WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: app(cons(X),YS) -> cons(X) app(nil(),YS) -> YS from(X) -> cons(X) prefix(L) -> cons(nil()) zWadr(XS,nil()) -> nil() zWadr(cons(X),cons(Y)) -> cons(app(Y,cons(X))) zWadr(nil(),YS) -> nil() - Signature: {app/2,from/1,prefix/1,zWadr/2} / {cons/1,nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {app,from,prefix,zWadr} and constructors {cons,nil} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- app :: [A(3) x A(0)] -(7)-> A(0) cons :: [A(3)] -(3)-> A(3) cons :: [A(1)] -(1)-> A(1) cons :: [A(14)] -(14)-> A(14) cons :: [A(0)] -(0)-> A(0) from :: [A(14)] -(15)-> A(0) nil :: [] -(0)-> A(3) nil :: [] -(0)-> A(1) nil :: [] -(0)-> A(14) nil :: [] -(0)-> A(12) nil :: [] -(0)-> A(0) prefix :: [A(0)] -(15)-> A(0) zWadr :: [A(1) x A(3)] -(8)-> A(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- cons_A :: [A(1)] -(1)-> A(1) nil_A :: [] -(0)-> A(1) * Step 2: Open MAYBE - Strict TRS: app(cons(X),YS) -> cons(X) app(nil(),YS) -> YS from(X) -> cons(X) prefix(L) -> cons(nil()) zWadr(XS,nil()) -> nil() zWadr(cons(X),cons(Y)) -> cons(app(Y,cons(X))) zWadr(nil(),YS) -> nil() - Signature: {app/2,from/1,prefix/1,zWadr/2} / {cons/1,nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {app,from,prefix,zWadr} and constructors {cons,nil} Following problems could not be solved: - Strict TRS: app(cons(X),YS) -> cons(X) app(nil(),YS) -> YS from(X) -> cons(X) prefix(L) -> cons(nil()) zWadr(XS,nil()) -> nil() zWadr(cons(X),cons(Y)) -> cons(app(Y,cons(X))) zWadr(nil(),YS) -> nil() - Signature: {app/2,from/1,prefix/1,zWadr/2} / {cons/1,nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {app,from,prefix,zWadr} and constructors {cons,nil} WORST_CASE(?,O(n^1))