Certificate for #1813 ⟨a, b | abbbaaaab=a⟩

Back:⟨a, b | abbbaaaab=a⟩

Completion settings:

[1] abbbaaaab=a

Axiom: abbbaaaab=a.

Defines rule #4.

Referenced by [2], [3], [4].

[2] abbaaaab=abbbaaaa

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

abbbaaa ab abbbaaaab

Critical pair: abbbaaaa=abbaaaab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] abaaaab=abbaaaa

Overlap of [1] abbbaaaab=a with [2] abbaaaab=abbbaaaa:

abbbaaa ab abbaaaab

Critical pair: abbbaaaabbbaaaa=abaaaab.

Reduce LHS:

[1](abbbaaaab)bbaaaa
⇒ abbaaaa

Flip LHS and RHS.

Defines rule #2.

[4] aaaaab=abaaaa

Overlap of [2] abbaaaab=abbbaaaa with [2] abbaaaab=abbbaaaa:

abbaaa ab abbaaaab

Critical pair: abbaaaabbbaaaa=abbbaaaabaaaab.

Reduce LHS:

[2](abbaaaab)bbaaaa
[1]⇒ (abbbaaaab)baaaa
⇒ abaaaa

Reduce RHS:

[1](abbbaaaab)aaaab
⇒ aaaaab

Flip LHS and RHS.

Defines rule #1.