Decision tree (rpart) will not split even with cp=0

Question

I have an example of dataset where decision tree (rpart) would not split, even with cp = 0. Here is link to the date unsplittable. I think even if you take purely random dataset, it will split, it is pretty hard to find something that does not split completely. I am trying to compute splits manually and see any improvements in Gini index. Here is my code anyway:

library(rpart)
df<- read_csv(file = 'df.csv')
df$x <- as.factor(df$x)

fit <- rpart(x ~ ., method = 'class',
             data = df,
             control = rpart.control(cp=0))
summary(fit)
printcp(fit)

And here is output:

Classification tree:
rpart(formula = x ~ ., data = df, method = "class", control = rpart.control(cp = 0))

Variables actually used in tree construction:
character(0)

Root node error: 16/186 = 0.086022

n= 186 

  CP nsplit rel error xerror xstd
1  0      0         1      0    0