Certificate for #5275 ⟨a, b | aabbbba=baba⟩

Completion settings:

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

Axiom: aabbbba=baba.

Referenced by [3].

Axiom: baba=c.

Defines rule #2.

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

Simplify [1] aabbbba=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] aabbbba=c with [3] aabbbba=c:

Critical pair: aabbbbc=cabbbba.

Referenced by [8], [10].

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

Critical pair: aabbbc=cba.

Defines rule #3.

Referenced by [8].

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

Critical pair: babc=cabbbba.

Flip LHS and RHS.

Defines rule #6.

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

Overlap of [3] aabbbba=c with [6] aabbbc=cba:

Critical pair: aabbbbcba=cabbbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [7] cabbbba=babc with [3] aabbbba=c:

Critical pair: cabbbbc=babcabbbba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Simplify [5] aabbbbc=cabbbba.

Reduce RHS:

Defines rule #7.

Referenced by [11], [12].

Overlap of [3] aabbbba=c with [10] aabbbbc=babc:

Critical pair: aabbbbbabc=cabbbbc.

Defines rule #9.

Overlap of [7] cabbbba=babc with [10] aabbbbc=babc:

Critical pair: cabbbbbabc=babcabbbbc.

Defines rule #10.