Certificate for #5390 ⟨a, b | abbaaab=baab⟩

Completion settings:

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

Axiom: abbaaab=baab.

Referenced by [3].

Axiom: baab=c.

Defines rule #1.

Referenced by [3], [4], [6], [7], [9], [12], [14], [15].

Simplify [1] abbaaab=baab.

Reduce RHS:

Defines rule #10.

Referenced by [5], [6], [7], [8], [10], [14].

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

Critical pair: baac=caab.

Defines rule #2.

Referenced by [5], [8].

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

Critical pair: abbaac=cbaaab.

Reduce LHS:

Referenced by [11], [13].

Overlap of [3] abbaaab=c with [2] baab=c:

Critical pair: abbaaac=caab.

Defines rule #12.

Overlap of [2] baab=c with [3] abbaaab=c:

Critical pair: bac=cbaaab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [8], [9], [10], [11], [13].

Overlap of [7] cbaaab=bac with [3] abbaaab=c:

Critical pair: cbaac=bacbaaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [10], [11].

Overlap of [7] cbaaab=bac with [2] baab=c:

Critical pair: cbaaac=bacaab.

Defines rule #7.

Overlap of [8] babac=ccaab with [7] cbaaab=bac:

Critical pair: bababac=ccaabbaaab.

Reduce LHS:

Reduce RHS:

Defines rule #11.

Referenced by [11], [12], [16], [17].

Overlap of [8] babac=ccaab with [10] baccaab=ccac:

Critical pair: baccac=ccaabcaab.

Reduce RHS:

Defines rule #9.

Overlap of [10] baccaab=ccac with [2] baab=c:

Critical pair: baccaac=ccacaab.

Defines rule #13.

Simplify [5] abcaab=cbaaab.

Reduce RHS:

Defines rule #6.

Referenced by [14], [15], [16], [17].

Overlap of [3] abbaaab=c with [13] abcaab=bac:

Critical pair: abbaabac=ccaab.

Reduce LHS:

Defines rule #4.

Overlap of [13] abcaab=bac with [2] baab=c:

Critical pair: abcaac=bacaab.

Defines rule #8.

Overlap of [13] abcaab=bac with [13] abcaab=bac:

Critical pair: abcabac=baccaab.

Reduce RHS:

Defines rule #14.

Overlap of [10] baccaab=ccac with [13] abcaab=bac:

Critical pair: baccabac=ccaccaab.

Defines rule #15.