undecomposable
1. [ adjective ] representing the furthest possible extent of analysis or division into parts
Synonyms: unanalyzable
Examples:

"a feeling is a simple and undecomposable mental state"- G.S.Brett "this weight of evidence is something mystical and unanalyzable"-M.R.Cohen

Related terms: simple simple
Similar spelling:   undecomposed
  undecipherable
  undecipherably