Certificate for #3479 ⟨a, b, c | bb=aa, aac=a⟩

Back:⟨a, b, c | bb=aa, aac=a⟩

Completion settings:

[1] aa=bb

Axiom: bb=aa.

Flip LHS and RHS.

Referenced by [2], [3].

[2] a=bbc

Axiom: aac=a.

Reduce LHS:

[1](aa)c
⇒ bbc

Flip LHS and RHS.

Defines rule #3.

Referenced by [3].

[3] bbcbbc=bb

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

aa a

Critical pair: bbca=bb.

Reduce LHS:

[2]bbc(a)
⇒ bbcbbc

Defines rule #2.

Referenced by [4].

[4] bbbbc=bbcbb

Overlap of [3] bbcbbc=bb with [3] bbcbbc=bb:

bbc bbc bbcbbc

Critical pair: bbcbb=bbbbc.

Flip LHS and RHS.

Defines rule #1.