Certificate for #6546 ⟨a, b | aaa=a, abba=ab⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with b < a

Axiom: aaa=a.

Defines rule #2.

Referenced by [3].

Axiom: abba=ab.

Defines rule #4.

Referenced by [3], [4], [5].

Overlap of [2] abba=ab with [1] aaa=a:

Critical pair: abba=abaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [4].

Overlap of [2] abba=ab with [3] abaa=ab:

Critical pair: abbab=abbaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [5].

Overlap of [2] abba=ab with [4] aba=abb:

Critical pair: abbabb=abba.

Reduce LHS:

Reduce RHS:

Defines rule #3.