WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: eq0(0(),0()) -> S(0()) eq0(0(),S(x)) -> 0() eq0(S(x),0()) -> 0() eq0(S(x'),S(x)) -> eq0(x',x) - Signature: {eq0/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {eq0} and constructors {0,S} + Applied Processor: NaturalPI {shape = StronglyLinear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(stronglyLinear): The following argument positions are considered usable: none Following symbols are considered usable: {eq0} TcT has computed the following interpretation: p(0) = 2 p(S) = 2 + x1 p(eq0) = 8 + x1 Following rules are strictly oriented: eq0(0(),0()) = 10 > 4 = S(0()) eq0(0(),S(x)) = 10 > 2 = 0() eq0(S(x),0()) = 10 + x > 2 = 0() eq0(S(x'),S(x)) = 10 + x' > 8 + x' = eq0(x',x) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))