Certificate for #16067 ⟨a, b | aaa=bb, abbb=aa⟩

Back:⟨a, b | aaa=bb, abbb=aa⟩

Completion settings:

[1] aaa=bb

Axiom: aaa=bb.

Referenced by [3].

[2] aa=abbb

Axiom: abbb=aa.

Flip LHS and RHS.

Referenced by [3], [4], [5], [6], [9].

[3] abbba=bb

Overlap of [1] aaa=bb with [2] aa=abbb:

aaa aa

Critical pair: abbba=bb.

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

[4] abbbbbb=bb

Overlap of [2] aa=abbb with [2] aa=abbb:

a a aa

Critical pair: aabbb=abbba.

Reduce LHS:

[2](aa)bbb
⇒ abbbbbb

Reduce RHS:

[3](abbba)
⇒ bb

Referenced by [5].

[5] bba=abb

Overlap of [2] aa=abbb with [3] abbba=bb:

a a abbba

Critical pair: abb=abbbbbba.

Reduce RHS:

[4](abbbbbb)a
⇒ bba

Flip LHS and RHS.

Referenced by [6], [7].

[6] abb=bbbbb

Overlap of [3] abbba=bb with [2] aa=abbb:

abbb a aa

Critical pair: abbbabbb=bba.

Reduce LHS:

[3](abbba)bbb
⇒ bbbbb

Reduce RHS:

[5](bba)
⇒ abb

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [8], [9].

[7] bba=bbbbb

Simplify [5] bba=abb.

Reduce RHS:

[6](abb)
⇒ bbbbb

Defines rule #3.

Referenced by [8].

[8] bbbbbbbbb=bb

Overlap of [3] abbba=bb with [6] abb=bbbbb:

abbba abb

Critical pair: bbbbbba=bb.

Reduce LHS:

[7]bbbb(bba)
⇒ bbbbbbbbb

Defines rule #1.

[9] aa=bbbbbb

Simplify [2] aa=abbb.

Reduce RHS:

[6](abb)b
⇒ bbbbbb

Defines rule #4.