Certificate for #3435 ⟨a, b, c | ba=ac, aaa=a⟩

Completion settings:

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

Axiom: ba=ac.

Referenced by [4], [8].

Axiom: aaa=a.

Defines rule #5.

Referenced by [4], [5].

Axiom: caa=d.

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

Overlap of [1] ba=ac with [2] aaa=a:

Critical pair: ba=acaa.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [7], [8].

Overlap of [3] caa=d with [2] aaa=a:

Critical pair: ca=da.

Defines rule #4.

Referenced by [6].

Overlap of [3] caa=d with [5] ca=da:

Critical pair: daa=d.

Defines rule #6.

Referenced by [7].

Overlap of [6] daa=d with [4] ac=ad:

Critical pair: daad=dc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Simplify [1] ba=ac.

Reduce RHS:

Defines rule #2.