Certificate for #5305 ⟨a, b | aaa=aa, bab=aa⟩

Back:⟨a, b | aaa=aa, bab=aa⟩

Completion settings:

[1] aaa=aa

Axiom: aaa=aa.

Defines rule #1.

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

[2] bab=aa

Axiom: bab=aa.

Defines rule #3.

Referenced by [3], [5].

[3] baa=aab

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

ba b bab

Critical pair: baaa=aaab.

Reduce LHS:

[1]b(aaa)
⇒ baa

Reduce RHS:

[1](aaa)b
⇒ aab

Defines rule #2.

Referenced by [4].

[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 #4.

Referenced by [5].

[5] aabb=aa

Overlap of [4] aaba=aab with [2] bab=aa:

aa ba bab

Critical pair: aaaa=aabb.

Reduce LHS:

[1](aaa)a
[1]⇒ (aaa)
⇒ aa

Flip LHS and RHS.

Defines rule #5.