Certificate for #63 ⟨a, b | ab=a, ba=b⟩

Back:⟨a, b | ab=a, ba=b⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #2.

Referenced by [3], [4].

[2] ba=b

Axiom: ba=b.

Defines rule #3.

Referenced by [3], [4].

[3] aa=a

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

a b ba

Critical pair: ab=aa.

Reduce LHS:

[1](ab)
⇒ a

Flip LHS and RHS.

Defines rule #1.

[4] bb=b

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

b a ab

Critical pair: ba=bb.

Reduce LHS:

[2](ba)
⇒ b

Flip LHS and RHS.

Defines rule #4.