Certificate for #13133 ⟨a, b | aab=aaa, bab=ab⟩

Back:⟨a, b | aab=aaa, bab=ab⟩

Completion settings:

[1] aab=aaa

Axiom: aab=aaa.

Defines rule #1.

Referenced by [3], [4].

[2] bab=ab

Axiom: bab=ab.

Defines rule #2.

Referenced by [3], [4].

[3] baaa=aaa

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

ba b bab

Critical pair: baab=abab.

Reduce LHS:

[1]b(aab)
⇒ baaa

Reduce RHS:

[2]a(bab)
[1]⇒ (aab)
⇒ aaa

Defines rule #3.

[4] aaaaa=aaaa

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

aa b bab

Critical pair: aaab=aaaab.

Reduce LHS:

[1]a(aab)
⇒ aaaa

Reduce RHS:

[1]aa(aab)
⇒ aaaaa

Flip LHS and RHS.

Defines rule #4.