Certificate for #996 ⟨a, b | abbaaab=bb⟩

Back:⟨a, b | abbaaab=bb⟩

Completion settings:

[1] abbaaab=bb

Axiom: abbaaab=bb.

Referenced by [3].

[2] aaab=c

Axiom: aaab=c.

Defines rule #6.

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

[3] abbc=bb

Overlap of [1] abbaaab=bb with [2] aaab=c:

abb aaab aaab

Critical pair: abbc=bb.

Referenced by [4], [6], [7], [8].

[4] aabb=cbc

Overlap of [2] aaab=c with [3] abbc=bb:

aa ab abbc

Critical pair: aabb=cbc.

Referenced by [5], [6].

[5] acbc=cb

Overlap of [2] aaab=c with [4] aabb=cbc:

a aab aabb

Critical pair: acbc=cb.

Defines rule #4.

Referenced by [9].

[6] abb=cbcc

Overlap of [4] aabb=cbc with [3] abbc=bb:

a abb abbc

Critical pair: abb=cbcc.

Defines rule #3.

Referenced by [7], [8].

[7] cbccc=bb

Overlap of [3] abbc=bb with [6] abb=cbcc:

abbc abb

Critical pair: cbccc=bb.

Defines rule #1.

Referenced by [8], [9].

[8] cbccbb=bbbccc

Overlap of [3] abbc=bb with [7] cbccc=bb:

abb c cbccc

Critical pair: abbbb=bbbccc.

Reduce LHS:

[6](abb)bb
⇒ cbccbb

Defines rule #2.

[9] acbbb=cbbccc

Overlap of [5] acbc=cb with [7] cbccc=bb:

acb c cbccc

Critical pair: acbbb=cbbccc.

Defines rule #5.