WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y)) anchored(Nil(),y) -> y goal(x,y) -> anchored(x,y) - Signature: {anchored/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {anchored,goal} and constructors {Cons,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: none Following symbols are considered usable: {anchored,goal} TcT has computed the following interpretation: p(Cons) = 4 + x2 p(Nil) = 5 p(anchored) = 5 + 5*x1 + x2 p(goal) = 9 + 14*x1 + x2 Following rules are strictly oriented: anchored(Cons(x,xs),y) = 25 + 5*xs + y > 9 + 5*xs + y = anchored(xs,Cons(Cons(Nil(),Nil()),y)) anchored(Nil(),y) = 30 + y > y = y goal(x,y) = 9 + 14*x + y > 5 + 5*x + y = anchored(x,y) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))