Certificate for #5106 ⟨a, b | aaabbba=abab⟩

Completion settings:

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

Axiom: aaabbba=abab.

Referenced by [3].

Axiom: abab=c.

Defines rule #2.

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

Simplify [1] aaabbba=abab.

Reduce RHS:

Defines rule #3.

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

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

Critical pair: abc=cab.

Flip LHS and RHS.

Defines rule #1.

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

Critical pair: aaabbbc=caabbba.

Flip LHS and RHS.

Referenced by [8].

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

Critical pair: aaabbbc=cbab.

Defines rule #4.

Referenced by [7], [8], [10].

Overlap of [3] aaabbba=c with [6] aaabbbc=cbab:

Critical pair: aaabbbcbab=caabbbc.

Reduce LHS:

Defines rule #6.

Simplify [5] caabbba=aaabbbc.

Reduce RHS:

Defines rule #5.

Referenced by [9], [10].

Overlap of [8] caabbba=cbab with [3] aaabbba=c:

Critical pair: caabbbc=cbabaabbba.

Flip LHS and RHS.

Defines rule #7.

Overlap of [8] caabbba=cbab with [6] aaabbbc=cbab:

Critical pair: caabbbcbab=cbabaabbbc.

Flip LHS and RHS.

Defines rule #8.