Certificate for #19830 ⟨a, b | aaa=a, baab=aba⟩

Back:⟨a, b | aaa=a, baab=aba⟩

Completion settings:

[1] aaa=a

Axiom: aaa=a.

Defines rule #1.

Referenced by [3], [4].

[2] baab=aba

Axiom: baab=aba.

Defines rule #2.

Referenced by [3], [4].

[3] baba=abab

Overlap of [2] baab=aba with [2] baab=aba:

baa b baab

Critical pair: baaaba=abaaab.

Reduce LHS:

[1]b(aaa)ba
⇒ baba

Reduce RHS:

[1]ab(aaa)b
⇒ abab

Defines rule #3.

Referenced by [4].

[4] ababb=aabaa

Overlap of [2] baab=aba with [3] baba=abab:

baa b baba

Critical pair: baaabab=abaaba.

Reduce LHS:

[1]b(aaa)bab
[3]⇒ (baba)b
⇒ ababb

Reduce RHS:

[2]a(baab)a
⇒ aabaa

Defines rule #4.