on thin ice vs problematic

on thin ice

prep
  • In a dangerous, hazardous, or delicate situation; at risk. 

adv
  • dangerously, hazardously, delicately 

problematic

noun
  • A problem or difficulty in a particular field of study. 

adj
  • Difficult to overcome, solve, or decide. 

  • Contributing (especially if subtly) to discrimination (such as racism, sexism, homophobia, transphobia, or ageism). 

  • Not settled, uncertain, of uncertain outcome; debatable, questionable, open to doubt. 

  • a problematic analysis 

How often have the words on thin ice and problematic occurred in a corpus of books? (source: Google Ngram Viewer )