Certificate for #6664 ⟨a, b | aab=b, aaaa=ba⟩

Back:⟨a, b | aab=b, aaaa=ba⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #3.

Referenced by [3], [4].

[2] ba=aaaa

Axiom: aaaa=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] aaaaaa=aaaa

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

aa b ba

Critical pair: aaaaaa=ba.

Reduce RHS:

[2](ba)
⇒ aaaa

Defines rule #1.

[4] bb=ab

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

b a aab

Critical pair: bb=aaaaab.

Reduce RHS:

[1]aaa(aab)
[1]⇒ a(aab)
⇒ ab

Defines rule #4.