Certificate for #6552 ⟨a, b | aaa=a, baab=aa⟩

Back:⟨a, b | aaa=a, baab=aa⟩

Completion settings:

[1] aaa=a

Axiom: aaa=a.

Defines rule #1.

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

[2] baab=aa

Axiom: baab=aa.

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

[3] baa=aab

Overlap of [2] baab=aa with [2] baab=aa:

baa b baab

Critical pair: baaaa=aaaab.

Reduce LHS:

[1]b(aaa)a
⇒ baa

Reduce RHS:

[1](aaa)ab
⇒ aab

Defines rule #3.

Referenced by [4], [5].

[4] aabb=aa

Overlap of [2] baab=aa with [3] baa=aab:

baab baa

Critical pair: aabb=aa.

Referenced by [7].

[5] aaba=ba

Overlap of [3] baa=aab with [1] aaa=a:

b aa aaa

Critical pair: ba=aaba.

Flip LHS and RHS.

Defines rule #5.

Referenced by [6].

[6] bba=a

Overlap of [2] baab=aa with [5] aaba=ba:

b aab aaba

Critical pair: bba=aaa.

Reduce RHS:

[1](aaa)
⇒ a

Defines rule #4.

[7] abb=a

Overlap of [1] aaa=a with [4] aabb=aa:

a aa aabb

Critical pair: aaa=abb.

Reduce LHS:

[1](aaa)
⇒ a

Flip LHS and RHS.

Defines rule #2.