YES TRS: from(X) -> cons(X,n__from(s(X))) 2ndspos(0(),Z) -> rnil() 2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z))) 2ndsneg(0(),Z) -> rnil() 2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z))) pi(X) -> 2ndspos(X,from(0())) plus(0(),Y) -> Y plus(s(X),Y) -> s(plus(X,Y)) times(0(),Y) -> 0() times(s(X),Y) -> plus(Y,times(X,Y)) square(X) -> times(X,X) from(X) -> n__from(X) cons(X1,X2) -> n__cons(X1,X2) activate(n__from(X)) -> from(X) activate(n__cons(X1,X2)) -> cons(X1,X2) activate(X) -> X max/plus interpretations on N: from_A(x1) = max{60, 99 + x1} from#_A(x1) = max{80, 101 + x1} cons_A(x1,x2) = max{64, 60 + x1, 28 + x2} cons#_A(x1,x2) = max{52, 60, 14 + x2} n__from_A(x1) = max{61, 63 + x1} n__from#_A(x1) = max{0, 81 + x1} s_A(x1) = max{2, x1} s#_A(x1) = max{101, 101 + x1} 2ndspos_A(x1,x2) = max{41, -1, -5 + x2} 2ndspos#_A(x1,x2) = max{52, 45, -13 + x2} 0_A = 1 0#_A = 104 rnil_A = 12 rnil#_A = 0 n__cons_A(x1,x2) = max{22, 25 + x1, 28 + x2} n__cons#_A(x1,x2) = max{38, 40, 13} rcons_A(x1,x2) = max{12, 12, -1} rcons#_A(x1,x2) = max{52, 51 + x1, 24 + x2} posrecip_A(x1) = max{1, -50 + x1} posrecip#_A(x1) = max{44, 46} activate_A(x1) = max{4, 38 + x1} activate#_A(x1) = max{53, 39 + x1} 2ndsneg_A(x1,x2) = max{1, 12, -58 + x2} 2ndsneg#_A(x1,x2) = max{46, 24, 1 + x2} negrecip_A(x1) = max{14, -66 + x1} negrecip#_A(x1) = max{65, 41} pi_A(x1) = max{95, -2} pi#_A(x1) = max{105, 103} plus_A(x1,x2) = max{2, -3 + x1, x2} plus#_A(x1,x2) = max{104, 105 + x1, 106 + x2} times_A(x1,x2) = max{2, -4, -1 + x2} times#_A(x1,x2) = max{103, 108, 105 + x2} square_A(x1) = max{0, 2 + x1} square#_A(x1) = max{108, 105 + x1} precedence: square > pi = times > from = 2ndspos = 0 = plus > cons = n__from = s = 2ndsneg > rnil = rcons = activate > n__cons > posrecip = negrecip