Certificate for #4694 ⟨a, b | aaab=b, bbaa=b⟩

Back:⟨a, b | aaab=b, bbaa=b⟩

Completion settings:

[1] aaab=b

Axiom: aaab=b.

Defines rule #4.

Referenced by [3], [4].

[2] bbaa=b

Axiom: bbaa=b.

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

[3] bab=bbb

Overlap of [2] bbaa=b with [1] aaab=b:

bb aa aaab

Critical pair: bbb=bab.

Flip LHS and RHS.

Defines rule #1.

Referenced by [4].

[4] baab=bbbb

Overlap of [2] bbaa=b with [1] aaab=b:

bba a aaab

Critical pair: bbab=baab.

Reduce LHS:

[3]b(bab)
⇒ bbbb

Flip LHS and RHS.

Referenced by [5], [6].

[5] bbbbb=bb

Overlap of [2] bbaa=b with [4] baab=bbbb:

b baa baab

Critical pair: bbbbb=bb.

Referenced by [6].

[6] bbbb=b

Overlap of [4] baab=bbbb with [2] bbaa=b:

baa b bbaa

Critical pair: baab=bbbbbaa.

Reduce LHS:

[4](baab)
⇒ bbbb

Reduce RHS:

[5](bbbbb)aa
[2]⇒ (bbaa)
⇒ b

Defines rule #3.

Referenced by [7].

[7] baa=bbb

Overlap of [6] bbbb=b with [2] bbaa=b:

bb bb bbaa

Critical pair: bbb=baa.

Flip LHS and RHS.

Defines rule #2.