Certificate for #13165 ⟨a, b | aba=aab, baa=bb⟩

Back:⟨a, b | aba=aab, baa=bb⟩

Completion settings:

[1] aab=aba

Axiom: aba=aab.

Flip LHS and RHS.

Defines rule #1.

Referenced by [3], [4].

[2] bb=baa

Axiom: baa=bb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] baba=baaaa

Overlap of [2] bb=baa with [2] bb=baa:

b b bb

Critical pair: bbaa=baab.

Reduce LHS:

[2](bb)aa
⇒ baaaa

Reduce RHS:

[1]b(aab)
⇒ baba

Flip LHS and RHS.

Defines rule #3.

[4] abab=abaaa

Overlap of [1] aab=aba with [2] bb=baa:

aa b bb

Critical pair: aabaa=abab.

Reduce LHS:

[1](aab)aa
⇒ abaaa

Flip LHS and RHS.

Defines rule #4.