Certificate for #7147 ⟨a, b | bb=aa, aaba=ba⟩

Back:⟨a, b | bb=aa, aaba=ba⟩

Completion settings:

[1] bb=aa

Axiom: bb=aa.

Defines rule #1.

Referenced by [3], [5].

[2] aaba=ba

Axiom: aaba=ba.

Defines rule #3.

Referenced by [4], [5].

[3] baa=aab

Overlap of [1] bb=aa with [1] bb=aa:

b b bb

Critical pair: baa=aab.

Defines rule #2.

Referenced by [4], [5].

[4] aaaab=aab

Overlap of [2] aaba=ba with [3] baa=aab:

aa ba baa

Critical pair: aaaab=baa.

Reduce RHS:

[3](baa)
⇒ aab

Defines rule #5.

[5] aaaaa=aaa

Overlap of [3] baa=aab with [2] aaba=ba:

b aa aaba

Critical pair: bba=aabba.

Reduce LHS:

[1](bb)a
⇒ aaa

Reduce RHS:

[1]aa(bb)a
⇒ aaaaa

Flip LHS and RHS.

Defines rule #4.