WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: ++(x,nil()) -> x ++(++(x,y),z) -> ++(x,++(y,z)) ++(.(x,y),z) -> .(x,++(y,z)) ++(nil(),y) -> y - Signature: {++/2} / {./2,nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {++} and constructors {.,nil} + 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}, uargs(.) = {2} Following symbols are considered usable: {++} TcT has computed the following interpretation: p(++) = 3 + 4*x1 + x2 p(.) = 5 + x2 p(nil) = 7 Following rules are strictly oriented: ++(x,nil()) = 10 + 4*x > x = x ++(++(x,y),z) = 15 + 16*x + 4*y + z > 6 + 4*x + 4*y + z = ++(x,++(y,z)) ++(.(x,y),z) = 23 + 4*y + z > 8 + 4*y + z = .(x,++(y,z)) ++(nil(),y) = 31 + y > y = y Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))