Certificate for #20914 ⟨a, b | bb=aa, ababa=aa⟩

Back:⟨a, b | bb=aa, ababa=aa⟩

Completion settings:

[1] bb=aa

Axiom: bb=aa.

Defines rule #1.

Referenced by [3], [5].

[2] ababa=aa

Axiom: ababa=aa.

Defines rule #4.

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] aaba=aaab

Overlap of [2] ababa=aa with [2] ababa=aa:

ab aba ababa

Critical pair: abaa=aaba.

Reduce LHS:

[3]a(baa)
⇒ aaab

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] aaaaaa=aaa

Overlap of [2] ababa=aa with [3] baa=aab:

aba ba baa

Critical pair: abaaab=aaa.

Reduce LHS:

[3]a(baa)ab
[4]⇒ a(aaba)b
[1]⇒ aaaa(bb)
⇒ aaaaaa

Defines rule #5.