Certificate for #5119 ⟨a, b | aabaaab=aaba⟩

Completion settings:

• Reduction order:
  • Right-to-left shortlex with c < a < b
• Auxiliary generators:
  1. aaba=c

Axiom: aabaaab=aaba.

Referenced by [3].

Axiom: aaba=c.

Defines rule #3.

Referenced by [3], [4], [5], [6].

Simplify [1] aabaaab=aaba.

Reduce RHS:

Referenced by [4].

Overlap of [3] aabaaab=c with [2] aaba=c:

Critical pair: caab=c.

Referenced by [6], [7].

Overlap of [2] aaba=c with [2] aaba=c:

Critical pair: aabc=caba.

Flip LHS and RHS.

Referenced by [8].

Overlap of [4] caab=c with [2] aaba=c:

Critical pair: cc=ca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [7], [8].

Overlap of [4] caab=c with [6] ca=cc:

Critical pair: ccab=c.

Reduce LHS:

Defines rule #4.

Simplify [5] caba=aabc.

Reduce LHS:

Defines rule #2.