WORST_CASE(?,O(n^1)) * Step 1: Sum WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: p(m,n,s(r)) -> p(m,r,n) p(m,0(),0()) -> m p(m,s(n),0()) -> p(0(),n,m) - Signature: {p/3} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {p} and constructors {0,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: p(m,n,s(r)) -> p(m,r,n) p(m,0(),0()) -> m p(m,s(n),0()) -> p(0(),n,m) - Signature: {p/3} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {p} 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: none Following symbols are considered usable: {p} TcT has computed the following interpretation: p(0) = 0 p(p) = 2 + 8*x1 + 8*x2 + 8*x3 p(s) = 1 + x1 Following rules are strictly oriented: p(m,n,s(r)) = 10 + 8*m + 8*n + 8*r > 2 + 8*m + 8*n + 8*r = p(m,r,n) p(m,0(),0()) = 2 + 8*m > m = m p(m,s(n),0()) = 10 + 8*m + 8*n > 2 + 8*m + 8*n = p(0(),n,m) Following rules are (at-least) weakly oriented: * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: p(m,n,s(r)) -> p(m,r,n) p(m,0(),0()) -> m p(m,s(n),0()) -> p(0(),n,m) - Signature: {p/3} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {p} and constructors {0,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))