Certificate for #1615 ⟨a, b | aab=aa, baa=b⟩

Back:⟨a, b | aab=aa, baa=b⟩

Completion settings:

[1] aab=aa

Axiom: aab=aa.

Defines rule #2.

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

[2] baa=b

Axiom: baa=b.

Defines rule #3.

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

[3] aaaa=aa

Overlap of [1] aab=aa with [2] baa=b:

aa b baa

Critical pair: aab=aaaa.

Reduce LHS:

[1](aab)
⇒ aa

Flip LHS and RHS.

Defines rule #5.

[4] bb=b

Overlap of [2] baa=b with [1] aab=aa:

b aa aab

Critical pair: baa=bb.

Reduce LHS:

[2](baa)
⇒ b

Flip LHS and RHS.

Defines rule #1.

[5] bab=ba

Overlap of [2] baa=b with [1] aab=aa:

ba a aab

Critical pair: baaa=bab.

Reduce LHS:

[2](baa)a
⇒ ba

Flip LHS and RHS.

Defines rule #4.