Certificate for #7104 ⟨a, b | ab=aa, bbaa=ba

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3].

[2] bbaa=ba

Axiom: bbaa=ba.

Referenced by [3], [4], [5], [6].

[3] aaaaa=aaa

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

a b bbaa

Critical pair: aba=aabaa.

Reduce LHS:

[1](ab)a
aaa

Reduce RHS:

[1]a(ab)aa
aaaaa

Flip LHS and RHS.

Defines rule #4.

Referenced by [4].

[4] baaaa=baa

Overlap of [2] bbaa=ba with [3] aaaaa=aaa:

bb aa aaaaa

Critical pair: bbaaa=baaaa.

Reduce LHS:

[2](bbaa)a
baa

Flip LHS and RHS.

Referenced by [5].

[5] baaa=ba

Overlap of [2] bbaa=ba with [4] baaaa=baa:

b baa baaaa

Critical pair: bbaa=baaa.

Reduce LHS:

[2](bbaa)
ba

Flip LHS and RHS.

Defines rule #3.

Referenced by [6].

[6] bba=baa

Overlap of [2] bbaa=ba with [5] baaa=ba:

b baa baaa

Critical pair: bba=baa.

Defines rule #2.