Certificate for #19278 ⟨a, b | aaa=a, abbba=ab⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #1.

Referenced by [3].

Axiom: abbba=ab.

Referenced by [3], [4], [5], [6], [7].

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

Critical pair: abbba=abaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [6], [7].

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

Critical pair: abbbab=abbaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [5], [8].

Overlap of [2] abbba=ab with [4] abbaa=abb:

Critical pair: abbbabb=abbbaa.

Reduce LHS:

Reduce RHS:

Defines rule #4.

Referenced by [6], [7].

Overlap of [2] abbba=ab with [5] abbb=aba:

Critical pair: abbbaba=abbbb.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [7], [8].

Overlap of [2] abbba=ab with [6] abba=abab:

Critical pair: abbbabab=abbba.

Reduce LHS:

Reduce RHS:

Defines rule #6.

Overlap of [4] abbaa=abb with [6] abba=abab:

Critical pair: ababa=abb.

Defines rule #5.