WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: eq0(0(),0()) -> S(0()) eq0(0(),S(x)) -> 0() eq0(S(x),0()) -> 0() eq0(S(x'),S(x)) -> eq0(x',x) - Signature: {eq0/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {eq0} and constructors {0,S} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(13) 0 :: [] -(0)-> A(0) S :: [A(0)] -(0)-> A(0) S :: [A(13)] -(13)-> A(13) eq0 :: [A(13) x A(0)] -(8)-> A(0) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) S :: [A_cf(0)] -(0)-> A_cf(0) eq0 :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1) S_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: eq0(0(),0()) -> S(0()) eq0(0(),S(x)) -> 0() eq0(S(x),0()) -> 0() eq0(S(x'),S(x)) -> eq0(x',x) - Signature: {eq0/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {eq0} and constructors {0,S} Following problems could not be solved: - Strict TRS: eq0(0(),0()) -> S(0()) eq0(0(),S(x)) -> 0() eq0(S(x),0()) -> 0() eq0(S(x'),S(x)) -> eq0(x',x) - Signature: {eq0/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {eq0} and constructors {0,S} WORST_CASE(?,O(n^1))