Certificate for #12992 ⟨a, b | abb=aaa, bbba=a⟩

Back:⟨a, b | abb=aaa, bbba=a⟩

Completion settings:

[1] abb=aaa

Axiom: abb=aaa.

Defines rule #3.

Referenced by [3], [4].

[2] bbba=a

Axiom: bbba=a.

Defines rule #4.

Referenced by [3], [4].

[3] aaaba=aa

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

a bb bbba

Critical pair: aa=aaaba.

Flip LHS and RHS.

Referenced by [5].

[4] aba=aaaaaa

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

ab b bbba

Critical pair: aba=aaabba.

Reduce RHS:

[1]aa(abb)a
⇒ aaaaaa

Defines rule #2.

Referenced by [5].

[5] aaaaaaaa=aa

Simplify [3] aaaba=aa.

Reduce LHS:

[4]aa(aba)
⇒ aaaaaaaa

Defines rule #1.