Certificate for #20723 ⟨a, b | ab=aa, aaaaa=bb⟩

Back:⟨a, b | ab=aa, aaaaa=bb⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #3.

Referenced by [3], [4].

[2] bb=aaaaa

Axiom: aaaaa=bb.

Flip LHS and RHS.

Defines rule #4.

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

[3] aaaaaa=aaa

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

a b bb

Critical pair: aaaaaa=aab.

Reduce RHS:

[1]a(ab)
⇒ aaa

Defines rule #1.

Referenced by [4], [5].

[4] baaaaa=aaa

Overlap of [2] bb=aaaaa with [2] bb=aaaaa:

b b bb

Critical pair: baaaaa=aaaaab.

Reduce RHS:

[1]aaaa(ab)
[3]⇒ (aaaaaa)
⇒ aaa

Referenced by [5].

[5] baaa=aaaa

Overlap of [2] bb=aaaaa with [4] baaaaa=aaa:

b b baaaaa

Critical pair: baaa=aaaaaaaaaa.

Reduce RHS:

[3](aaaaaa)aaaa
[3]⇒ (aaaaaa)a
⇒ aaaa

Defines rule #2.