Certificate for #6268 ⟨a, b, c | aa=1, bcbbcb=1⟩

Back:⟨a, b, c | aa=1, bcbbcb=1⟩

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #1.

[2] bcbbcb=1

Axiom: bcbbcb=1.

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

[3] cbbcb=bcbbc

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

bcbbc b bcbbcb

Critical pair: bcbbc=cbbcb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4].

[4] cbbbcbbc=cb

Overlap of [3] cbbcb=bcbbc with [3] cbbcb=bcbbc:

cbb cb cbbcb

Critical pair: cbbbcbbc=bcbbcbcb.

Reduce RHS:

[2](bcbbcb)cb
⇒ cb

Referenced by [5].

[5] bbcbbc=1

Overlap of [2] bcbbcb=1 with [4] cbbbcbbc=cb:

bcbb cb cbbbcbbc

Critical pair: bcbbcb=bbcbbc.

Reduce LHS:

[2](bcbbcb)
⇒ 1

Flip LHS and RHS.

Defines rule #3.