There will be no public block chain with Turing complete scripts ever, because that would mean that absolutely any algorithm would be accepted in a script, including non-terminating ones. A smart contract with an infinite loop would be a very bad thing.
But, but Etherium is Turing complete, isn't it??? No it is not, it can't be. It would be killed by DOS in no time. The language may be Turing complete in theory, but since the system must guarantee that all scripts terminate in finite time (I think they do it by requiring that each instruction has a cost) it is not Turing complete in practice. They could have used a total language in the first place, where you have a guarantee that every program terminates.
I know this isn't really an answer to the OP question but I wanted to point it out
If I understand it correctly, I think thats exactly the point, they wish to include loops (and by including loops in general, also infinite loops), the infinite loops are then solved practically by the gas mechanism. The problem isn't with the halting problem, but that the system produces the first shared computer, that has the most slow and expensive computation, and so won't be used for computation but only computationally enhanced verification, and thats just not as cool. But, but Etherium is Turing complete, isn't it??? No it is not, it can't be. It would be killed by DOS in no time. The language may be Turing complete in theory, but since the system must guarantee that all scripts terminate in finite time (I think they do it by requiring that each instruction has a cost) it is not Turing complete in practice. They could have used a total language in the first place, where you have a guarantee that every program terminates.
I know this isn't really an answer to the OP question but I wanted to point it out