Certificate for #13500 ⟨a, b | aaabb=1, bbbbbb=1⟩

Completion settings:

[1] aaabb=1

Axiom: aaabb=1.

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

[2] bbbbbb=1

Axiom: bbbbbb=1.

Referenced by [3].

[3] bbbb=aaa

Overlap of [1] aaabb=1 with [2] bbbbbb=1:

aaa bb bbbbbb

Critical pair: aaa=bbbb.

Flip LHS and RHS.

Referenced by [4], [5].

[4] bb=aaaaaa

Overlap of [1] aaabb=1 with [3] bbbb=aaa:

aaa bb bbbb

Critical pair: aaaaaa=bb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [6].

[5] aaab=baaa

Overlap of [3] bbbb=aaa with [3] bbbb=aaa:

b bbb bbbb

Critical pair: baaa=aaab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [6].

[6] aaaaaaaaa=1

Overlap of [1] aaabb=1 with [5] aaab=baaa:

aaabb aaab

Critical pair: baaab=1.

Reduce LHS:

[5]b(aaab)
[4](bb)aaa
aaaaaaaaa

Defines rule #1.