WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: b(u(x)) -> a(e(x)) c(u(x)) -> b(x) d(x) -> e(u(x)) d(u(x)) -> c(x) v(e(x)) -> x - Signature: {b/1,c/1,d/1,v/1} / {a/1,e/1,u/1} - Obligation: innermost runtime complexity wrt. defined symbols {b,c,d,v} and constructors {a,e,u} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- a :: [A(0)] -(14)-> A(14) b :: [A(1)] -(14)-> A(0) c :: [A(1)] -(15)-> A(0) d :: [A(1)] -(15)-> A(0) e :: [A(4)] -(4)-> A(4) e :: [A(0)] -(0)-> A(0) u :: [A(1)] -(1)-> A(1) u :: [A(0)] -(0)-> A(0) v :: [A(4)] -(15)-> A(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- a_A :: [A(0)] -(1)-> A(1) e_A :: [A(1)] -(1)-> A(1) u_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: b(u(x)) -> a(e(x)) c(u(x)) -> b(x) d(x) -> e(u(x)) d(u(x)) -> c(x) v(e(x)) -> x - Signature: {b/1,c/1,d/1,v/1} / {a/1,e/1,u/1} - Obligation: innermost runtime complexity wrt. defined symbols {b,c,d,v} and constructors {a,e,u} Following problems could not be solved: - Strict TRS: b(u(x)) -> a(e(x)) c(u(x)) -> b(x) d(x) -> e(u(x)) d(u(x)) -> c(x) v(e(x)) -> x - Signature: {b/1,c/1,d/1,v/1} / {a/1,e/1,u/1} - Obligation: innermost runtime complexity wrt. defined symbols {b,c,d,v} and constructors {a,e,u} WORST_CASE(?,O(n^1))