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Let's say a C program comprises two translation units, each of which declares the following type:
struct list {
struct list *next;
void *payload;
};
For deciding whether they are compatible, the following clause of the language standard applies:
"there shall be a one-to-one correspondence between their members such that each pair of corresponding members are declared with compatible types;"
Apparently the implementation may claim that such self-referential types are not compatible! 
Now suppose the program contains not two, but three such translation units. Let's say the instances of the struct type are A, B, and C. Can the implementation choose to A be compatible with B, B with C, but C incompatible with A?
@amonakov Not specific to your example, but yes compatibility of structs is non transitive. We intentionally make use of something like this in the musl c11 thread primitives IIRC, to reuse pthread ones:
https://git.musl-libc.org/cgit/musl/commit/?id=b7cf71a190813590860af25b32532b6c360ac502
@dalias I do not see how this relates to [non-]transitivity. What would be the hypothetical third struct that would be compatible with exactly one of pthread_mutex_t and mtx_t?
Generally speaking, do you have an example that illustrates non-transitivity of compatibility relation that does not involve unprototyped function type?
@amonakov Maybe this isn't quite the same thing, but it's related. I'll think about it more.