IsBase←(∧´<∘⊣≡¨(1-˜+`∘(≠∘⊢↑⍷))⊔⊢)
"abcd"IsBase"abcdabcdabcdabcd"
"aa"IsBase"aaa"

(⌈´⊸=≠¨)⊸/(IsBase⟜x¨)⊸/1↓↑⊑((⌊´=⊢)≠¨)⊸/d←"abcdabcd"⋈x←"abcdabcdabcdabcd"
(⌈´⊸=≠¨)⊸/(IsBase⟜x¨)⊸/1↓↑⊑((⌊´=⊢)≠¨)⊸/d←"aa"⋈x←"aaa"