Certificate for #2255 ⟨a, b | ab=aa, bba=bb⟩

Back:⟨a, b | ab=aa, bba=bb⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] bba=bb

Axiom: bba=bb.

Defines rule #2.

Referenced by [3], [4].

[3] aaaa=aaa

Overlap of [1] ab=aa with [2] bba=bb:

a b bba

Critical pair: abb=aaba.

Reduce LHS:

[1](ab)b
[1]⇒ a(ab)
⇒ aaa

Reduce RHS:

[1]a(ab)a
⇒ aaaa

Flip LHS and RHS.

Defines rule #4.

[4] bbb=bb

Overlap of [2] bba=bb with [1] ab=aa:

bb a ab

Critical pair: bbaa=bbb.

Reduce LHS:

[2](bba)a
[2]⇒ (bba)
⇒ bb

Flip LHS and RHS.

Defines rule #3.