WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(s(x),y,y) -> f(y,x,s(x)) g(x,y) -> x g(x,y) -> y - Signature: {f/3,g/2} / {s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {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: none Following symbols are considered usable: {f,g} TcT has computed the following interpretation: p(f) = 4 + 8*x1 + 7*x2 + x3 p(g) = 8 + 8*x1 + 8*x2 p(s) = 1 + x1 Following rules are strictly oriented: f(s(x),y,y) = 12 + 8*x + 8*y > 5 + 8*x + 8*y = f(y,x,s(x)) g(x,y) = 8 + 8*x + 8*y > x = x g(x,y) = 8 + 8*x + 8*y > y = y Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))