Certificate for #4690 ⟨a, b | aaab=b, baba=b⟩

Back:⟨a, b | aaab=b, baba=b⟩

Completion settings:

[1] aaab=b

Axiom: aaab=b.

Defines rule #3.

Referenced by [4], [5].

[2] baba=b

Axiom: baba=b.

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

[3] bab=bba

Overlap of [2] baba=b with [2] baba=b:

ba ba baba

Critical pair: bab=bba.

Referenced by [4], [5].

[4] bbaa=b

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

aaa b baba

Critical pair: aaab=baba.

Reduce LHS:

[1](aaab)
⇒ b

Reduce RHS:

[3](bab)a
⇒ bbaa

Flip LHS and RHS.

Referenced by [5], [6].

[5] bba=bbb

Overlap of [4] bbaa=b with [1] aaab=b:

bb aa aaab

Critical pair: bbb=bab.

Reduce RHS:

[3](bab)
⇒ bba

Flip LHS and RHS.

Referenced by [6], [7].

[6] bbbb=b

Overlap of [4] bbaa=b with [5] bba=bbb:

bbaa bba

Critical pair: bbba=b.

Reduce LHS:

[5]b(bba)
⇒ bbbb

Defines rule #2.

Referenced by [7].

[7] ba=bb

Overlap of [5] bba=bbb with [2] baba=b:

b ba baba

Critical pair: bb=bbbba.

Reduce RHS:

[6](bbbb)a
⇒ ba

Flip LHS and RHS.

Defines rule #1.