WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: cond_insTree_t_xs_1(False(),Node(x54,Elem(x8),x38),Node(x30,Elem(x4),x14),Nil()) -> Cons(cond_link_t1_t2_2(leq#2(x8,x4) ,Node(x54,Elem(x8),x38) ,Node(x30,Elem(x4),x14) ,x54 ,Elem(x8) ,x38 ,Elem(x4) ,x14) ,Nil()) cond_insTree_t_xs_1(True(),Node(x5,x6,x7),Node(x2,x3,x4),x1) -> Cons(Node(x5,x6,x7),Cons(Node(x2,x3,x4),x1)) cond_link_t1_t2_2(False(),Node(x11,Elem(x10),x9),Node(x8,Elem(x7),x6),x5,Elem(x4),x3,Elem(x2),x1) -> Node(S(x5),Elem(x2),Cons(Node(x11,Elem(x10),x9),x1)) cond_link_t1_t2_2(True(),Node(x11,Elem(x10),x9),Node(x8,Elem(x7),x6),x5,Elem(x4),x3,Elem(x2),x1) -> Node(S(x5),Elem(x4),Cons(Node(x8,Elem(x7),x6),x3)) leq#2(0(),x20) -> True() leq#2(S(x24),0()) -> False() leq#2(S(x4),S(x2)) -> leq#2(x4,x2) lt#2(0(),0()) -> False() lt#2(0(),S(x20)) -> True() lt#2(S(x20),0()) -> False() lt#2(S(x4),S(x2)) -> lt#2(x4,x2) main(x4,Nil()) -> Cons(x4,Nil()) main(Node(x100,x132,x164),Cons(Node(x48,x64,x80),x28)) -> cond_insTree_t_xs_1(lt#2(x100,x48) ,Node(x100,x132,x164) ,Node(x48,x64,x80) ,x28) - Signature: {cond_insTree_t_xs_1/4,cond_link_t1_t2_2/8,leq#2/2,lt#2/2,main/2} / {0/0,Cons/2,Elem/1,False/0,Nil/0,Node/3 ,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond_insTree_t_xs_1,cond_link_t1_t2_2,leq#2,lt#2 ,main} and constructors {0,Cons,Elem,False,Nil,Node,S,True} + Applied Processor: Ara {minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- F (TrsFun "0") :: [] -(0)-> "A"(2) F (TrsFun "0") :: [] -(0)-> "A"(0) F (TrsFun "0") :: [] -(0)-> "A"(1) F (TrsFun "Cons") :: ["A"(9) x "A"(0)] -(9)-> "A"(9) F (TrsFun "Cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(0) F (TrsFun "Cons") :: ["A"(3) x "A"(0)] -(3)-> "A"(3) F (TrsFun "Elem") :: ["A"(8)] -(8)-> "A"(8) F (TrsFun "Elem") :: ["A"(0)] -(0)-> "A"(0) F (TrsFun "Elem") :: ["A"(1)] -(1)-> "A"(1) F (TrsFun "Elem") :: ["A"(3)] -(3)-> "A"(3) F (TrsFun "False") :: [] -(0)-> "A"(4) F (TrsFun "False") :: [] -(0)-> "A"(3) F (TrsFun "False") :: [] -(0)-> "A"(15) F (TrsFun "Nil") :: [] -(0)-> "A"(0) F (TrsFun "Nil") :: [] -(0)-> "A"(9) F (TrsFun "Nil") :: [] -(0)-> "A"(15) F (TrsFun "Node") :: ["A"(8) x "A"(8) x "A"(0)] -(0)-> "A"(8) F (TrsFun "Node") :: ["A"(0) x "A"(0) x "A"(0)] -(0)-> "A"(0) F (TrsFun "Node") :: ["A"(1) x "A"(1) x "A"(0)] -(0)-> "A"(1) F (TrsFun "Node") :: ["A"(9) x "A"(9) x "A"(0)] -(0)-> "A"(9) F (TrsFun "Node") :: ["A"(6) x "A"(6) x "A"(0)] -(0)-> "A"(6) F (TrsFun "S") :: ["A"(2)] -(2)-> "A"(2) F (TrsFun "S") :: ["A"(0)] -(0)-> "A"(0) F (TrsFun "S") :: ["A"(1)] -(1)-> "A"(1) F (TrsFun "True") :: [] -(0)-> "A"(4) F (TrsFun "True") :: [] -(0)-> "A"(3) F (TrsFun "True") :: [] -(0)-> "A"(15) F (TrsFun "cond_insTree_t_xs_1") :: ["A"(4) x "A"(8) x "A"(8) x "A"(0)] -(7)-> "A"(0) F (TrsFun "cond_link_t1_t2_2") :: ["A"(3) x "A"(0) x "A"(1) x "A"(0) x "A"(0) x "A"(0) x "A"(3) x "A"(0)] -(0)-> "A"(0) F (TrsFun "leq#2") :: ["A"(2) x "A"(0)] -(9)-> "A"(14) F (TrsFun "lt#2") :: ["A"(0) x "A"(1)] -(2)-> "A"(9) F (TrsFun "main") :: ["A"(9) x "A"(9)] -(14)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "F (TrsFun \"0\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"Cons\")_A" :: ["A"(1) x "A"(0)] -(1)-> "A"(1) "F (TrsFun \"Elem\")_A" :: ["A"(1)] -(1)-> "A"(1) "F (TrsFun \"False\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"Nil\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"Node\")_A" :: ["A"(1) x "A"(1) x "A"(0)] -(0)-> "A"(1) "F (TrsFun \"S\")_A" :: ["A"(1)] -(1)-> "A"(1) "F (TrsFun \"True\")_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))