Certificate for #16205 ⟨a, b | aab=ab, bbbb=aa⟩

Back:⟨a, b | aab=ab, bbbb=aa⟩

Completion settings:

[1] aab=ab

Axiom: aab=ab.

Referenced by [3], [4], [5].

[2] bbbb=aa

Axiom: bbbb=aa.

Defines rule #4.

Referenced by [3], [4].

[3] aaaa=aaa

Overlap of [1] aab=ab with [2] bbbb=aa:

aa b bbbb

Critical pair: aaaa=abbbb.

Reduce RHS:

[2]a(bbbb)
⇒ aaa

Defines rule #1.

Referenced by [5].

[4] ab=baa

Overlap of [2] bbbb=aa with [2] bbbb=aa:

b bbb bbbb

Critical pair: baa=aab.

Reduce RHS:

[1](aab)
⇒ ab

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] baaa=baa

Overlap of [3] aaaa=aaa with [4] ab=baa:

aaa a ab

Critical pair: aaabaa=aaab.

Reduce LHS:

[1]a(aab)aa
[1]⇒ (aab)aa
[4]⇒ (ab)aa
[3]⇒ b(aaaa)
⇒ baaa

Reduce RHS:

[1]a(aab)
[1]⇒ (aab)
[4]⇒ (ab)
⇒ baa

Defines rule #2.