Where does “ありがたし” come from?

ありがたし (Japanese) comes from Japanese 有り, from Japanese 有る.

Ancestry of “ありがたし”, step by step

ありがたし traces back through two separate lines of ancestry.

via Japanese 有り

StepLanguageWordMeaning
1Japanese有りexistence; handling; OK, acceptable
2Japanese有る

via Japanese 難い

StepLanguageWordMeaning
1Japanese難いdifficult; difficult or hard to do
2Japanese難し

Words derived from “ありがたし

Every word from Japanese 有るEvery word from Japanese 有り