Certificate for #6657 ⟨a, b | aab=a, bbba=bb⟩

Back:⟨a, b | aab=a, bbba=bb⟩

Completion settings:

[1] aab=a

Axiom: aab=a.

Defines rule #1.

Referenced by [3], [4], [5].

[2] bbba=bb

Axiom: bbba=bb.

Defines rule #5.

Referenced by [3], [4].

[3] abba=ab

Overlap of [1] aab=a with [2] bbba=bb:

aa b bbba

Critical pair: aabb=abba.

Reduce LHS:

[1](aab)b
⇒ ab

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[4] bbab=bb

Overlap of [2] bbba=bb with [1] aab=a:

bbb a aab

Critical pair: bbba=bbab.

Reduce LHS:

[2](bbba)
⇒ bb

Flip LHS and RHS.

Defines rule #4.

[5] aba=a

Overlap of [1] aab=a with [3] abba=ab:

a ab abba

Critical pair: aab=aba.

Reduce LHS:

[1](aab)
⇒ a

Flip LHS and RHS.

Defines rule #2.