Certificate for #13040 ⟨a, b | abb=aba, bbba=a⟩

Back:⟨a, b | abb=aba, bbba=a⟩

Completion settings:

[1] abb=aba

Axiom: abb=aba.

Referenced by [3], [4], [6].

[2] bbba=a

Axiom: bbba=a.

Defines rule #3.

Referenced by [3], [4].

[3] ababa=aa

Overlap of [1] abb=aba with [2] bbba=a:

a bb bbba

Critical pair: aa=ababa.

Flip LHS and RHS.

Referenced by [4], [5].

[4] aba=aaa

Overlap of [1] abb=aba with [2] bbba=a:

ab b bbba

Critical pair: aba=ababba.

Reduce RHS:

[1]ab(abb)a
[3]⇒ (ababa)a
⇒ aaa

Defines rule #1.

Referenced by [5], [6].

[5] aaaaa=aa

Simplify [3] ababa=aa.

Reduce LHS:

[4](aba)ba
[4]⇒ aa(aba)
⇒ aaaaa

Defines rule #4.

[6] abb=aaa

Simplify [1] abb=aba.

Reduce RHS:

[4](aba)
⇒ aaa

Defines rule #2.