WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: copy(0(),y,z) -> f(z) copy(s(x),y,z) -> copy(x,y,cons(f(y),z)) f(cons(f(cons(nil(),y)),z)) -> copy(n(),y,z) f(cons(nil(),y)) -> y - Signature: {copy/3,f/1} / {0/0,cons/2,n/0,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {copy,f} and constructors {0,cons,n,nil,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(15) cons :: [A(0) x A(0)] -(0)-> A(0) cons :: [A(0) x A(0)] -(0)-> A(1) copy :: [A(15) x A(0) x A(0)] -(7)-> A(0) f :: [A(0)] -(6)-> A(0) n :: [] -(0)-> A(15) nil :: [] -(0)-> A(0) s :: [A(15)] -(15)-> A(15) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) copy :: [A_cf(0) x A_cf(0) x A_cf(0)] -(0)-> A_cf(0) f :: [A_cf(0)] -(0)-> A_cf(0) n :: [] -(0)-> A_cf(0) nil :: [] -(0)-> A_cf(0) s :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1) cons_A :: [A(0) x A(0)] -(0)-> A(1) n_A :: [] -(0)-> A(1) nil_A :: [] -(0)-> A(1) s_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: copy(0(),y,z) -> f(z) copy(s(x),y,z) -> copy(x,y,cons(f(y),z)) f(cons(f(cons(nil(),y)),z)) -> copy(n(),y,z) f(cons(nil(),y)) -> y - Signature: {copy/3,f/1} / {0/0,cons/2,n/0,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {copy,f} and constructors {0,cons,n,nil,s} Following problems could not be solved: - Strict TRS: copy(0(),y,z) -> f(z) copy(s(x),y,z) -> copy(x,y,cons(f(y),z)) f(cons(f(cons(nil(),y)),z)) -> copy(n(),y,z) f(cons(nil(),y)) -> y - Signature: {copy/3,f/1} / {0/0,cons/2,n/0,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {copy,f} and constructors {0,cons,n,nil,s} WORST_CASE(?,O(n^1))