Certificate for #5243 ⟨a, b | aabbbaa=abab⟩

Completion settings:

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

Axiom: aabbbaa=abab.

Referenced by [3].

Axiom: abbbaa=c.

Defines rule #5.

Referenced by [3], [5], [6], [7], [8].

Overlap of [1] aabbbaa=abab with [2] abbbaa=c:

Critical pair: ac=abab.

Flip LHS and RHS.

Defines rule #1.

Referenced by [4], [6], [7], [9].

Overlap of [3] abab=ac with [3] abab=ac:

Critical pair: abac=acab.

Flip LHS and RHS.

Defines rule #2.

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

Critical pair: abbbac=cbbbaa.

Flip LHS and RHS.

Defines rule #7.

Overlap of [2] abbbaa=c with [3] abab=ac:

Critical pair: abbbaac=cbab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [8], [9].

Overlap of [3] abab=ac with [2] abbbaa=c:

Critical pair: abc=acbbaa.

Flip LHS and RHS.

Defines rule #6.

Overlap of [6] cbab=cc with [2] abbbaa=c:

Critical pair: cbc=ccbbaa.

Flip LHS and RHS.

Defines rule #8.

Overlap of [6] cbab=cc with [3] abab=ac:

Critical pair: cbac=ccab.

Flip LHS and RHS.

Defines rule #4.