Certificate for #15835 ⟨a, b | aba=aa, babbb=a⟩

Back:⟨a, b | aba=aa, babbb=a⟩

Completion settings:

[1] aba=aa

Axiom: aba=aa.

Defines rule #1.

Referenced by [3], [6].

[2] babbb=a

Axiom: babbb=a.

Defines rule #6.

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

[3] aabbb=aa

Overlap of [1] aba=aa with [2] babbb=a:

a ba babbb

Critical pair: aa=aabbb.

Flip LHS and RHS.

Defines rule #4.

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

[4] babba=aa

Overlap of [2] babbb=a with [2] babbb=a:

babb b babbb

Critical pair: babba=aabbb.

Reduce RHS:

[3](aabbb)
⇒ aa

Defines rule #5.

Referenced by [6].

[5] aabba=aaa

Overlap of [3] aabbb=aa with [2] babbb=a:

aabb b babbb

Critical pair: aabba=aaabbb.

Reduce RHS:

[3]a(aabbb)
⇒ aaa

Defines rule #3.

[6] baa=aa

Overlap of [4] babba=aa with [2] babbb=a:

bab ba babbb

Critical pair: baba=aabbb.

Reduce LHS:

[1]b(aba)
⇒ baa

Reduce RHS:

[3](aabbb)
⇒ aa

Defines rule #2.