WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: =(x,y) -> xor(x,xor(y,true())) implies(x,y) -> xor(and(x,y),xor(x,true())) not(x) -> xor(x,true()) or(x,y) -> xor(and(x,y),xor(x,y)) - Signature: {=/2,implies/2,not/1,or/2} / {and/2,true/0,xor/2} - Obligation: innermost runtime complexity wrt. defined symbols {=,implies,not,or} and constructors {and,true,xor} + 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: {=,implies,not,or} TcT has computed the following interpretation: p(=) = 8 p(and) = x1 + x2 p(implies) = 1 + x1 p(not) = 2 p(or) = 4 + x2 p(true) = 0 p(xor) = 0 Following rules are strictly oriented: =(x,y) = 8 > 0 = xor(x,xor(y,true())) implies(x,y) = 1 + x > 0 = xor(and(x,y),xor(x,true())) not(x) = 2 > 0 = xor(x,true()) or(x,y) = 4 + y > 0 = xor(and(x,y),xor(x,y)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))