Certificate for #16441 ⟨a, b | aba=bb, aaab=ab⟩

Completion settings:

Reduction order:
- Left-to-right shortlex with a < b

[1] aba=bb

Axiom: aba=bb.

Defines rule #1.

Referenced by [3], [4], [5], [6], [7], [8].

[2] aaab=ab

Axiom: aaab=ab.

Defines rule #2.

Referenced by [4], [5].

[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 #4.

Referenced by [7], [8].

[4] bbaab=bbb

Overlap of [1] aba=bb with [2] aaab=ab:

ab a aaab

Critical pair: abab=bbaab.

Reduce LHS:

[1]	(aba)b
	⇒ bbb

Flip LHS and RHS.

Defines rule #5.

[5] aabb=bb

Overlap of [2] aaab=ab with [1] aba=bb:

aa ab aba

Critical pair: aabb=aba.

Reduce RHS:

[1]	(aba)
	⇒ bb

Defines rule #3.

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

[6] bbabb=abbb

Overlap of [1] aba=bb with [5] aabb=bb:

ab a aabb

Critical pair: abbb=bbabb.

Flip LHS and RHS.

Defines rule #6.

Referenced by [8].

[7] abbbbb=babbb

Overlap of [5] 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 #7.

Referenced by [8].

[8] bbbbbbb=bbbb

Overlap of [6] bbabb=abbb with [3] bbba=abbb:

bbab b bbba

Critical pair: bbababbb=abbbbba.

Reduce LHS:

[1]	bb(aba)bbb
	⇒ bbbbbbb

Reduce RHS:

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

Defines rule #8.