Certificate for #5294 ⟨a, b | abaaaab=bbab⟩

Completion settings:

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

Axiom: abaaaab=bbab.

Referenced by [3].

Axiom: bbab=c.

Defines rule #1.

Referenced by [3], [4], [6], [7], [9].

Simplify [1] abaaaab=bbab.

Reduce RHS:

Defines rule #7.

Referenced by [5], [6], [7], [8], [12].

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

Critical pair: bbac=cbab.

Defines rule #2.

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

Critical pair: abaaac=caaaab.

Referenced by [11].

Overlap of [3] abaaaab=c with [2] bbab=c:

Critical pair: abaaaac=cbab.

Defines rule #8.

Overlap of [2] bbab=c with [3] abaaaab=c:

Critical pair: bbc=caaaab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [8], [9], [10], [11].

Overlap of [7] caaaab=bbc with [3] abaaaab=c:

Critical pair: caaac=bbcaaaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [10].

Overlap of [7] caaaab=bbc with [2] bbab=c:

Critical pair: caaaac=bbcbab.

Defines rule #5.

Overlap of [8] bbbbc=caaac with [7] caaaab=bbc:

Critical pair: bbbbbbc=caaacaaaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #9.

Simplify [5] abaaac=caaaab.

Reduce RHS:

Defines rule #6.

Referenced by [12].

Overlap of [3] abaaaab=c with [11] abaaac=bbc:

Critical pair: abaaabbc=caaac.

Defines rule #10.