Certificate for #13155 ⟨a, b | aba=aaa, bbb=aa⟩

Back:⟨a, b | aba=aaa, bbb=aa⟩

Completion settings:

[1] aba=aaa

Axiom: aba=aaa.

Defines rule #1.

Referenced by [4], [5].

[2] bbb=aa

Axiom: bbb=aa.

Defines rule #3.

Referenced by [3], [6].

[3] baa=aab

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

b bb bbb

Critical pair: baa=aab.

Defines rule #2.

Referenced by [4], [5].

[4] aaab=aaaa

Overlap of [1] aba=aaa with [3] baa=aab:

a ba baa

Critical pair: aaab=aaaa.

Defines rule #4.

Referenced by [6].

[5] aabba=aaaaa

Overlap of [3] baa=aab with [1] aba=aaa:

ba a aba

Critical pair: baaaa=aabba.

Reduce LHS:

[3](baa)aa
[1]⇒ a(aba)a
⇒ aaaaa

Flip LHS and RHS.

Defines rule #5.

[6] aaaaaa=aaaaa

Overlap of [4] aaab=aaaa with [2] bbb=aa:

aaa b bbb

Critical pair: aaaaa=aaaabb.

Reduce RHS:

[4]a(aaab)b
[4]⇒ aa(aaab)
⇒ aaaaaa

Flip LHS and RHS.

Defines rule #6.