Certificate for #12195 ⟨a, b | aaaa=ab, bbbb=b⟩

Back:⟨a, b | aaaa=ab, bbbb=b⟩

Completion settings:

[1] ab=aaaa

Axiom: aaaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3].

[2] bbbb=b

Axiom: bbbb=b.

Defines rule #3.

Referenced by [3].

[3] aaaaaaaaaaaaa=aaaa

Overlap of [1] ab=aaaa with [2] bbbb=b:

a b bbbb

Critical pair: ab=aaaabbb.

Reduce LHS:

[1](ab)
⇒ aaaa

Reduce RHS:

[1]aaa(ab)bb
[1]⇒ aaaaaa(ab)b
[1]⇒ aaaaaaaaa(ab)
⇒ aaaaaaaaaaaaa

Flip LHS and RHS.

Defines rule #1.