Certificate for #20818 ⟨a, b | ab=aa, bbaaa=ba⟩

Back:⟨a, b | ab=aa, bbaaa=ba⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3].

[2] bbaaa=ba

Axiom: bbaaa=ba.

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

[3] aaaaaa=aaa

Overlap of [1] ab=aa with [2] bbaaa=ba:

a b bbaaa

Critical pair: aba=aabaaa.

Reduce LHS:

[1](ab)a
⇒ aaa

Reduce RHS:

[1]a(ab)aaa
⇒ aaaaaa

Flip LHS and RHS.

Defines rule #4.

Referenced by [4].

[4] baaaa=ba

Overlap of [2] bbaaa=ba with [3] aaaaaa=aaa:

bb aaa aaaaaa

Critical pair: bbaaa=baaaa.

Reduce LHS:

[2](bbaaa)
⇒ ba

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] bba=baa

Overlap of [2] bbaaa=ba with [4] baaaa=ba:

b baaa baaaa

Critical pair: bba=baa.

Defines rule #2.