WORST_CASE(?,O(1)) * Step 1: Sum WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: f(s(X),Y) -> h(s(f(h(Y),X))) - Signature: {f/2} / {h/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {h,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: NaturalPI WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: f(s(X),Y) -> h(s(f(h(Y),X))) - Signature: {f/2} / {h/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {h,s} + 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: none Following symbols are considered usable: {f} TcT has computed the following interpretation: p(f) = 2 p(h) = 0 p(s) = 0 Following rules are strictly oriented: f(s(X),Y) = 2 > 0 = h(s(f(h(Y),X))) Following rules are (at-least) weakly oriented: * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(s(X),Y) -> h(s(f(h(Y),X))) - Signature: {f/2} / {h/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {h,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(1))