WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) +(s(x),y) -> s(+(x,y)) not(false()) -> true() not(true()) -> false() odd(0()) -> false() odd(s(x)) -> not(odd(x)) - Signature: {+/2,not/1,odd/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {+,not,odd} and constructors {0,false,s,true} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- + :: [A(5) x A(4)] -(4)-> A(0) 0 :: [] -(0)-> A(4) 0 :: [] -(0)-> A(3) false :: [] -(0)-> A(0) not :: [A(0)] -(2)-> A(0) odd :: [A(3)] -(1)-> A(0) s :: [A(4)] -(4)-> A(4) s :: [A(5)] -(5)-> A(5) s :: [A(3)] -(3)-> A(3) s :: [A(0)] -(0)-> A(0) true :: [] -(0)-> A(0) Cost-free Signatures used: -------------------------- + :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) 0 :: [] -(0)-> A_cf(0) false :: [] -(0)-> A_cf(0) not :: [A_cf(0)] -(0)-> A_cf(0) odd :: [A_cf(0)] -(0)-> A_cf(0) s :: [A_cf(0)] -(0)-> A_cf(0) true :: [] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1) false_A :: [] -(0)-> A(1) s_A :: [A(1)] -(1)-> A(1) true_A :: [] -(0)-> A(1) * Step 2: Open MAYBE - Strict TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) +(s(x),y) -> s(+(x,y)) not(false()) -> true() not(true()) -> false() odd(0()) -> false() odd(s(x)) -> not(odd(x)) - Signature: {+/2,not/1,odd/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {+,not,odd} and constructors {0,false,s,true} Following problems could not be solved: - Strict TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) +(s(x),y) -> s(+(x,y)) not(false()) -> true() not(true()) -> false() odd(0()) -> false() odd(s(x)) -> not(odd(x)) - Signature: {+/2,not/1,odd/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {+,not,odd} and constructors {0,false,s,true} WORST_CASE(?,O(n^1))