Certificate for #5334 ⟨a, b | aaa=ab, bba=bb⟩

Back:⟨a, b | aaa=ab, bba=bb⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[2] bba=bb

Axiom: bba=bb.

Defines rule #3.

Referenced by [3], [4].

[3] aaaaaa=aaaaa

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

a b bba

Critical pair: abb=aaaba.

Reduce LHS:

[1](ab)b
[1]⇒ aa(ab)
⇒ aaaaa

Reduce RHS:

[1]aa(ab)a
⇒ aaaaaa

Flip LHS and RHS.

Defines rule #1.

[4] bbb=bb

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

bb a ab

Critical pair: bbaaa=bbb.

Reduce LHS:

[2](bba)aa
[2]⇒ (bba)a
[2]⇒ (bba)
⇒ bb

Flip LHS and RHS.

Defines rule #4.