Certificate for #15433 ⟨a, b | aaa=aa, babab=a⟩

Back:⟨a, b | aaa=aa, babab=a⟩

Completion settings:

[1] aaa=aa

Axiom: aaa=aa.

Defines rule #1.

Referenced by [4], [6].

[2] babab=a

Axiom: babab=a.

Defines rule #6.

Referenced by [3], [6].

[3] baa=aab

Overlap of [2] babab=a with [2] babab=a:

ba bab babab

Critical pair: baa=aab.

Defines rule #2.

Referenced by [4], [5].

[4] aaba=aab

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

b aa aaa

Critical pair: baa=aaba.

Reduce LHS:

[3](baa)
⇒ aab

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [6].

[5] aabba=aabb

Overlap of [3] baa=aab with [4] aaba=aab:

b aa aaba

Critical pair: baab=aabba.

Reduce LHS:

[3](baa)b
⇒ aabb

Flip LHS and RHS.

Defines rule #4.

Referenced by [6].

[6] aabbb=aa

Overlap of [4] aaba=aab with [2] babab=a:

aa ba babab

Critical pair: aaa=aabbab.

Reduce LHS:

[1](aaa)
⇒ aa

Reduce RHS:

[5](aabba)b
⇒ aabbb

Flip LHS and RHS.

Defines rule #5.