Certificate for #8907 ⟨a, b | aa=a, bbabb=ab⟩

Back:⟨a, b | aa=a, bbabb=ab⟩

Completion settings:

[1] aa=a

Axiom: aa=a.

Defines rule #1.

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

[2] bbabb=ab

Axiom: bbabb=ab.

Referenced by [3], [4], [6], [7], [8].

[3] ababb=bbab

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

bba bb bbabb

Critical pair: bbaab=ababb.

Reduce LHS:

[1]bb(aa)b
⇒ bbab

Flip LHS and RHS.

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

[4] bbabab=ab

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

bbab b bbabb

Critical pair: bbabab=abbabb.

Reduce RHS:

[2]a(bbabb)
[1]⇒ (aa)b
⇒ ab

Referenced by [6].

[5] abbab=bbab

Overlap of [1] aa=a with [3] ababb=bbab:

a a ababb

Critical pair: abbab=ababb.

Reduce RHS:

[3](ababb)
⇒ bbab

Referenced by [7].

[6] abab=abb

Overlap of [3] ababb=bbab with [2] bbabb=ab:

aba bb bbabb

Critical pair: abaab=bbababb.

Reduce LHS:

[1]ab(aa)b
⇒ abab

Reduce RHS:

[4](bbabab)b
⇒ abb

Defines rule #2.

Referenced by [7].

[7] bbab=abbb

Overlap of [3] ababb=bbab with [2] bbabb=ab:

abab b bbabb

Critical pair: ababab=bbabbabb.

Reduce LHS:

[6](abab)ab
[5]⇒ (abbab)
⇒ bbab

Reduce RHS:

[2](bbabb)abb
[6]⇒ (abab)b
⇒ abbb

Defines rule #3.

Referenced by [8].

[8] abbbb=ab

Overlap of [2] bbabb=ab with [7] bbab=abbb:

bbabb bbab

Critical pair: abbbb=ab.

Defines rule #4.