Certificate for #19506 ⟨a, b | aab=b, aaaaa=ba⟩

Back:⟨a, b | aab=b, aaaaa=ba⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #3.

Referenced by [3], [4].

[2] ba=aaaaa

Axiom: aaaaa=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] aaaaaaa=aaaaa

Overlap of [1] aab=b with [2] ba=aaaaa:

aa b ba

Critical pair: aaaaaaa=ba.

Reduce RHS:

[2](ba)
⇒ aaaaa

Defines rule #1.

[4] bb=b

Overlap of [2] ba=aaaaa with [1] aab=b:

b a aab

Critical pair: bb=aaaaaab.

Reduce RHS:

[1]aaaa(aab)
[1]⇒ aa(aab)
[1]⇒ (aab)
⇒ b

Defines rule #4.