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

Back:⟨a, b | aaabb=1, bbbbbb=1⟩

Completion settings:

[1] aaabb=1

Axiom: aaabb=1.

Referenced by [3], [5].

[2] bbbbbb=1

Axiom: bbbbbb=1.

Defines rule #1.

Referenced by [3], [5].

[3] aaa=bbbb

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

aaa bb bbbbbb

Critical pair: aaa=bbbb.

Defines rule #3.

Referenced by [4], [5].

[4] bbbba=abbbb

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

a aa aaa

Critical pair: abbbb=bbbba.

Flip LHS and RHS.

Referenced by [5].

[5] bba=abb

Overlap of [1] aaabb=1 with [4] bbbba=abbbb:

aaa bb bbbba

Critical pair: aaaabbbb=bba.

Reduce LHS:

[3](aaa)abbbb
[4]⇒ (bbbba)bbbb
[2]⇒ a(bbbbbb)bb
⇒ abb

Flip LHS and RHS.

Defines rule #2.