Certificate for #5411 ⟨a, b | aab=bb, bab=ab⟩

Back:⟨a, b | aab=bb, bab=ab⟩

Completion settings:

[1] aab=bb

Axiom: aab=bb.

Defines rule #1.

Referenced by [3], [4].

[2] bab=ab

Axiom: bab=ab.

Defines rule #3.

Referenced by [3], [4].

[3] abb=ab

Overlap of [1] aab=bb with [2] bab=ab:

aa b bab

Critical pair: aaab=bbab.

Reduce LHS:

[1]a(aab)
⇒ abb

Reduce RHS:

[2]b(bab)
[2]⇒ (bab)
⇒ ab

Defines rule #2.

[4] bbb=bb

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

ba b bab

Critical pair: baab=abab.

Reduce LHS:

[1]b(aab)
⇒ bbb

Reduce RHS:

[2]a(bab)
[1]⇒ (aab)
⇒ bb

Defines rule #4.