WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: b(u(x)) -> a(e(x)) c(u(x)) -> b(x) d(x) -> e(u(x)) d(u(x)) -> c(x) v(e(x)) -> x - Signature: {b/1,c/1,d/1,v/1} / {a/1,e/1,u/1} - Obligation: innermost runtime complexity wrt. defined symbols {b,c,d,v} and constructors {a,e,u} + 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: {b,c,d,v} TcT has computed the following interpretation: p(a) = 4 p(b) = 10 p(c) = 14 p(d) = 15 p(e) = 2 + x1 p(u) = 2 p(v) = 2 + 8*x1 Following rules are strictly oriented: b(u(x)) = 10 > 4 = a(e(x)) c(u(x)) = 14 > 10 = b(x) d(x) = 15 > 4 = e(u(x)) d(u(x)) = 15 > 14 = c(x) v(e(x)) = 18 + 8*x > x = x Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))