WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a(c(d(x))) -> c(x) u(b(d(d(x)))) -> b(x) v(a(a(x))) -> u(v(x)) v(a(c(x))) -> u(b(d(x))) v(c(x)) -> b(x) w(a(a(x))) -> u(w(x)) w(a(c(x))) -> u(b(d(x))) w(c(x)) -> b(x) - Signature: {a/1,u/1,v/1,w/1} / {b/1,c/1,d/1} - Obligation: innermost runtime complexity wrt. defined symbols {a,u,v,w} and constructors {b,c,d} + Applied Processor: NaturalPI {shape = StronglyLinear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(stronglyLinear): The following argument positions are considered usable: uargs(u) = {1} Following symbols are considered usable: {a,u,v,w} TcT has computed the following interpretation: p(a) = 8 + x1 p(b) = x1 p(c) = 12 + x1 p(d) = 4 + x1 p(u) = x1 p(v) = x1 p(w) = x1 Following rules are strictly oriented: a(c(d(x))) = 24 + x > 12 + x = c(x) u(b(d(d(x)))) = 8 + x > x = b(x) v(a(a(x))) = 16 + x > x = u(v(x)) v(a(c(x))) = 20 + x > 4 + x = u(b(d(x))) v(c(x)) = 12 + x > x = b(x) w(a(a(x))) = 16 + x > x = u(w(x)) w(a(c(x))) = 20 + x > 4 + x = u(b(d(x))) w(c(x)) = 12 + x > x = b(x) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))