Certificate for #16323 ⟨a, b | aab=bb, bbaa=ba⟩

Back:⟨a, b | aab=bb, bbaa=ba⟩

Completion settings:

[1] aab=bb

Axiom: aab=bb.

Defines rule #4.

Referenced by [3], [4].

[2] bbaa=ba

Axiom: bbaa=ba.

Referenced by [3], [4], [5], [6], [7].

[3] bab=bbbb

Overlap of [2] bbaa=ba with [1] aab=bb:

bb aa aab

Critical pair: bbbb=bab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4].

[4] bbbbbb=bbb

Overlap of [2] bbaa=ba with [1] aab=bb:

bba a aab

Critical pair: bbabb=baab.

Reduce LHS:

[3]b(bab)b
⇒ bbbbbb

Reduce RHS:

[1]b(aab)
⇒ bbb

Defines rule #1.

Referenced by [5].

[5] bbbbba=bba

Overlap of [4] bbbbbb=bbb with [2] bbaa=ba:

bbbb bb bbaa

Critical pair: bbbbba=bbbaa.

Reduce RHS:

[2]b(bbaa)
⇒ bba

Referenced by [6].

[6] bbbba=ba

Overlap of [5] bbbbba=bba with [2] bbaa=ba:

bbb bba bbaa

Critical pair: bbbba=bbaa.

Reduce RHS:

[2](bbaa)
⇒ ba

Defines rule #3.

Referenced by [7].

[7] baa=bbba

Overlap of [6] bbbba=ba with [2] bbaa=ba:

bb bba bbaa

Critical pair: bbba=baa.

Flip LHS and RHS.

Defines rule #5.