Certificate for #3483 ⟨a, b, c | bb=aa, abc=a⟩

Back:⟨a, b, c | bb=aa, abc=a⟩

Completion settings:

[1] aa=bb

Axiom: bb=aa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4].

[2] abc=a

Axiom: abc=a.

Defines rule #2.

Referenced by [4].

[3] bba=abb

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

a a aa

Critical pair: abb=bba.

Flip LHS and RHS.

Defines rule #3.

[4] bbbc=bb

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

a a abc

Critical pair: aa=bbbc.

Reduce LHS:

[1](aa)
⇒ bb

Flip LHS and RHS.

Defines rule #1.