\[ \left \{x'(t)=y(t)-z(t),y'(t)=x(t)^2+y(t),z'(t)=x(t)^2+z(t)\right \} \] ✓ Mathematica : cpu = 0.0523279 (sec), leaf count = 127
\[\left \{\left \{x(t)\to e^{t-c_3}+c_1,y(t)\to e^{2 t-2 c_3}+\left (c_1+c_2\right ) e^{t-c_3}+2 c_1 e^{t-c_3} \log \left (e^{t-c_3}\right )-c_1^2,z(t)\to e^{2 t-2 c_3}+\left (c_1+c_2-1\right ) e^{t-c_3}+2 c_1 e^{t-c_3} \log \left (e^{t-c_3}\right )-c_1^2\right \}\right \}\]
✓ Maple : cpu = 0.046 (sec), leaf count = 45
\[ \left \{ [ \left \{ x \left ( t \right ) ={\it \_C2}+{\it \_C3}\,{{\rm e}^{t}} \right \} , \left \{ y \left ( t \right ) = \left ( \int \! \left ( x \left ( t \right ) \right ) ^{2}{{\rm e}^{-t}}\,{\rm d}t+{\it \_C1} \right ) {{\rm e}^{t}} \right \} , \left \{ z \left ( t \right ) =-{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) +y \left ( t \right ) \right \} ] \right \} \]