Certificate for #5419 ⟨a, b | aba=ab, bab=ab⟩

Back:⟨a, b | aba=ab, bab=ab⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Defines rule #1.

Referenced by [3], [4].

[2] bab=ab

Axiom: bab=ab.

Defines rule #3.

Referenced by [3], [5].

[3] abb=aab

Overlap of [1] aba=ab with [2] bab=ab:

a ba bab

Critical pair: aab=abb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5].

[4] aaab=aab

Overlap of [1] aba=ab with [3] abb=aab:

ab a abb

Critical pair: abaab=abbb.

Reduce LHS:

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

Reduce RHS:

[3](abb)b
[3]⇒ a(abb)
⇒ aaab

Flip LHS and RHS.

Defines rule #4.

[5] baab=aab

Overlap of [2] bab=ab with [3] abb=aab:

b ab abb

Critical pair: baab=abb.

Reduce RHS:

[3](abb)
⇒ aab

Defines rule #5.