WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: a__tail(X) -> tail(X) a__tail(cons(X,XS)) -> mark(XS) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(tail(X)) -> a__tail(mark(X)) mark(zeros()) -> a__zeros() - Signature: {a__tail/1,a__zeros/0,mark/1} / {0/0,cons/2,tail/1,zeros/0} - Obligation: innermost runtime complexity wrt. defined symbols {a__tail,a__zeros,mark} and constructors {0,cons,tail ,zeros} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(5, 5) 0 :: [] -(0)-> A(1, 6) 0 :: [] -(0)-> A(5, 6) a__tail :: [A(1, 5)] -(4)-> A(1, 5) a__zeros :: [] -(3)-> A(1, 5) cons :: [A(1, 5) x A(5, 5)] -(1)-> A(1, 5) cons :: [A(5, 5) x A(5, 5)] -(5)-> A(5, 5) mark :: [A(5, 5)] -(4)-> A(1, 5) tail :: [A(5, 5)] -(5)-> A(5, 5) tail :: [A(1, 5)] -(1)-> A(1, 5) zeros :: [] -(0)-> A(5, 5) zeros :: [] -(0)-> A(3, 7) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0, 0) a__tail :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) a__zeros :: [] -(0)-> A_cf(0, 0) cons :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) mark :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) tail :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) zeros :: [] -(0)-> A_cf(0, 0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1, 0) 0_A :: [] -(0)-> A(0, 1) cons_A :: [A(1, 0) x A(0, 0)] -(1)-> A(1, 0) cons_A :: [A(0, 1) x A(1, 1)] -(0)-> A(0, 1) tail_A :: [A(1, 0)] -(1)-> A(1, 0) tail_A :: [A(0, 1)] -(0)-> A(0, 1) zeros_A :: [] -(0)-> A(1, 0) zeros_A :: [] -(0)-> A(0, 1) * Step 2: Open MAYBE - Strict TRS: a__tail(X) -> tail(X) a__tail(cons(X,XS)) -> mark(XS) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(tail(X)) -> a__tail(mark(X)) mark(zeros()) -> a__zeros() - Signature: {a__tail/1,a__zeros/0,mark/1} / {0/0,cons/2,tail/1,zeros/0} - Obligation: innermost runtime complexity wrt. defined symbols {a__tail,a__zeros,mark} and constructors {0,cons,tail ,zeros} Following problems could not be solved: - Strict TRS: a__tail(X) -> tail(X) a__tail(cons(X,XS)) -> mark(XS) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(tail(X)) -> a__tail(mark(X)) mark(zeros()) -> a__zeros() - Signature: {a__tail/1,a__zeros/0,mark/1} / {0/0,cons/2,tail/1,zeros/0} - Obligation: innermost runtime complexity wrt. defined symbols {a__tail,a__zeros,mark} and constructors {0,cons,tail ,zeros} WORST_CASE(?,O(n^2))