WORST_CASE(?,O(n^1)) * Step 1: Sum WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: +(0(),y) -> y +(s(x),0()) -> s(x) +(s(x),s(y)) -> s(+(s(x),+(y,0()))) - Signature: {+/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {0,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: +(0(),y) -> y +(s(x),0()) -> s(x) +(s(x),s(y)) -> s(+(s(x),+(y,0()))) - Signature: {+/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {0,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: uargs(+) = {2}, uargs(s) = {1} Following symbols are considered usable: {+} TcT has computed the following interpretation: p(+) = 1 + x1 + 8*x2 p(0) = 0 p(s) = 2 + x1 Following rules are strictly oriented: +(0(),y) = 1 + 8*y > y = y +(s(x),0()) = 3 + x > 2 + x = s(x) +(s(x),s(y)) = 19 + x + 8*y > 13 + x + 8*y = s(+(s(x),+(y,0()))) Following rules are (at-least) weakly oriented: * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: +(0(),y) -> y +(s(x),0()) -> s(x) +(s(x),s(y)) -> s(+(s(x),+(y,0()))) - Signature: {+/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {0,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))