Certificate for #16244 ⟨a, b | aab=ba, baaa=bb⟩

Back:⟨a, b | aab=ba, baaa=bb⟩

Completion settings:

[1] ba=aab

Axiom: aab=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [2], [3].

[2] bb=aaaaaab

Axiom: baaa=bb.

Reduce LHS:

[1](ba)aa
[1]⇒ aa(ba)a
[1]⇒ aaaa(ba)
⇒ aaaaaab

Flip LHS and RHS.

Defines rule #3.

Referenced by [3].

[3] aaaaaaaaaab=aaaaaaaab

Overlap of [2] bb=aaaaaab with [1] ba=aab:

b b ba

Critical pair: baab=aaaaaaba.

Reduce LHS:

[1](ba)ab
[1]⇒ aa(ba)b
[2]⇒ aaaa(bb)
⇒ aaaaaaaaaab

Reduce RHS:

[1]aaaaaa(ba)
⇒ aaaaaaaab

Defines rule #1.