Certificate for #25600 ⟨a, b | ab=a, bbaaa=baa⟩

Back:⟨a, b | ab=a, bbaaa=baa⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3].

[2] bbaaa=baa

Axiom: bbaaa=baa.

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

[3] aaaa=aaa

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

a b bbaaa

Critical pair: abaa=abaaa.

Reduce LHS:

[1](ab)aa
⇒ aaa

Reduce RHS:

[1](ab)aaa
⇒ aaaa

Flip LHS and RHS.

Defines rule #2.

Referenced by [4].

[4] baaa=baa

Overlap of [2] bbaaa=baa with [3] aaaa=aaa:

bb aaa aaaa

Critical pair: bbaaa=baaa.

Reduce LHS:

[2](bbaaa)
⇒ baa

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] bbaa=baa

Overlap of [2] bbaaa=baa with [4] baaa=baa:

b baaa baaa

Critical pair: bbaa=baa.

Defines rule #4.