Certificate for #2890 ⟨a, b, c | aab=a, caa=a⟩

Completion settings:

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

Axiom: aab=a.

Referenced by [4], [6], [7], [12].

Axiom: caa=a.

Referenced by [6], [7], [8].

Axiom: abb=d.

Referenced by [4], [5], [13].

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

Critical pair: ad=ab.

Flip LHS and RHS.

Referenced by [5], [6], [13], [14].

Overlap of [3] abb=d with [4] ab=ad:

Critical pair: adb=d.

Referenced by [8], [9].

Overlap of [2] caa=a with [1] aab=a:

Critical pair: ca=ab.

Reduce RHS:

Referenced by [7], [8], [9], [10], [11], [15].

Overlap of [2] caa=a with [1] aab=a:

Critical pair: caa=aab.

Reduce LHS:

Reduce RHS:

Referenced by [11], [12].

Overlap of [2] caa=a with [5] adb=d:

Critical pair: cad=adb.

Reduce LHS:

Reduce RHS:

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

Overlap of [6] ca=ad with [5] adb=d:

Critical pair: cd=addb.

Reduce RHS:

Referenced by [10], [16].

Overlap of [6] ca=ad with [8] add=d:

Critical pair: cd=addd.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [16].

Overlap of [6] ca=ad with [7] ada=a:

Critical pair: ca=adda.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Referenced by [12], [13], [14], [15].

Overlap of [7] ada=a with [1] aab=a:

Critical pair: ada=aab.

Reduce LHS:

Reduce RHS:

Defines rule #7.

Overlap of [3] abb=d with [4] ab=ad:

Critical pair: adb=d.

Reduce LHS:

Defines rule #6.

Simplify [4] ab=ad.

Reduce RHS:

Defines rule #3.

Simplify [6] ca=ad.

Reduce RHS:

Defines rule #5.

Simplify [9] cd=db.

Reduce RHS:

Defines rule #4.