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

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(b) = 0; deg(a) = 1

Axiom: aaa=a.

Defines rule #6.

Referenced by [3].

Axiom: abbba=ab.

Defines rule #4.

Referenced by [3], [4], [5], [6], [8].

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

Critical pair: abbba=abaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [5].

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

Critical pair: abbbab=abbbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [7], [8].

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

Critical pair: abbbab=abbaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [7], [8].

Overlap of [2] abbba=ab with [5] abbaa=abb:

Critical pair: abbbabb=abbbaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

Overlap of [5] abbaa=abb with [5] abbaa=abb:

Critical pair: abbaabb=abbbbaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [8].

Overlap of [5] abbaa=abb with [6] aba=abbb:

Critical pair: abbaabbb=abbba.

Reduce LHS:

Reduce RHS:

Defines rule #1.