WORST_CASE(?,O(n^1)) * Step 1: NaturalMI 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: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: none Following symbols are considered usable: {=,implies,not,or} TcT has computed the following interpretation: p(=) = [2] x1 + [2] x2 + [8] p(and) = [1] x1 + [1] x2 + [0] p(implies) = [13] p(not) = [6] p(or) = [1] x2 + [7] p(true) = [0] p(xor) = [4] Following rules are strictly oriented: =(x,y) = [2] x + [2] y + [8] > [4] = xor(x,xor(y,true())) implies(x,y) = [13] > [4] = xor(and(x,y),xor(x,true())) not(x) = [6] > [4] = xor(x,true()) or(x,y) = [1] y + [7] > [4] = xor(and(x,y),xor(x,y)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))