WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X) u21(ackout(X),Y) -> u22(ackin(Y,X)) - Signature: {ackin/2,u21/2} / {ackout/1,s/1,u22/1} - Obligation: innermost runtime complexity wrt. defined symbols {ackin,u21} and constructors {ackout,s,u22} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- ackin :: [A(0) x A(4)] -(0)-> A(4) ackout :: [A(4)] -(4)-> A(4) s :: [A(0)] -(0)-> A(0) s :: [A(4)] -(4)-> A(4) u21 :: [A(4) x A(0)] -(1)-> A(4) u22 :: [A(0)] -(0)-> A(4) Cost-free Signatures used: -------------------------- ackin :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) ackout :: [A_cf(0)] -(0)-> A_cf(0) s :: [A_cf(0)] -(0)-> A_cf(0) u21 :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) u22 :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- ackout_A :: [A(1)] -(1)-> A(1) s_A :: [A(1)] -(1)-> A(1) u22_A :: [A(0)] -(0)-> A(1) * Step 2: Open MAYBE - Strict TRS: ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X) u21(ackout(X),Y) -> u22(ackin(Y,X)) - Signature: {ackin/2,u21/2} / {ackout/1,s/1,u22/1} - Obligation: innermost runtime complexity wrt. defined symbols {ackin,u21} and constructors {ackout,s,u22} Following problems could not be solved: - Strict TRS: ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X) u21(ackout(X),Y) -> u22(ackin(Y,X)) - Signature: {ackin/2,u21/2} / {ackout/1,s/1,u22/1} - Obligation: innermost runtime complexity wrt. defined symbols {ackin,u21} and constructors {ackout,s,u22} WORST_CASE(?,O(n^1))