[tex]\delta (q_0,a)=q_1[/tex]
[tex]\delta (q_1,a)=q_2[/tex]
[tex]\delta (q_2,a)=q_3[/tex]
[tex]\delta (q_3,a)=q_4[/tex]
[tex]\delta (q_4,a)=q_5[/tex]
[tex]\delta (q_5,a)=q_6[/tex]
[tex]\delta (q_6,a)=q_6[/tex]
[tex]\delta (q_6,b)=q_7[/tex]
[tex]\delta (q_6,c)=q_{10}[/tex]
[tex]\delta (q_7,b)=q_{8}[/tex]
[tex]\delta (q_7,c)=q_{10}[/tex]
[tex]\delta (q_8,b)=q_{9}[/tex]
[tex]\delta (q_8,c)=q_{10}[/tex]
[tex]\delta (q_9,c)=q_{10}[/tex]
[tex]\delta (q_{10},c)=q_{11}[/tex]
[tex]\delta (q_{11},c)=q_{11}[/tex]

[tex]\delta (q_0,a)=q_1[/tex]
[tex]\delta (q_1,a)=q_0[/tex]

[tex]uvxyz=a^m\in L[/tex]
[tex]uv^ixy^iz=a^{m (i-1)t};1\leq t\leq m[/tex]

[tex]m (m 1-1)t=m mt=m(t 1);1\leq t\leq m[/tex]

[tex]uvxyz=a^m \in L[/tex]
[tex]uv^{m 1}xy^{m 1}z=a^{m(t 1)} \notin L ;1\leq t\leq m[/tex]