WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: +(0(),y) -> y +(s(x),0()) -> s(x) +(s(x),s(y)) -> s(+(s(x),+(y,0()))) - Signature: {+/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {0,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- + :: [A(0, 1) x A(0, 8)] -(1)-> A(0, 1) 0 :: [] -(0)-> A(0, 1) 0 :: [] -(0)-> A(0, 8) 0 :: [] -(0)-> A(7, 15) s :: [A(0, 1)] -(1)-> A(0, 1) s :: [A(0, 8)] -(8)-> A(0, 8) Cost-free Signatures used: -------------------------- + :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) + :: [A_cf(0, 7) x A_cf(0, 7)] -(0)-> A_cf(0, 7) 0 :: [] -(0)-> A_cf(0, 0) 0 :: [] -(0)-> A_cf(0, 7) 0 :: [] -(0)-> A_cf(3, 11) s :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) s :: [A_cf(0, 7)] -(7)-> A_cf(0, 7) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1, 0) 0_A :: [] -(0)-> A(0, 1) s_A :: [A(1, 0)] -(1)-> A(1, 0) s_A :: [A(0, 1)] -(1)-> A(0, 1) * Step 2: Open MAYBE - Strict TRS: +(0(),y) -> y +(s(x),0()) -> s(x) +(s(x),s(y)) -> s(+(s(x),+(y,0()))) - Signature: {+/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {0,s} Following problems could not be solved: - Strict TRS: +(0(),y) -> y +(s(x),0()) -> s(x) +(s(x),s(y)) -> s(+(s(x),+(y,0()))) - Signature: {+/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {0,s} WORST_CASE(?,O(n^2))