WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(s(X)) -> f(X) g(cons(0(),Y)) -> g(Y) g(cons(s(X),Y)) -> s(X) h(cons(X,Y)) -> h(g(cons(X,Y))) - Signature: {f/1,g/1,h/1} / {0/0,cons/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g,h} and constructors {0,cons,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(7, 7) cons :: [A(7, 7) x A(7, 7)] -(7)-> A(7, 7) cons :: [A(7, 7) x A(12, 7)] -(12)-> A(12, 7) cons :: [A(7, 7) x A(8, 7)] -(8)-> A(8, 7) f :: [A(15, 15)] -(0)-> A(0, 0) g :: [A(7, 7)] -(0)-> A(12, 7) h :: [A(12, 7)] -(1)-> A(0, 0) s :: [A(15, 15)] -(15)-> A(15, 15) s :: [A(7, 7)] -(7)-> A(7, 7) s :: [A(7, 7)] -(12)-> A(12, 7) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0, 0) cons :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) f :: [A_cf(0, 0)] -(8)-> A_cf(0, 0) g :: [A_cf(0, 0)] -(3)-> A_cf(0, 0) g :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) h :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) s :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) s :: [A_cf(0, 0)] -(2)-> A_cf(2, 0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1, 0) 0_A :: [] -(0)-> A(0, 1) cons_A :: [A(0, 0) x A(1, 0)] -(1)-> A(1, 0) cons_A :: [A(1, 1) x A(0, 1)] -(0)-> A(0, 1) s_A :: [A(0, 0)] -(1)-> A(1, 0) s_A :: [A(1, 1)] -(0)-> A(0, 1) * Step 2: Open MAYBE - Strict TRS: f(s(X)) -> f(X) g(cons(0(),Y)) -> g(Y) g(cons(s(X),Y)) -> s(X) h(cons(X,Y)) -> h(g(cons(X,Y))) - Signature: {f/1,g/1,h/1} / {0/0,cons/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g,h} and constructors {0,cons,s} Following problems could not be solved: - Strict TRS: f(s(X)) -> f(X) g(cons(0(),Y)) -> g(Y) g(cons(s(X),Y)) -> s(X) h(cons(X,Y)) -> h(g(cons(X,Y))) - Signature: {f/1,g/1,h/1} / {0/0,cons/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g,h} and constructors {0,cons,s} WORST_CASE(?,O(n^2))