Certificate for #16451 ⟨a, b | aba=bb, aabb=bb⟩

Back:⟨a, b | aba=bb, aabb=bb⟩

Completion settings:

[1] aba=bb

Axiom: aba=bb.

Defines rule #1.

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

[2] aabb=bb

Axiom: aabb=bb.

Defines rule #2.

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

[3] bbba=abbb

Overlap of [1] aba=bb with [1] aba=bb:

ab a aba

Critical pair: abbb=bbba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [6].

[4] bbabb=abbb

Overlap of [1] aba=bb with [2] aabb=bb:

ab a aabb

Critical pair: abbb=bbabb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [6].

[5] abbbbb=babbb

Overlap of [2] aabb=bb with [3] bbba=abbb:

aab b bbba

Critical pair: aababbb=bbbba.

Reduce LHS:

[1]a(aba)bbb
⇒ abbbbb

Reduce RHS:

[3]b(bbba)
⇒ babbb

Defines rule #5.

Referenced by [6].

[6] bbbbbbb=bbbb

Overlap of [4] bbabb=abbb with [3] bbba=abbb:

bbab b bbba

Critical pair: bbababbb=abbbbba.

Reduce LHS:

[1]bb(aba)bbb
⇒ bbbbbbb

Reduce RHS:

[5](abbbbb)a
[3]⇒ ba(bbba)
[2]⇒ b(aabb)b
⇒ bbbb

Defines rule #6.