Certificate for #2099 ⟨a, b | aba=a, baab=b

Completion settings:

[1] aba=a

Axiom: aba=a.

Defines rule #2.

Referenced by [3], [4].

[2] baab=b

Axiom: baab=b.

Referenced by [3], [5].

[3] aab=ab

Overlap of [1] aba=a with [2] baab=b:

a ba baab

Critical pair: ab=aab.

Flip LHS and RHS.

Referenced by [4].

[4] aa=a

Overlap of [3] aab=ab with [1] aba=a:

a ab aba

Critical pair: aa=aba.

Reduce RHS:

[1](aba)
a

Defines rule #1.

Referenced by [5].

[5] bab=b

Overlap of [2] baab=b with [4] aa=a:

b aab aa

Critical pair: bab=b.

Defines rule #3.