Certificate for #16578 ⟨a, b | aaaa=1, aabaabb=1⟩

Back:⟨a, b | aaaa=1, aabaabb=1⟩

Completion settings:

[1] aaaa=1

Axiom: aaaa=1.

Defines rule #3.

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

[2] aabaabb=1

Axiom: aabaabb=1.

Referenced by [3].

[3] baabb=aa

Overlap of [1] aaaa=1 with [2] aabaabb=1:

aa aa aabaabb

Critical pair: aa=baabb.

Flip LHS and RHS.

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

[4] baabaa=bb

Overlap of [3] baabb=aa with [3] baabb=aa:

baab b baabb

Critical pair: baabaa=aaaabb.

Reduce RHS:

[1](aaaa)bb
⇒ bb

Referenced by [5].

[5] baa=aab

Overlap of [3] baabb=aa with [4] baabaa=bb:

baab b baabaa

Critical pair: baabbb=aaaabaa.

Reduce LHS:

[3](baabb)b
⇒ aab

Reduce RHS:

[1](aaaa)baa
⇒ baa

Flip LHS and RHS.

Defines rule #1.

Referenced by [6].

[6] aabbb=aa

Overlap of [3] baabb=aa with [5] baa=aab:

baabb baa

Critical pair: aabbb=aa.

Referenced by [7].

[7] bbb=1

Overlap of [1] aaaa=1 with [6] aabbb=aa:

aa aa aabbb

Critical pair: aaaa=bbb.

Reduce LHS:

[1](aaaa)
⇒ 1

Flip LHS and RHS.

Defines rule #2.