Certificate for #16429 ⟨a, b | aba=ab, bbba=aa⟩

Back:⟨a, b | aba=ab, bbba=aa⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Defines rule #2.

Referenced by [3], [4], [5], [6].

[2] bbba=aa

Axiom: bbba=aa.

Defines rule #6.

Referenced by [4], [7].

[3] abba=abb

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

ab a aba

Critical pair: abab=abba.

Reduce LHS:

[1](aba)b
⇒ abb

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5].

[4] abbb=aaa

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

ab a abba

Critical pair: ababb=abbba.

Reduce LHS:

[1](aba)bb
⇒ abbb

Reduce RHS:

[2]a(bbba)
⇒ aaa

Defines rule #5.

Referenced by [5], [6].

[5] aaaa=aaa

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

abb a aba

Critical pair: abbab=abbba.

Reduce LHS:

[3](abba)b
[4]⇒ (abbb)
⇒ aaa

Reduce RHS:

[4](abbb)a
⇒ aaaa

Flip LHS and RHS.

Defines rule #3.

Referenced by [7].

[6] aaab=ab

Overlap of [1] aba=ab with [4] abbb=aaa:

ab a abbb

Critical pair: abaaa=abbbb.

Reduce LHS:

[1](aba)aa
[1]⇒ (aba)a
[1]⇒ (aba)
⇒ ab

Reduce RHS:

[4](abbb)b
⇒ aaab

Flip LHS and RHS.

Referenced by [7].

[7] aab=ab

Overlap of [2] bbba=aa with [6] aaab=ab:

bbb a aaab

Critical pair: bbbab=aaaab.

Reduce LHS:

[2](bbba)b
⇒ aab

Reduce RHS:

[5](aaaa)b
[6]⇒ (aaab)
⇒ ab

Defines rule #1.