Certificate for #11369 ⟨a, b | aabab=a, bbbbb=1⟩

Completion settings:

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

Axiom: aabab=a.

Defines rule #2.

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

Axiom: bbbbb=1.

Defines rule #6.

Referenced by [3].

Overlap of [1] aabab=a with [2] bbbbb=1:

Critical pair: aaba=abbbb.

Flip LHS and RHS.

Referenced by [4].

Overlap of [1] aabab=a with [3] abbbb=aaba:

Critical pair: aabaaba=abbb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

Overlap of [1] aabab=a with [4] abbb=aabaaba:

Critical pair: aabaabaaba=abb.

Defines rule #5.

Referenced by [6].

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

Critical pair: aababb=abbaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [7].

Overlap of [1] aabab=a with [6] abbaba=ab:

Critical pair: aabab=ababa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.