Certificate for #16299 ⟨a, b | aab=bb, abba=ba⟩

Back:⟨a, b | aab=bb, abba=ba⟩

Completion settings:

[1] aab=bb

Axiom: aab=bb.

Defines rule #4.

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

[2] abba=ba

Axiom: abba=ba.

Defines rule #6.

Referenced by [3], [5].

[3] aba=bbba

Overlap of [1] aab=bb with [2] abba=ba:

a ab abba

Critical pair: aba=bbba.

Defines rule #5.

Referenced by [4], [5].

[4] abbb=bbbbb

Overlap of [3] aba=bbba with [1] aab=bb:

ab a aab

Critical pair: abbb=bbbaab.

Reduce RHS:

[1]bbb(aab)
⇒ bbbbb

Defines rule #2.

[5] bbbba=ba

Overlap of [3] aba=bbba with [2] abba=ba:

ab a abba

Critical pair: abba=bbbabba.

Reduce LHS:

[2](abba)
⇒ ba

Reduce RHS:

[2]bbb(abba)
⇒ bbbba

Flip LHS and RHS.

Defines rule #3.

Referenced by [6].

[6] bbbbbb=bbb

Overlap of [5] bbbba=ba with [1] aab=bb:

bbbb a aab

Critical pair: bbbbbb=baab.

Reduce RHS:

[1]b(aab)
⇒ bbb

Defines rule #1.