Certificate for #6342 ⟨a, b | aab=a, abbaa=a⟩

Completion settings:

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

Axiom: aab=a.

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

Axiom: abbaa=a.

Referenced by [4].

Axiom: abb=c.

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

Overlap of [2] abbaa=a with [3] abb=c:

Critical pair: caa=a.

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

Overlap of [1] aab=a with [3] abb=c:

Critical pair: ac=ab.

Flip LHS and RHS.

Defines rule #1.

Referenced by [6], [7].

Overlap of [3] abb=c with [5] ab=ac:

Critical pair: acb=c.

Referenced by [9], [10].

Overlap of [4] caa=a with [1] aab=a:

Critical pair: ca=ab.

Reduce RHS:

Defines rule #2.

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

Overlap of [4] caa=a with [1] aab=a:

Critical pair: caa=aab.

Reduce LHS:

Reduce RHS:

Defines rule #4.

Overlap of [4] caa=a with [6] acb=c:

Critical pair: cac=acb.

Reduce LHS:

Reduce RHS:

Defines rule #5.

Referenced by [10].

Overlap of [7] ca=ac with [6] acb=c:

Critical pair: cc=accb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.