Certificate for #5371 ⟨a, b, c | ab=a, bbcb=a⟩

Back:⟨a, b, c | ab=a, bbcb=a⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

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

[2] bbcb=a

Axiom: bbcb=a.

Defines rule #5.

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

[3] acb=aa

Overlap of [1] ab=a with [2] bbcb=a:

a b bbcb

Critical pair: aa=abcb.

Reduce RHS:

[1](ab)cb
⇒ acb

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5].

[4] bbca=aa

Overlap of [2] bbcb=a with [2] bbcb=a:

bbc b bbcb

Critical pair: bbca=abcb.

Reduce RHS:

[1](ab)cb
[3]⇒ (acb)
⇒ aa

Defines rule #4.

[5] aca=aaa

Overlap of [3] acb=aa with [2] bbcb=a:

ac b bbcb

Critical pair: aca=aabcb.

Reduce RHS:

[1]a(ab)cb
[3]⇒ a(acb)
⇒ aaa

Defines rule #2.