Certificate for #5394 ⟨a, b | aab=ba, abb=aa⟩

Back:⟨a, b | aab=ba, abb=aa⟩

Completion settings:

[1] ba=aab

Axiom: aab=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[2] abb=aa

Axiom: abb=aa.

Defines rule #3.

Referenced by [3], [4].

[3] aaaab=aaab

Overlap of [1] ba=aab with [2] abb=aa:

b a abb

Critical pair: baa=aabbb.

Reduce LHS:

[1](ba)a
[1]⇒ aa(ba)
⇒ aaaab

Reduce RHS:

[2]a(abb)b
⇒ aaab

Referenced by [4].

[4] aaaa=aaa

Overlap of [2] abb=aa with [1] ba=aab:

ab b ba

Critical pair: abaab=aaa.

Reduce LHS:

[1]a(ba)ab
[1]⇒ aaa(ba)b
[3]⇒ a(aaaab)b
[3]⇒ (aaaab)b
[2]⇒ aa(abb)
⇒ aaaa

Defines rule #1.