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