Certificate for #4925 ⟨a, b | aaaaaba=baba⟩

Completion settings:

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

Axiom: aaaaaba=baba.

Referenced by [3].

Axiom: baba=c.

Defines rule #2.

Referenced by [3], [4], [6], [7].

Simplify [1] aaaaaba=baba.

Reduce RHS:

Defines rule #5.

Referenced by [5], [6], [7], [8], [9], [11].

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

Critical pair: bac=cba.

Defines rule #1.

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

Critical pair: aaaaabc=caaaaba.

Referenced by [8], [10].

Overlap of [3] aaaaaba=c with [2] baba=c:

Critical pair: aaaaac=cba.

Defines rule #3.

Referenced by [8].

Overlap of [2] baba=c with [3] aaaaaba=c:

Critical pair: babc=caaaaba.

Flip LHS and RHS.

Defines rule #6.

Referenced by [8], [9], [10], [12].

Overlap of [3] aaaaaba=c with [6] aaaaac=cba:

Critical pair: aaaaabcba=caaaac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [7] caaaaba=babc with [3] aaaaaba=c:

Critical pair: caaaabc=babcaaaaba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Simplify [5] aaaaabc=caaaaba.

Reduce RHS:

Defines rule #7.

Referenced by [11], [12].

Overlap of [3] aaaaaba=c with [10] aaaaabc=babc:

Critical pair: aaaaabbabc=caaaabc.

Defines rule #9.

Overlap of [7] caaaaba=babc with [10] aaaaabc=babc:

Critical pair: caaaabbabc=babcaaaabc.

Defines rule #10.