WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: implies(x,or(y,z)) -> or(y,implies(x,z)) implies(not(x),y) -> or(x,y) implies(not(x),or(y,z)) -> implies(y,or(x,z)) - Signature: {implies/2} / {not/1,or/2} - Obligation: innermost runtime complexity wrt. defined symbols {implies} and constructors {not,or} + Applied Processor: NaturalPI {shape = Linear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(or) = {2} Following symbols are considered usable: {implies} TcT has computed the following interpretation: p(implies) = 2*x1 + 2*x2 p(not) = 6 + x1 p(or) = 8 + x1 + x2 Following rules are strictly oriented: implies(x,or(y,z)) = 16 + 2*x + 2*y + 2*z > 8 + 2*x + y + 2*z = or(y,implies(x,z)) implies(not(x),y) = 12 + 2*x + 2*y > 8 + x + y = or(x,y) implies(not(x),or(y,z)) = 28 + 2*x + 2*y + 2*z > 16 + 2*x + 2*y + 2*z = implies(y,or(x,z)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))