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)) double(x) -> +(x,x) double(0()) -> 0() double(s(x)) -> s(s(double(x))) - Signature: {+/2,double/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,double} and constructors {0,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- + :: [A(1) x A(8)] -(13)-> A(0) 0 :: [] -(0)-> A(8) 0 :: [] -(0)-> A(13) double :: [A(13)] -(15)-> A(0) s :: [A(8)] -(8)-> A(8) s :: [A(1)] -(1)-> A(1) s :: [A(13)] -(13)-> A(13) s :: [A(0)] -(0)-> A(0) Cost-free Signatures used: -------------------------- + :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) 0 :: [] -(0)-> A_cf(0) double :: [A_cf(0)] -(0)-> A_cf(0) s :: [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: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) +(s(x),y) -> s(+(x,y)) double(x) -> +(x,x) double(0()) -> 0() double(s(x)) -> s(s(double(x))) - Signature: {+/2,double/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,double} and constructors {0,s} Following problems could not be solved: - Strict TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) +(s(x),y) -> s(+(x,y)) double(x) -> +(x,x) double(0()) -> 0() double(s(x)) -> s(s(double(x))) - Signature: {+/2,double/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,double} and constructors {0,s} WORST_CASE(?,O(n^1))