Certificate for #19288 ⟨a, b | aaa=a, baabb=ab⟩

Back:⟨a, b | aaa=a, baabb=ab⟩

Completion settings:

[1] aaa=a

Axiom: aaa=a.

Defines rule #1.

Referenced by [4], [5], [6], [7].

[2] baabb=ab

Axiom: baabb=ab.

Referenced by [3], [4], [5].

[3] baabab=aab

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

baab b baabb

Critical pair: baabab=abaabb.

Reduce RHS:

[2]a(baabb)
⇒ aab

Referenced by [4], [6], [7].

[4] baabaab=ab

Overlap of [2] baabb=ab with [3] baabab=aab:

baab b baabab

Critical pair: baabaab=abaabab.

Reduce RHS:

[3]a(baabab)
[1]⇒ (aaa)b
⇒ ab

Referenced by [5], [6].

[5] bab=abb

Overlap of [4] baabaab=ab with [2] baabb=ab:

baa baab baabb

Critical pair: baaab=abb.

Reduce LHS:

[1]b(aaa)b
⇒ bab

Defines rule #2.

Referenced by [6], [7].

[6] baab=aabb

Overlap of [4] baabaab=ab with [3] baabab=aab:

baa baab baabab

Critical pair: baaaab=abab.

Reduce LHS:

[1]b(aaa)ab
⇒ baab

Reduce RHS:

[5]a(bab)
⇒ aabb

Defines rule #4.

Referenced by [7].

[7] abbb=aab

Overlap of [3] baabab=aab with [6] baab=aabb:

baabab baab

Critical pair: aabbab=aab.

Reduce LHS:

[5]aab(bab)
[5]⇒ aa(bab)b
[1]⇒ (aaa)bbb
⇒ abbb

Defines rule #3.