Pettitt - significance levels in R

I am trying to implement the Pettitt test on R. I am coding by myself but with the reference of the built-in function pettitt.test of R.(https://www.rdocumentation.org/packages/trend/versions/1.1.4/topics/pettitt.test)

I could implement it successfully, but my question is about the p-value. I am calculating the p-value with this equation:

p=2e^((-6U ̂^2)/(n^3+n^2 ))

being U the value of the test statistic and n the length of my sample. (I have checked and I got the same than with the built-in function pettitt.test)

For a 5% confidence interval, the alternative hypothesis should be true if this p-value is lower than 0.5? or 0.05? I am confused by the documentation of R (weblink previously shared) that says lower or equal than 0.5, and for the Pettitt's paper (1979) page 5 that also indicates lower or equal than 0.5

Any help to clarify this question?