Certificate for #20142 ⟨a, b | aab=b, babb=bba⟩

Back:⟨a, b | aab=b, babb=bba⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #3.

Referenced by [3].

[2] bba=babb

Axiom: babb=bba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] bababbb=bbb

Overlap of [2] bba=babb with [1] aab=b:

bb a aab

Critical pair: bbb=babbab.

Reduce RHS:

[2]ba(bba)b
⇒ bababbb

Flip LHS and RHS.

Defines rule #4.

Referenced by [4].

[4] bbbbbbb=bbbb

Overlap of [2] bba=babb with [3] bababbb=bbb:

b ba bababbb

Critical pair: bbbb=babbbabbb.

Reduce RHS:

[2]bab(bba)bbb
[2]⇒ ba(bba)bbbbb
[3]⇒ (bababbb)bbbb
⇒ bbbbbbb

Flip LHS and RHS.

Defines rule #1.