Certificate for #2686 ⟨a, b | ababa=abaab⟩

Completion settings:

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

Axiom: ababa=abaab.

Referenced by [3].

Axiom: abaab=c.

Defines rule #9.

Referenced by [3], [4], [6], [7], [8], [10].

Simplify [1] ababa=abaab.

Reduce RHS:

Defines rule #10.

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

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

Critical pair: abac=caab.

Flip LHS and RHS.

Defines rule #6.

Overlap of [3] ababa=c with [3] ababa=c:

Critical pair: abc=cba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [8], [9].

Overlap of [3] ababa=c with [2] abaab=c:

Critical pair: abc=cab.

Flip LHS and RHS.

Defines rule #1.

Referenced by [7], [9], [11], [12].

Overlap of [2] abaab=c with [3] ababa=c:

Critical pair: abac=caba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [8], [10], [11].

Overlap of [5] cba=abc with [2] abaab=c:

Critical pair: cbc=abcbaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [9].

Overlap of [8] ccb=cbc with [5] cba=abc:

Critical pair: cabc=cbca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Overlap of [2] abaab=c with [7] abca=abac:

Critical pair: abaabac=cca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [12].

Overlap of [7] abca=abac with [6] cab=abc:

Critical pair: ababc=abacb.

Flip LHS and RHS.

Defines rule #11.

Overlap of [10] cca=cac with [6] cab=abc:

Critical pair: cabc=cacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.