Certificate for #4275 ⟨a, b | aaabb=1, aabba=1⟩

Completion settings:

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

Axiom: aaabb=1.

Referenced by [4].

Axiom: aabba=1.

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

Axiom: aaa=c.

Defines rule #3.

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

Overlap of [1] aaabb=1 with [3] aaa=c:

Critical pair: cbb=1.

Referenced by [9].

Overlap of [3] aaa=c with [3] aaa=c:

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [10].

Overlap of [2] aabba=1 with [3] aaa=c:

Critical pair: aabbc=aa.

Referenced by [7].

Overlap of [2] aabba=1 with [6] aabbc=aa:

Critical pair: aabbaa=abbc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [2] aabba=1 with [7] abbc=a:

Critical pair: aabba=bbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [9], [10], [12].

Overlap of [4] cbb=1 with [8] bbc=1:

Critical pair: cb=bc.

Defines rule #2.

Referenced by [11], [12].

Overlap of [8] bbc=1 with [5] ca=ac:

Critical pair: bbac=a.

Referenced by [11].

Overlap of [10] bbac=a with [9] cb=bc:

Critical pair: bbabc=ab.

Referenced by [12].

Overlap of [11] bbabc=ab with [9] cb=bc:

Critical pair: bbabbc=abb.

Reduce LHS:

Defines rule #4.