Certificate for #2138 ⟨a, b | aaaabba=aab⟩

Completion settings:

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

Axiom: aaaabba=aab.

Referenced by [3].

Axiom: aab=c.

Defines rule #1.

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

Simplify [1] aaaabba=aab.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaaabba=c with [2] aab=c:

Critical pair: aacba=c.

Defines rule #2.

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

Overlap of [4] aacba=c with [2] aab=c:

Critical pair: aacbc=cab.

Defines rule #3.

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

Overlap of [4] aacba=c with [4] aacba=c:

Critical pair: aacbc=cacba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [8], [9].

Overlap of [4] aacba=c with [5] aacbc=cab:

Critical pair: aacbcab=cacbc.

Reduce LHS:

Defines rule #5.

Referenced by [8].

Overlap of [5] aacbc=cab with [6] cacba=cab:

Critical pair: aacbcab=cabacba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [6] cacba=cab with [5] aacbc=cab:

Critical pair: cacbcab=cabacbc.

Flip LHS and RHS.

Defines rule #7.