WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: comp_f_g#1(comp_f_g(x7,x9),walk_xs_3(x8),x12) -> comp_f_g#1(x7,x9,Cons(x8,x12)) comp_f_g#1(walk_xs(),walk_xs_3(x8),x12) -> Cons(x8,x12) main(Cons(x4,x5)) -> comp_f_g#1(walk#1(x5),walk_xs_3(x4),Nil()) main(Nil()) -> Nil() walk#1(Cons(x4,x3)) -> comp_f_g(walk#1(x3),walk_xs_3(x4)) walk#1(Nil()) -> walk_xs() - Signature: {comp_f_g#1/3,main/1,walk#1/1} / {Cons/2,Nil/0,comp_f_g/2,walk_xs/0,walk_xs_3/1} - Obligation: innermost runtime complexity wrt. defined symbols {comp_f_g#1,main,walk#1} and constructors {Cons,Nil ,comp_f_g,walk_xs,walk_xs_3} + Applied Processor: Ara {minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- F (TrsFun "Cons") :: ["A"(11) x "A"(11)] -(11)-> "A"(11) F (TrsFun "Cons") :: ["A"(8) x "A"(8)] -(8)-> "A"(8) F (TrsFun "Cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(0) F (TrsFun "Nil") :: [] -(0)-> "A"(11) F (TrsFun "Nil") :: [] -(0)-> "A"(8) F (TrsFun "Nil") :: [] -(0)-> "A"(6) F (TrsFun "Nil") :: [] -(0)-> "A"(2) F (TrsFun "comp_f_g") :: ["A"(7) x "A"(7)] -(7)-> "A"(7) F (TrsFun "comp_f_g#1") :: ["A"(7) x "A"(0) x "A"(0)] -(3)-> "A"(0) F (TrsFun "main") :: ["A"(11)] -(11)-> "A"(0) F (TrsFun "walk#1") :: ["A"(8)] -(8)-> "A"(7) F (TrsFun "walk_xs") :: [] -(0)-> "A"(7) F (TrsFun "walk_xs") :: [] -(0)-> "A"(15) F (TrsFun "walk_xs_3") :: ["A"(0)] -(0)-> "A"(0) F (TrsFun "walk_xs_3") :: ["A"(8)] -(0)-> "A"(8) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "F (TrsFun \"Cons\")_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "F (TrsFun \"Nil\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"comp_f_g\")_A" :: ["A"(0) x "A"(0)] -(1)-> "A"(1) "F (TrsFun \"walk_xs\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"walk_xs_3\")_A" :: ["A"(0)] -(0)-> "A"(1) WORST_CASE(?,O(n^1))