Certificate for #3368 ⟨a, b | aaaabaaaab=a⟩

Back:⟨a, b | aaaabaaaab=a⟩

Completion settings:

[1] aaaabaaaab=a

Axiom: aaaabaaaab=a.

Referenced by [2], [3].

[2] aaaaba=aaaaab

Overlap of [1] aaaabaaaab=a with [1] aaaabaaaab=a:

aaaab aaaab aaaabaaaab

Critical pair: aaaaba=aaaaab.

Defines rule #1.

Referenced by [3].

[3] aaaaaaaabb=a

Overlap of [1] aaaabaaaab=a with [2] aaaaba=aaaaab:

aaaabaaaab aaaaba

Critical pair: aaaaabaaab=a.

Reduce LHS:

[2]a(aaaaba)aab
[2]⇒ aa(aaaaba)ab
[2]⇒ aaa(aaaaba)b
⇒ aaaaaaaabb

Defines rule #2.