WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(g(x),y,y) -> g(f(x,x,y)) - Signature: {f/3} / {g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(g) = {1} Following symbols are considered usable: {f} TcT has computed the following interpretation: p(f) = 1 + 6*x1 p(g) = 1 + x1 Following rules are strictly oriented: f(g(x),y,y) = 7 + 6*x > 2 + 6*x = g(f(x,x,y)) Following rules are (at-least) weakly oriented: * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(g(x),y,y) -> g(f(x,x,y)) - Signature: {f/3} / {g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))