Certificate for #19248 ⟨a, b | aaa=a, aabaa=ab⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #4.

Referenced by [6], [7].

Axiom: aabaa=ab.

Referenced by [4].

Axiom: ab=c.

Defines rule #2.

Referenced by [4], [5], [6], [8].

Simplify [2] aabaa=ab.

Reduce RHS:

Referenced by [5].

Overlap of [4] aabaa=c with [3] ab=c:

Critical pair: acaa=c.

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

Overlap of [1] aaa=a with [3] ab=c:

Critical pair: aac=ab.

Reduce RHS:

Referenced by [9].

Overlap of [5] acaa=c with [1] aaa=a:

Critical pair: aca=ca.

Referenced by [8], [10].

Overlap of [5] acaa=c with [3] ab=c:

Critical pair: acac=cb.

Reduce LHS:

Referenced by [11].

Overlap of [6] aac=c with [5] acaa=c:

Critical pair: ac=caa.

Flip LHS and RHS.

Referenced by [10], [12].

Overlap of [5] acaa=c with [7] aca=ca:

Critical pair: caa=c.

Reduce LHS:

Defines rule #1.

Referenced by [11], [12].

Overlap of [5] acaa=c with [10] ac=c:

Critical pair: acac=cc.

Reduce LHS:

Defines rule #3.

Simplify [9] caa=ac.

Reduce RHS:

Defines rule #5.