Certificate for #16073 ⟨a, b | aaa=bb, baab=bb⟩

Completion settings:

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

[1] aaa=bb

Axiom: aaa=bb.

Defines rule #1.

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

[2] baab=bb

Axiom: baab=bb.

Defines rule #3.

Referenced by [4], [5].

[3] bba=abb

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

a aa aaa

Critical pair: abb=bba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5].

[4] aabbb=bbb

Overlap of [2] baab=bb with [2] baab=bb:

baa b baab

Critical pair: baabb=bbaab.

Reduce LHS:

[2]	(baab)b
	⇒ bbb

Reduce RHS:

[3]	(bba)ab
[3]	⇒ a(bba)b
	⇒ aabbb

Flip LHS and RHS.

Defines rule #5.

Referenced by [6].

[5] bbbbb=babb

Overlap of [2] baab=bb with [3] bba=abb:

baa b bba

Critical pair: baaabb=bbba.

Reduce LHS:

[1]	b(aaa)bb
	⇒ bbbbb

Reduce RHS:

[3]	b(bba)
	⇒ babb

Referenced by [6], [7].

[6] babb=abbb

Overlap of [1] aaa=bb with [4] aabbb=bbb:

a aa aabbb

Critical pair: abbb=bbbbb.

Reduce RHS:

[5]	(bbbbb)
	⇒ babb

Flip LHS and RHS.

Defines rule #4.

Referenced by [7].

[7] bbbbb=abbb

Simplify [5] bbbbb=babb.

Reduce RHS:

[6]	(babb)
	⇒ abbb

Defines rule #6.