Certificate for #591 ⟨a, b | aab=a, bba=b⟩

Back:⟨a, b | aab=a, bba=b⟩

Completion settings:

[1] aab=a

Axiom: aab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bba=b

Axiom: bba=b.

Defines rule #4.

Referenced by [3], [4].

[3] aba=a

Overlap of [1] aab=a with [2] bba=b:

aa b bba

Critical pair: aab=aba.

Reduce LHS:

[1](aab)
⇒ a

Flip LHS and RHS.

Defines rule #2.

[4] bab=b

Overlap of [2] bba=b with [1] aab=a:

bb a aab

Critical pair: bba=bab.

Reduce LHS:

[2](bba)
⇒ b

Flip LHS and RHS.

Defines rule #3.