Certificate for #6556 ⟨a, b | aaa=a, babb=ab⟩

Completion settings:

• Auxiliary generators:
  1. c = ab
• Reduction order:
  • Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1

Axiom: aaa=a.

Defines rule #1.

Referenced by [6].

Axiom: babb=ab.

Referenced by [4].

Axiom: ab=c.

Defines rule #7.

Referenced by [4], [5], [6], [7], [9].

Simplify [2] babb=ab.

Reduce RHS:

Referenced by [5].

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

Critical pair: bcb=c.

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

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

Critical pair: aac=ab.

Reduce RHS:

Defines rule #2.

Referenced by [9], [13].

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

Critical pair: ac=ccb.

Flip LHS and RHS.

Referenced by [8], [14], [15].

Overlap of [5] bcb=c with [5] bcb=c:

Critical pair: bcc=ccb.

Reduce RHS:

Referenced by [9], [10], [11], [14].

Overlap of [3] ab=c with [8] bcc=ac:

Critical pair: aac=ccc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [10], [11], [15].

Overlap of [5] bcb=c with [8] bcc=ac:

Critical pair: bcac=ccc.

Reduce RHS:

Referenced by [12].

Overlap of [8] bcc=ac with [9] ccc=c:

Critical pair: bc=acc.

Defines rule #5.

Referenced by [12].

Simplify [10] bcac=c.

Reduce LHS:

Referenced by [13].

Overlap of [6] aac=c with [12] accac=c:

Critical pair: ac=ccac.

Flip LHS and RHS.

Defines rule #4.

Overlap of [8] bcc=ac with [7] ccb=ac:

Critical pair: bac=acb.

Flip LHS and RHS.

Referenced by [16].

Overlap of [9] ccc=c with [7] ccb=ac:

Critical pair: cac=cb.

Flip LHS and RHS.

Defines rule #8.

Referenced by [16].

Overlap of [14] acb=bac with [15] cb=cac:

Critical pair: acac=bac.

Flip LHS and RHS.

Defines rule #6.