WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: *(x,0()) -> 0() *(*(x,y),z) -> *(x,*(y,z)) *(1(),y) -> y *(i(x),x) -> 1() - Signature: {*/2} / {0/0,1/0,i/1} - Obligation: innermost runtime complexity wrt. defined symbols {*} and constructors {0,1,i} + 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(*) = {2} Following symbols are considered usable: {*} TcT has computed the following interpretation: p(*) = 8 + 2*x1 + x2 p(0) = 0 p(1) = 0 p(i) = 0 Following rules are strictly oriented: *(x,0()) = 8 + 2*x > 0 = 0() *(*(x,y),z) = 24 + 4*x + 2*y + z > 16 + 2*x + 2*y + z = *(x,*(y,z)) *(1(),y) = 8 + y > y = y *(i(x),x) = 8 + x > 0 = 1() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))