WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: +(0(),y) -> y +(s(x),y) -> s(+(x,y)) -(x,0()) -> x -(0(),y) -> 0() -(s(x),s(y)) -> -(x,y) - Signature: {+/2,-/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,-} 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: {+,-} TcT has computed the following interpretation: p(+) = 9 + 5*x1 + 8*x2 p(-) = 2 + 8*x1 + x2 p(0) = 3 p(s) = 1 + x1 Following rules are strictly oriented: +(0(),y) = 24 + 8*y > y = y +(s(x),y) = 14 + 5*x + 8*y > 10 + 5*x + 8*y = s(+(x,y)) -(x,0()) = 5 + 8*x > x = x -(0(),y) = 26 + y > 3 = 0() -(s(x),s(y)) = 11 + 8*x + y > 2 + 8*x + y = -(x,y) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))