*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: goal(xs,ys) -> revapp(xs,ys) revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest)) revapp(Nil(),rest) -> rest Weak DP Rules: Weak TRS Rules: Signature: {goal/2,revapp/2} / {Cons/2,Nil/0} Obligation: Innermost basic terms: {goal,revapp}/{Cons,Nil} Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules, greedy = NoGreedy} Proof: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: none Following symbols are considered usable: {goal,revapp} TcT has computed the following interpretation: p(Cons) = [1] x1 + [1] x2 + [2] p(Nil) = [0] p(goal) = [10] x1 + [8] x2 + [9] p(revapp) = [9] x1 + [8] x2 + [7] Following rules are strictly oriented: goal(xs,ys) = [10] xs + [8] ys + [9] > [9] xs + [8] ys + [7] = revapp(xs,ys) revapp(Cons(x,xs),rest) = [8] rest + [9] x + [9] xs + [25] > [8] rest + [8] x + [9] xs + [23] = revapp(xs,Cons(x,rest)) revapp(Nil(),rest) = [8] rest + [7] > [1] rest + [0] = rest Following rules are (at-least) weakly oriented: *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: goal(xs,ys) -> revapp(xs,ys) revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest)) revapp(Nil(),rest) -> rest Signature: {goal/2,revapp/2} / {Cons/2,Nil/0} Obligation: Innermost basic terms: {goal,revapp}/{Cons,Nil} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).