Certificate for #802 ⟨a, b, c | ab=a, bbcb=1⟩

Back:⟨a, b, c | ab=a, bbcb=1⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [5].

[2] bbcb=1

Axiom: bbcb=1.

Referenced by [3], [4], [5], [6], [7].

[3] acb=a

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

a b bbcb

Critical pair: a=abcb.

Reduce RHS:

[1](ab)cb
⇒ acb

Flip LHS and RHS.

Referenced by [5].

[4] bcb=bbc

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

bbc b bbcb

Critical pair: bbc=bcb.

Flip LHS and RHS.

Referenced by [6], [7].

[5] ac=a

Overlap of [3] acb=a with [2] bbcb=1:

ac b bbcb

Critical pair: ac=abcb.

Reduce RHS:

[1](ab)cb
[3]⇒ (acb)
⇒ a

Defines rule #2.

[6] cb=bc

Overlap of [2] bbcb=1 with [4] bcb=bbc:

bbc b bcb

Critical pair: bbcbbc=cb.

Reduce LHS:

[2](bbcb)bc
⇒ bc

Flip LHS and RHS.

Defines rule #3.

[7] bbbc=1

Overlap of [2] bbcb=1 with [4] bcb=bbc:

b bcb bcb

Critical pair: bbbc=1.

Defines rule #4.