WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: average(x,s(s(s(y)))) -> s(average(s(x),y)) average(0(),0()) -> 0() average(0(),s(0())) -> 0() average(0(),s(s(0()))) -> s(0()) average(s(x),y) -> average(x,s(y)) - Signature: {average/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {average} and constructors {0,s} + 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(s) = {1} Following symbols are considered usable: {average} TcT has computed the following interpretation: p(0) = 2 p(average) = 5*x1 + 3*x2 p(s) = 2 + x1 Following rules are strictly oriented: average(x,s(s(s(y)))) = 18 + 5*x + 3*y > 12 + 5*x + 3*y = s(average(s(x),y)) average(0(),0()) = 16 > 2 = 0() average(0(),s(0())) = 22 > 2 = 0() average(0(),s(s(0()))) = 28 > 4 = s(0()) average(s(x),y) = 10 + 5*x + 3*y > 6 + 5*x + 3*y = average(x,s(y)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))