Certificate for #5354 ⟨a, b | aab=aa, aba=ab⟩

Back:⟨a, b | aab=aa, aba=ab⟩

Completion settings:

[1] aab=aa

Axiom: aab=aa.

Defines rule #2.

Referenced by [3], [4].

[2] aba=ab

Axiom: aba=ab.

Defines rule #3.

Referenced by [3], [4].

[3] aaa=aa

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

a ab aba

Critical pair: aab=aaa.

Reduce LHS:

[1](aab)
⇒ aa

Flip LHS and RHS.

Defines rule #1.

[4] abb=ab

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

ab a aab

Critical pair: abaa=abab.

Reduce LHS:

[2](aba)a
[2]⇒ (aba)
⇒ ab

Reduce RHS:

[2](aba)b
⇒ abb

Flip LHS and RHS.

Defines rule #4.