Consider the language L of bitstrings that start with an even$-$length palindrome, followed by a multiple of four $1\text{'}$s i$.$e$.14$n $,$ where n is any positive integer. For example $00110011111111$ would be in L since it starts with $001100$ which is an even$-$length palindrome and ends with $11111111$ which is eight $1\text{'}$s$.$ On the other hand, the string $101011111$ would not be in L even though it has four $1\text{'}$s at the end, because the preceding string $10101$ is not an even$-$length palindrome.