -> s proper X, proper p X -> p 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, [mark](x0) = x0 + 1, [f](x0) = x0 + 1, [s](x0) = x0 + 1, [active](x0) = x0 + 1, [p](x0) = x0 + 1, [proper](x0) = x0 + 1, [ok](x0) = x0 + 1, [top](x0) = x0 + 1, [0] = 1, [cons#](x0, x1) = x0 Strict: cons#(mark X1, X2) -> cons#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: top ok X -> top active X 2 + 1X >= 2 + 1X top mark X -> top proper X 2 + 1X >= 2 + 1X proper p X -> p proper X 2 + 1X >= 2 + 1X proper s X -> s proper X 2 + 1X >= 2 + 1X proper f X -> f proper X 2 + 1X >= 2 + 1X proper 0() -> ok 0() 2 >= 2 proper cons(X1, X2) -> cons(proper X1, proper X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 p ok X -> ok p X 2 + 1X >= 2 + 1X p mark X -> mark p X 2 + 1X >= 2 + 1X active p s X -> mark X 3 + 1X >= 1 + 1X active p X -> p active X 2 + 1X >= 2 + 1X active s X -> s active X 2 + 1X >= 2 + 1X active f s 0() -> mark f p s 0() 4 >= 5 active f 0() -> mark cons(0(), f s 0()) 3 >= 3 active f X -> f active X 2 + 1X >= 2 + 1X active cons(X1, X2) -> cons(active X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 s ok X -> ok s X 2 + 1X >= 2 + 1X s mark X -> mark s X 2 + 1X >= 2 + 1X f ok X -> ok f X 2 + 1X >= 2 + 1X f mark X -> mark f X 2 + 1X >= 2 + 1X cons(ok X1, ok X2) -> ok cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 cons(mark X1, X2) -> mark cons(X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 Qed