Checking if Post Correspondence Problem has a Solution

Question

I have the following problem

I think that solution is wrong because x1=b and y1=b3(cube).They do not match,So how is this solution possible?

Answer 1

Post Correspondence Problem (PCP) :

Given a PCP instance P, a match is a nonempty sequence $$i_1, i_2, . . . , i_l$$ of numbers from $\{1, 2, . . . , k\}$ (with repetition) such that

$$t_{i1}. t_{i2}· · · t_i = b_{i1} .b_{i2}· · · b_i$$

Modified PCP (MPCP):

$MPCP = \{< P > | P$ is a PCP instance and it has a match which starts with index $1\}$.

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Given solution is correct, since you are thinking about MPCP and question asking is about PCP.