"rely entirely" is a correct phrase in written English.
It means to completely depend on something or someone. Example: I cannot rely entirely on my memory for the exam, so I need to study harder.
Let him then rely entirely on the past.
So why not rely entirely on the private sector?
The council did not rely entirely on colour coded mapping.
Few advertisers want to rely entirely on traditional research, particularly America's Nielsen television-ratings system.
As demand for fresh, local food rises, we cannot continue to rely entirely on farmers' markets.
The forces rely entirely on their own resources for all goods and services.
That is, we do not have to rely entirely upon selling our labor.
These stabs at accountability rely entirely on standardized tests, which seem like a reasonable measure.
The trouble is that its effects rely entirely on dazzlement, an over-the-top gigantism that gets old fast.
They rely entirely on metabolic water that is, on water released from chemical bonds through the metabolism of food.
Either we're supposed to rely entirely on large institutions, or we're supposed to rely only on ourselves.
