Certificate for #19255 ⟨a, b | aaa=a, aabba=ab⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #1.

Referenced by [3], [4].

Axiom: aabba=ab.

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

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

Critical pair: aab=abba.

Flip LHS and RHS.

Referenced by [5].

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

Critical pair: aabba=abaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

Overlap of [2] aabba=ab with [4] abaa=ab:

Critical pair: aabbab=abbaa.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [6].

Overlap of [2] aabba=ab with [5] abb=aaba:

Critical pair: aabbaaba=abbb.

Reduce LHS:

Reduce RHS:

Defines rule #4.