Certificate for #16422 ⟨a, b | aba=ab, bbaa=ab⟩

Back:⟨a, b | aba=ab, bbaa=ab⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Defines rule #1.

Referenced by [3], [5].

[2] bbaa=ab

Axiom: bbaa=ab.

Defines rule #4.

Referenced by [4].

[3] abba=abb

Overlap of [1] aba=ab with [1] aba=ab:

ab a aba

Critical pair: abab=abba.

Reduce LHS:

[1](aba)b
⇒ abb

Flip LHS and RHS.

Referenced by [4].

[4] abb=aab

Overlap of [3] abba=abb with [2] bbaa=ab:

a bba bbaa

Critical pair: aab=abba.

Reduce RHS:

[3](abba)
⇒ abb

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] aaab=aab

Overlap of [1] aba=ab with [4] abb=aab:

ab a abb

Critical pair: abaab=abbb.

Reduce LHS:

[1](aba)ab
[1]⇒ (aba)b
[4]⇒ (abb)
⇒ aab

Reduce RHS:

[4](abb)b
[4]⇒ a(abb)
⇒ aaab

Flip LHS and RHS.

Defines rule #3.