WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: a__f(X1,X2) -> f(X1,X2) a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y)) mark(f(X1,X2)) -> a__f(mark(X1),X2) mark(g(X)) -> g(mark(X)) - Signature: {a__f/2,mark/1} / {f/2,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {f,g} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- a__f :: [A(1, 2) x A(0, 0)] -(2)-> A(1, 2) f :: [A(3, 2) x A(0, 0)] -(3)-> A(3, 2) f :: [A(1, 2) x A(0, 0)] -(1)-> A(1, 2) f :: [A(0, 0) x A(0, 0)] -(0)-> A(0, 0) g :: [A(3, 2)] -(1)-> A(1, 2) g :: [A(5, 2)] -(3)-> A(3, 2) g :: [A(0, 0)] -(0)-> A(0, 0) mark :: [A(3, 2)] -(0)-> A(1, 2) Cost-free Signatures used: -------------------------- a__f :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) a__f :: [A_cf(2, 0) x A_cf(0, 0)] -(2)-> A_cf(2, 0) f :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) f :: [A_cf(2, 0) x A_cf(0, 0)] -(2)-> A_cf(2, 0) g :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) g :: [A_cf(2, 0)] -(2)-> A_cf(2, 0) mark :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) mark :: [A_cf(2, 0)] -(0)-> A_cf(2, 0) Base Constructor Signatures used: --------------------------------- f_A :: [A(1, 0) x A(0, 0)] -(1)-> A(1, 0) f_A :: [A(0, 1) x A(0, 0)] -(0)-> A(0, 1) g_A :: [A(1, 0)] -(1)-> A(1, 0) g_A :: [A(1, 1)] -(0)-> A(0, 1) * Step 2: Open MAYBE - Strict TRS: a__f(X1,X2) -> f(X1,X2) a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y)) mark(f(X1,X2)) -> a__f(mark(X1),X2) mark(g(X)) -> g(mark(X)) - Signature: {a__f/2,mark/1} / {f/2,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {f,g} Following problems could not be solved: - Strict TRS: a__f(X1,X2) -> f(X1,X2) a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y)) mark(f(X1,X2)) -> a__f(mark(X1),X2) mark(g(X)) -> g(mark(X)) - Signature: {a__f/2,mark/1} / {f/2,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {f,g} WORST_CASE(?,O(n^2))