WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a(b(x)) -> b(a(x)) a(c(x)) -> x - Signature: {a/1} / {b/1,c/1} - Obligation: innermost runtime complexity wrt. defined symbols {a} and constructors {b,c} + Applied Processor: NaturalPI {shape = Linear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(b) = {1} Following symbols are considered usable: {a} TcT has computed the following interpretation: p(a) = 2 + 2*x1 p(b) = 9 + x1 p(c) = 4 + x1 Following rules are strictly oriented: a(b(x)) = 20 + 2*x > 11 + 2*x = b(a(x)) a(c(x)) = 10 + 2*x > x = x Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))