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SuiteSparse_config can itself be compiled without OpenMP, but the package that #include's it might have OpenMP available. If that's the case, the SuiteSparse_time() function defined in SuiteSparse_config.c will use the POSIX timer instead.
If the Package wants omp_get_wtime(), it can use the new SUITESPARSE_TIME macro, which becomes omp_get_wtime() if _OPENMP is #define'd, or SuiteSparse_time otherwise. Or it is zero if the timer is entirely disabled.