Certificate for #3489 ⟨a, b, c | bb=aa, acb=a⟩

Back:⟨a, b, c | bb=aa, acb=a⟩

Completion settings:

[1] aa=bb

Axiom: bb=aa.

Flip LHS and RHS.

Defines rule #1.

Referenced by [3], [4].

[2] acb=a

Axiom: acb=a.

Defines rule #3.

Referenced by [4], [5].

[3] abb=bba

Overlap of [1] aa=bb with [1] aa=bb:

a a aa

Critical pair: abb=bba.

Defines rule #2.

[4] bbcb=bb

Overlap of [1] aa=bb with [2] acb=a:

a a acb

Critical pair: aa=bbcb.

Reduce LHS:

[1](aa)
⇒ bb

Flip LHS and RHS.

Defines rule #4.

Referenced by [5].

[5] abcb=ab

Overlap of [2] acb=a with [4] bbcb=bb:

ac b bbcb

Critical pair: acbb=abcb.

Reduce LHS:

[2](acb)b
⇒ ab

Flip LHS and RHS.

Defines rule #5.