WORST_CASE(?,O(n^1)) * Step 1: Sum WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: g(f(x),y) -> f(h(x,y)) h(x,y) -> g(x,f(y)) - Signature: {g/2,h/2} / {f/1} - Obligation: innermost runtime complexity wrt. defined symbols {g,h} and constructors {f} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: g(f(x),y) -> f(h(x,y)) h(x,y) -> g(x,f(y)) - Signature: {g/2,h/2} / {f/1} - Obligation: innermost runtime complexity wrt. defined symbols {g,h} and constructors {f} + 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(f) = {1} Following symbols are considered usable: {g,h} TcT has computed the following interpretation: p(f) = 4 + x1 p(g) = 6 + 4*x1 p(h) = 7 + 4*x1 Following rules are strictly oriented: g(f(x),y) = 22 + 4*x > 11 + 4*x = f(h(x,y)) h(x,y) = 7 + 4*x > 6 + 4*x = g(x,f(y)) Following rules are (at-least) weakly oriented: * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: g(f(x),y) -> f(h(x,y)) h(x,y) -> g(x,f(y)) - Signature: {g/2,h/2} / {f/1} - Obligation: innermost runtime complexity wrt. defined symbols {g,h} and constructors {f} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))