Certificate for #15587 ⟨a, b | aab=aa, babab=a⟩

Back:⟨a, b | aab=aa, babab=a⟩

Completion settings:

[1] aab=aa

Axiom: aab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] babab=a

Axiom: babab=a.

Defines rule #4.

Referenced by [3], [4].

[3] aaaa=aaa

Overlap of [1] aab=aa with [2] babab=a:

aa b babab

Critical pair: aaa=aaabab.

Reduce RHS:

[1]a(aab)ab
[1]⇒ aa(aab)
⇒ aaaa

Flip LHS and RHS.

Defines rule #3.

[4] baa=aa

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

ba bab babab

Critical pair: baa=aab.

Reduce RHS:

[1](aab)
⇒ aa

Defines rule #2.