The syntax of Expensive is identical to brainfuck, except that the SHA-512 of the source code must start with at least 4 zero bytes (8 hexadecimal zeros). Only characters
<>+-,. are allowed (brainfuck allows any character in the source code and ignores any irrelevant character, but Expensive forbids anything except those 8 characters).
It is very probably Turing-complete, but in order to prove that, one would need to implement an interpreter for a Turing-complete language. This has not been done yet.