Certificate for #268 ⟨a, b | ab=a, baa=b⟩

Back:⟨a, b | ab=a, baa=b⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] baa=b

Axiom: baa=b.

Defines rule #4.

Referenced by [3], [4].

[3] aaa=a

Overlap of [1] ab=a with [2] baa=b:

a b baa

Critical pair: ab=aaa.

Reduce LHS:

[1](ab)
⇒ a

Flip LHS and RHS.

Defines rule #3.

[4] bb=b

Overlap of [2] baa=b with [1] ab=a:

ba a ab

Critical pair: baa=bb.

Reduce LHS:

[2](baa)
⇒ b

Flip LHS and RHS.

Defines rule #2.