WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: add(0(),X) -> X add(s(),Y) -> s() from(X) -> cons(X) fst(0(),Z) -> nil() fst(s(),cons(Y)) -> cons(Y) len(cons(X)) -> s() len(nil()) -> 0() - Signature: {add/2,from/1,fst/2,len/1} / {0/0,cons/1,nil/0,s/0} - Obligation: innermost runtime complexity wrt. defined symbols {add,from,fst,len} and constructors {0,cons,nil,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(0) add :: [A(0) x A(0)] -(4)-> A(0) cons :: [A(0)] -(0)-> A(0) from :: [A(0)] -(8)-> A(0) fst :: [A(0) x A(0)] -(8)-> A(0) len :: [A(0)] -(8)-> A(0) nil :: [] -(0)-> A(0) s :: [] -(0)-> A(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1) cons_A :: [A(0)] -(0)-> A(1) nil_A :: [] -(0)-> A(1) s_A :: [] -(0)-> A(1) * Step 2: Open MAYBE - Strict TRS: add(0(),X) -> X add(s(),Y) -> s() from(X) -> cons(X) fst(0(),Z) -> nil() fst(s(),cons(Y)) -> cons(Y) len(cons(X)) -> s() len(nil()) -> 0() - Signature: {add/2,from/1,fst/2,len/1} / {0/0,cons/1,nil/0,s/0} - Obligation: innermost runtime complexity wrt. defined symbols {add,from,fst,len} and constructors {0,cons,nil,s} Following problems could not be solved: - Strict TRS: add(0(),X) -> X add(s(),Y) -> s() from(X) -> cons(X) fst(0(),Z) -> nil() fst(s(),cons(Y)) -> cons(Y) len(cons(X)) -> s() len(nil()) -> 0() - Signature: {add/2,from/1,fst/2,len/1} / {0/0,cons/1,nil/0,s/0} - Obligation: innermost runtime complexity wrt. defined symbols {add,from,fst,len} and constructors {0,cons,nil,s} WORST_CASE(?,O(n^1))