Certificate for #13936 ⟨a, b | aaab=a, bbbbbb=1⟩

Completion settings:

[1] aaab=a

Axiom: aaab=a.

Referenced by [3], [4], [5], [6], [7], [8].

[2] bbbbbb=1

Axiom: bbbbbb=1.

Defines rule #3.

Referenced by [3].

[3] abbbbb=aaa

Overlap of [1] aaab=a with [2] bbbbbb=1:

aaa b bbbbbb

Critical pair: aaa=abbbbb.

Flip LHS and RHS.

Referenced by [4].

[4] abbbb=aaaaa

Overlap of [1] aaab=a with [3] abbbbb=aaa:

aa ab abbbbb

Critical pair: aaaaa=abbbb.

Flip LHS and RHS.

Referenced by [5].

[5] abbb=aaaaaaa

Overlap of [1] aaab=a with [4] abbbb=aaaaa:

aa ab abbbb

Critical pair: aaaaaaa=abbb.

Flip LHS and RHS.

Referenced by [6].

[6] abb=aaaaaaaaa

Overlap of [1] aaab=a with [5] abbb=aaaaaaa:

aa ab abbb

Critical pair: aaaaaaaaa=abb.

Flip LHS and RHS.

Referenced by [7].

[7] ab=aaaaaaaaaaa

Overlap of [1] aaab=a with [6] abb=aaaaaaaaa:

aa ab abb

Critical pair: aaaaaaaaaaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

[8] aaaaaaaaaaaaa=a

Overlap of [1] aaab=a with [7] ab=aaaaaaaaaaa:

aa ab ab

Critical pair: aaaaaaaaaaaaa=a.

Defines rule #1.