WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: div(0(),s(Y)) -> 0() div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y))) minus(X,0()) -> X minus(s(X),s(Y)) -> p(minus(X,Y)) p(s(X)) -> X - Signature: {div/2,minus/2,p/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {div,minus,p} 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(div) = {1}, uargs(p) = {1}, uargs(s) = {1} Following symbols are considered usable: {div,minus,p} TcT has computed the following interpretation: p(0) = 3 p(div) = 6 + 2*x1 p(minus) = 1 + x1 p(p) = x1 p(s) = 6 + x1 Following rules are strictly oriented: div(0(),s(Y)) = 12 > 3 = 0() div(s(X),s(Y)) = 18 + 2*X > 14 + 2*X = s(div(minus(X,Y),s(Y))) minus(X,0()) = 1 + X > X = X minus(s(X),s(Y)) = 7 + X > 1 + X = p(minus(X,Y)) p(s(X)) = 6 + X > X = X Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))