Certificate for #1201 ⟨a, b | aabaa=abab⟩

Completion settings:

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

Axiom: aabaa=abab.

Referenced by [3].

Axiom: ab=c.

Defines rule #1.

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

Simplify [1] aabaa=abab.

Reduce RHS:

Referenced by [4].

Overlap of [3] aabaa=cc with [2] ab=c:

Critical pair: acaa=cc.

Defines rule #2.

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

Overlap of [4] acaa=cc with [2] ab=c:

Critical pair: acac=ccb.

Defines rule #3.

Referenced by [6], [7], [8], [9], [10], [11].

Overlap of [4] acaa=cc with [4] acaa=cc:

Critical pair: acacc=cccaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [10], [11].

Overlap of [4] acaa=cc with [5] acac=ccb:

Critical pair: acaccb=cccac.

Reduce LHS:

Defines rule #7.

Referenced by [10].

Overlap of [5] acac=ccb with [4] acaa=cc:

Critical pair: accc=ccbaa.

Flip LHS and RHS.

Defines rule #5.

Overlap of [5] acac=ccb with [5] acac=ccb:

Critical pair: acccb=ccbac.

Flip LHS and RHS.

Defines rule #6.

Overlap of [5] acac=ccb with [6] cccaa=ccbc:

Critical pair: acaccbc=ccbccaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Overlap of [6] cccaa=ccbc with [5] acac=ccb:

Critical pair: cccaccb=ccbccac.

Flip LHS and RHS.

Defines rule #9.