WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: comp_f_g#1(comp_f_g(x4,x5),comp_f_g(x2,x3),x1) -> comp_f_g#1(x4,x5,comp_f_g#1(x2,x3,x1)) comp_f_g#1(comp_f_g(x7,x9),cons_x(x2),x4) -> comp_f_g#1(x7,x9,Cons(x2,x4)) comp_f_g#1(cons_x(x2),comp_f_g(x5,x7),x3) -> Cons(x2,comp_f_g#1(x5,x7,x3)) comp_f_g#1(cons_x(x5),cons_x(x2),x4) -> Cons(x5,Cons(x2,x4)) main(Leaf(x4)) -> Cons(x4,Nil()) main(Node(x9,x5)) -> comp_f_g#1(walk#1(x9),walk#1(x5),Nil()) walk#1(Leaf(x2)) -> cons_x(x2) walk#1(Node(x5,x3)) -> comp_f_g(walk#1(x5),walk#1(x3)) - Signature: {comp_f_g#1/3,main/1,walk#1/1} / {Cons/2,Leaf/1,Nil/0,Node/2,comp_f_g/2,cons_x/1} - Obligation: innermost runtime complexity wrt. defined symbols {comp_f_g#1,main,walk#1} and constructors {Cons,Leaf,Nil ,Node,comp_f_g,cons_x} + Applied Processor: Ara {minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- F (TrsFun "Cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(15) F (TrsFun "Cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(12) F (TrsFun "Cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(8) F (TrsFun "Cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(11) F (TrsFun "Leaf") :: ["A"(13)] -(13)-> "A"(13) F (TrsFun "Nil") :: [] -(0)-> "A"(15) F (TrsFun "Node") :: ["A"(13) x "A"(13)] -(13)-> "A"(13) F (TrsFun "comp_f_g") :: ["A"(12) x "A"(12)] -(12)-> "A"(12) F (TrsFun "comp_f_g#1") :: ["A"(12) x "A"(12) x "A"(1)] -(1)-> "A"(8) F (TrsFun "cons_x") :: ["A"(0)] -(12)-> "A"(12) F (TrsFun "main") :: ["A"(13)] -(5)-> "A"(5) F (TrsFun "walk#1") :: ["A"(13)] -(0)-> "A"(12) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "F (TrsFun \"Cons\")_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(1) "F (TrsFun \"Leaf\")_A" :: ["A"(1)] -(1)-> "A"(1) "F (TrsFun \"Nil\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"Node\")_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "F (TrsFun \"comp_f_g\")_A" :: ["A"(0) x "A"(0)] -(1)-> "A"(1) "F (TrsFun \"cons_x\")_A" :: ["A"(0)] -(1)-> "A"(1) WORST_CASE(?,O(n^1))