MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { from(X) -> cons(X, n__from(s(X))) , from(X) -> n__from(X) , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z))) , 2ndspos(s(N), cons2(X, cons(Y, Z))) -> rcons(posrecip(Y), 2ndsneg(N, activate(Z))) , 2ndspos(0(), Z) -> rnil() , activate(X) -> X , activate(n__from(X)) -> from(X) , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z))) , 2ndsneg(s(N), cons2(X, cons(Y, Z))) -> rcons(negrecip(Y), 2ndspos(N, activate(Z))) , 2ndsneg(0(), Z) -> rnil() , pi(X) -> 2ndspos(X, from(0())) , plus(s(X), Y) -> s(plus(X, Y)) , plus(0(), Y) -> Y , times(s(X), Y) -> plus(Y, times(X, Y)) , times(0(), Y) -> 0() , square(X) -> times(X, X) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..