Certificate for #68 ⟨a, b, c | aab=1, bcc=1⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with b < a < c

Axiom: aab=1.

Referenced by [3], [8], [10], [11].

Axiom: bcc=1.

Referenced by [3], [4].

Overlap of [1] aab=1 with [2] bcc=1:

Critical pair: aa=cc.

Flip LHS and RHS.

Defines rule #3.

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

Overlap of [2] bcc=1 with [3] cc=aa:

Critical pair: bcaa=c.

Referenced by [6].

Overlap of [3] cc=aa with [3] cc=aa:

Critical pair: caa=aac.

Defines rule #5.

Referenced by [6], [8].

Simplify [4] bcaa=c.

Reduce LHS:

Referenced by [7], [9].

Overlap of [6] baac=c with [3] cc=aa:

Critical pair: baaaa=cc.

Reduce RHS:

Referenced by [10].

Overlap of [5] caa=aac with [1] aab=1:

Critical pair: c=aacb.

Flip LHS and RHS.

Referenced by [9].

Overlap of [6] baac=c with [8] aacb=c:

Critical pair: bc=cb.

Flip LHS and RHS.

Defines rule #2.

Overlap of [7] baaaa=aa with [1] aab=1:

Critical pair: baa=aab.

Reduce RHS:

Defines rule #4.

Referenced by [11].

Overlap of [10] baa=1 with [1] aab=1:

Critical pair: ba=ab.

Flip LHS and RHS.

Defines rule #1.