WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: mem(x,nil()) -> false() mem(x,set(y)) -> =(x,y) mem(x,union(y,z)) -> or(mem(x,y),mem(x,z)) or(x,true()) -> true() or(false(),false()) -> false() or(true(),y) -> true() - Signature: {mem/2,or/2} / {=/2,false/0,nil/0,set/1,true/0,union/2} - Obligation: innermost runtime complexity wrt. defined symbols {mem,or} and constructors {=,false,nil,set,true,union} + Applied Processor: NaturalPI {shape = StronglyLinear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(stronglyLinear): The following argument positions are considered usable: uargs(or) = {1,2} Following symbols are considered usable: {mem,or} TcT has computed the following interpretation: p(=) = 1 p(false) = 0 p(mem) = x2 p(nil) = 8 p(or) = 2 + x1 + x2 p(set) = 6 + x1 p(true) = 2 p(union) = 8 + x1 + x2 Following rules are strictly oriented: mem(x,nil()) = 8 > 0 = false() mem(x,set(y)) = 6 + y > 1 = =(x,y) mem(x,union(y,z)) = 8 + y + z > 2 + y + z = or(mem(x,y),mem(x,z)) or(x,true()) = 4 + x > 2 = true() or(false(),false()) = 2 > 0 = false() or(true(),y) = 4 + y > 2 = true() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))