Certificate for #4739 ⟨a, b | aabb=a, bbaa=a⟩

Completion settings:

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

Axiom: aabb=a.

Referenced by [4].

Axiom: bbaa=a.

Referenced by [5].

Axiom: bb=c.

Defines rule #1.

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

Overlap of [1] aabb=a with [3] bb=c:

Critical pair: aac=a.

Defines rule #4.

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

Overlap of [2] bbaa=a with [3] bb=c:

Critical pair: caa=a.

Referenced by [8].

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

Critical pair: bc=cb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

Overlap of [4] aac=a with [6] cb=bc:

Critical pair: aabc=ab.

Defines rule #6.

Referenced by [9].

Overlap of [5] caa=a with [4] aac=a:

Critical pair: ca=ac.

Defines rule #3.

Referenced by [9], [10].

Overlap of [7] aabc=ab with [8] ca=ac:

Critical pair: aabac=aba.

Referenced by [10].

Overlap of [9] aabac=aba with [8] ca=ac:

Critical pair: aabaac=abaa.

Reduce LHS:

Defines rule #5.