Certificate for #1988 ⟨a, b | aaa=a, abab=a

Completion settings:

[1] aaa=a

Axiom: aaa=a.

Defines rule #1.

Referenced by [4].

[2] abab=a

Axiom: abab=a.

Referenced by [3], [4].

[3] aba=aab

Overlap of [2] abab=a with [2] abab=a:

ab ab abab

Critical pair: aba=aab.

Defines rule #2.

Referenced by [4].

[4] abb=aa

Overlap of [2] abab=a with [3] aba=aab:

ab ab aba

Critical pair: abaab=aa.

Reduce LHS:

[3](aba)ab
[3]a(aba)b
[1](aaa)bb
abb

Defines rule #3.