Certificate for #5348 ⟨a, b | ababaab=baab⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with a < c < b
• Auxiliary generators:
  1. baab=c

Axiom: ababaab=baab.

Referenced by [3].

Axiom: baab=c.

Defines rule #6.

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

Simplify [1] ababaab=baab.

Reduce RHS:

Referenced by [4].

Overlap of [3] ababaab=c with [2] baab=c:

Critical pair: abac=c.

Referenced by [6], [7].

Overlap of [2] baab=c with [2] baab=c:

Critical pair: baac=caab.

Defines rule #5.

Overlap of [2] baab=c with [4] abac=c:

Critical pair: bac=cac.

Referenced by [7], [8], [10].

Overlap of [4] abac=c with [6] bac=cac:

Critical pair: acac=c.

Referenced by [8], [9], [11].

Overlap of [6] bac=cac with [7] acac=c:

Critical pair: bc=cacac.

Reduce RHS:

Defines rule #1.

Overlap of [7] acac=c with [7] acac=c:

Critical pair: acc=cac.

Flip LHS and RHS.

Defines rule #2.

Referenced by [10], [11].

Simplify [6] bac=cac.

Reduce RHS:

Defines rule #3.

Overlap of [7] acac=c with [9] cac=acc:

Critical pair: aacc=c.

Defines rule #4.