Certificate for #20885 ⟨a, b | bb=aa, aaaaa=ab⟩

Back:⟨a, b | bb=aa, aaaaa=ab⟩

Completion settings:

[1] bb=aa

Axiom: bb=aa.

Defines rule #4.

Referenced by [3], [4].

[2] ab=aaaaa

Axiom: aaaaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] baa=aaaaaa

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

b b bb

Critical pair: baa=aab.

Reduce RHS:

[2]a(ab)
⇒ aaaaaa

Defines rule #2.

[4] aaaaaaaaa=aaa

Overlap of [2] ab=aaaaa with [1] bb=aa:

a b bb

Critical pair: aaa=aaaaab.

Reduce RHS:

[2]aaaa(ab)
⇒ aaaaaaaaa

Flip LHS and RHS.

Defines rule #1.