Certificate for #5224 ⟨a, b | aabbaba=aaab⟩

Completion settings:

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

Axiom: aabbaba=aaab.

Referenced by [3].

Axiom: aaab=c.

Defines rule #1.

Referenced by [3], [5], [6], [7].

Simplify [1] aabbaba=aaab.

Reduce RHS:

Defines rule #4.

Referenced by [4], [5], [6], [8], [10].

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

Critical pair: aabbabc=cabbaba.

Flip LHS and RHS.

Referenced by [9].

Overlap of [3] aabbaba=c with [2] aaab=c:

Critical pair: aabbabc=caab.

Defines rule #5.

Referenced by [8], [9], [11].

Overlap of [2] aaab=c with [3] aabbaba=c:

Critical pair: ac=cbaba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

Overlap of [6] cbaba=ac with [2] aaab=c:

Critical pair: cbabc=acaab.

Defines rule #3.

Overlap of [3] aabbaba=c with [5] aabbabc=caab:

Critical pair: aabbabcaab=cabbabc.

Reduce LHS:

Defines rule #7.

Simplify [4] cabbaba=aabbabc.

Reduce RHS:

Defines rule #6.

Referenced by [10], [11].

Overlap of [9] cabbaba=caab with [3] aabbaba=c:

Critical pair: cabbabc=caababbaba.

Flip LHS and RHS.

Defines rule #8.

Overlap of [9] cabbaba=caab with [5] aabbabc=caab:

Critical pair: cabbabcaab=caababbabc.

Flip LHS and RHS.

Defines rule #9.