WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: compS_f#1(compS_f(x2),x1) -> compS_f#1(x2,S(x1)) compS_f#1(id(),x3) -> S(x3) iter#3(0()) -> id() iter#3(S(x6)) -> compS_f(iter#3(x6)) main(0()) -> 0() main(S(x9)) -> compS_f#1(iter#3(x9),0()) - Signature: {compS_f#1/2,iter#3/1,main/1} / {0/0,S/1,compS_f/1,id/0} - Obligation: innermost runtime complexity wrt. defined symbols {compS_f#1,iter#3,main} and constructors {0,S,compS_f,id} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(15) 0 :: [] -(0)-> A(12) 0 :: [] -(0)-> A(14) S :: [A(15)] -(15)-> A(15) S :: [A(0)] -(0)-> A(0) compS_f :: [A(12)] -(12)-> A(12) compS_f :: [A(14)] -(14)-> A(14) compS_f#1 :: [A(12) x A(0)] -(15)-> A(0) id :: [] -(0)-> A(12) id :: [] -(0)-> A(14) iter#3 :: [A(15)] -(8)-> A(14) main :: [A(15)] -(14)-> A(0) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) S :: [A_cf(0)] -(0)-> A_cf(0) compS_f :: [A_cf(0)] -(0)-> A_cf(0) compS_f#1 :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) id :: [] -(0)-> A_cf(0) iter#3 :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1) S_A :: [A(1)] -(1)-> A(1) compS_f_A :: [A(0)] -(1)-> A(1) id_A :: [] -(0)-> A(1) * Step 2: Open MAYBE - Strict TRS: compS_f#1(compS_f(x2),x1) -> compS_f#1(x2,S(x1)) compS_f#1(id(),x3) -> S(x3) iter#3(0()) -> id() iter#3(S(x6)) -> compS_f(iter#3(x6)) main(0()) -> 0() main(S(x9)) -> compS_f#1(iter#3(x9),0()) - Signature: {compS_f#1/2,iter#3/1,main/1} / {0/0,S/1,compS_f/1,id/0} - Obligation: innermost runtime complexity wrt. defined symbols {compS_f#1,iter#3,main} and constructors {0,S,compS_f,id} Following problems could not be solved: - Strict TRS: compS_f#1(compS_f(x2),x1) -> compS_f#1(x2,S(x1)) compS_f#1(id(),x3) -> S(x3) iter#3(0()) -> id() iter#3(S(x6)) -> compS_f(iter#3(x6)) main(0()) -> 0() main(S(x9)) -> compS_f#1(iter#3(x9),0()) - Signature: {compS_f#1/2,iter#3/1,main/1} / {0/0,S/1,compS_f/1,id/0} - Obligation: innermost runtime complexity wrt. defined symbols {compS_f#1,iter#3,main} and constructors {0,S,compS_f,id} WORST_CASE(?,O(n^1))