Certificate for #13214 ⟨a, b | abb=aba, bba=aa⟩

Back:⟨a, b | abb=aba, bba=aa⟩

Completion settings:

[1] aba=abb

Axiom: abb=aba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[2] bba=aa

Axiom: bba=aa.

Defines rule #1.

Referenced by [3], [4].

[3] abbbb=aaa

Overlap of [1] aba=abb with [1] aba=abb:

ab a aba

Critical pair: ababb=abbba.

Reduce LHS:

[1](aba)bb
⇒ abbbb

Reduce RHS:

[2]ab(bba)
[1]⇒ (aba)a
[2]⇒ a(bba)
⇒ aaa

Defines rule #3.

Referenced by [4].

[4] aaabb=aaaa

Overlap of [1] aba=abb with [3] abbbb=aaa:

ab a abbbb

Critical pair: abaaa=abbbbbb.

Reduce LHS:

[1](aba)aa
[2]⇒ a(bba)a
⇒ aaaa

Reduce RHS:

[3](abbbb)bb
⇒ aaabb

Flip LHS and RHS.

Defines rule #4.