Certificate for #5111 ⟨a, b | aaabbba=baba⟩

Completion settings:

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

Axiom: aaabbba=baba.

Referenced by [3].

Axiom: baba=c.

Defines rule #2.

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

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

Critical pair: aaabbbc=caabbba.

Referenced by [8], [10].

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

Critical pair: aaabbc=cba.

Defines rule #3.

Referenced by [8].

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

Critical pair: babc=caabbba.

Flip LHS and RHS.

Defines rule #6.

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

Overlap of [3] aaabbba=c with [6] aaabbc=cba:

Critical pair: aaabbbcba=caabbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [7] caabbba=babc with [3] aaabbba=c:

Critical pair: caabbbc=babcaabbba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Simplify [5] aaabbbc=caabbba.

Reduce RHS:

Defines rule #7.

Referenced by [11], [12].

Overlap of [3] aaabbba=c with [10] aaabbbc=babc:

Critical pair: aaabbbbabc=caabbbc.

Defines rule #9.

Overlap of [7] caabbba=babc with [10] aaabbbc=babc:

Critical pair: caabbbbabc=babcaabbbc.

Defines rule #10.