Certificate for #13195 ⟨a, b | abb=aab, baa=ab⟩

Back:⟨a, b | abb=aab, baa=ab⟩

Completion settings:

[1] abb=aab

Axiom: abb=aab.

Referenced by [3].

[2] ab=baa

Axiom: baa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4], [5].

[3] abb=baaaa

Simplify [1] abb=aab.

Reduce RHS:

[2]a(ab)
[2]⇒ (ab)aa
⇒ baaaa

Referenced by [4].

[4] bbaaaa=baaaa

Overlap of [3] abb=baaaa with [2] ab=baa:

abb ab

Critical pair: baab=baaaa.

Reduce LHS:

[2]ba(ab)
[2]⇒ b(ab)aa
⇒ bbaaaa

Defines rule #3.

Referenced by [5].

[5] baaaaaaaa=baaaaaa

Overlap of [2] ab=baa with [4] bbaaaa=baaaa:

a b bbaaaa

Critical pair: abaaaa=baabaaaa.

Reduce LHS:

[2](ab)aaaa
⇒ baaaaaa

Reduce RHS:

[2]ba(ab)aaaa
[2]⇒ b(ab)aaaaaa
[4]⇒ (bbaaaa)aaaa
⇒ baaaaaaaa

Flip LHS and RHS.

Defines rule #1.