Certificate for #5240 ⟨a, b | aabbbaa=aaab⟩

Completion settings:

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

Axiom: aabbbaa=aaab.

Referenced by [3].

Axiom: aaab=c.

Defines rule #1.

Referenced by [3], [5], [6], [7], [8], [9].

Simplify [1] aabbbaa=aaab.

Reduce RHS:

Defines rule #10.

Referenced by [4], [5], [6], [7], [10], [15], [17], [20].

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

Critical pair: aabbbc=cbbbaa.

Flip LHS and RHS.

Referenced by [19].

Overlap of [3] aabbbaa=c with [2] aaab=c:

Critical pair: aabbbc=cab.

Defines rule #6.

Referenced by [10], [11], [12], [13], [14], [15], [19].

Overlap of [3] aabbbaa=c with [2] aaab=c:

Critical pair: aabbbac=caab.

Defines rule #11.

Referenced by [11], [12], [13], [15], [16], [18], [21].

Overlap of [2] aaab=c with [3] aabbbaa=c:

Critical pair: ac=cbbaa.

Flip LHS and RHS.

Defines rule #3.

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

Overlap of [7] cbbaa=ac with [2] aaab=c:

Critical pair: cbbc=acab.

Defines rule #2.

Referenced by [12].

Overlap of [7] cbbaa=ac with [2] aaab=c:

Critical pair: cbbac=acaab.

Defines rule #4.

Referenced by [13].

Overlap of [3] aabbbaa=c with [5] aabbbc=cab:

Critical pair: aabbbcab=cbbbc.

Reduce LHS:

Defines rule #5.

Referenced by [14], [16].

Overlap of [5] aabbbc=cab with [7] cbbaa=ac:

Critical pair: aabbbac=cabbbaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.

Referenced by [17], [18].

Overlap of [5] aabbbc=cab with [8] cbbc=acab:

Critical pair: aabbbacab=cabbbc.

Reduce LHS:

Defines rule #9.

Referenced by [16].

Overlap of [5] aabbbc=cab with [9] cbbac=acaab:

Critical pair: aabbbacaab=cabbbac.

Reduce LHS:

Defines rule #14.

Overlap of [5] aabbbc=cab with [10] cabab=cbbbc:

Critical pair: aabbbcbbbc=cababab.

Reduce LHS:

Reduce RHS:

Defines rule #12.

Overlap of [3] aabbbaa=c with [6] aabbbac=caab:

Critical pair: aabbbcaab=cbbbac.

Reduce LHS:

Defines rule #8.

Overlap of [6] aabbbac=caab with [10] cabab=cbbbc:

Critical pair: aabbbacbbbc=caababab.

Reduce LHS:

Reduce RHS:

Defines rule #17.

Overlap of [11] cabbbaa=caab with [3] aabbbaa=c:

Critical pair: cabbbc=caabbbbaa.

Flip LHS and RHS.

Defines rule #18.

Overlap of [11] cabbbaa=caab with [6] aabbbac=caab:

Critical pair: cabbbcaab=caabbbbac.

Flip LHS and RHS.

Defines rule #19.

Simplify [4] cbbbaa=aabbbc.

Reduce RHS:

Defines rule #7.

Referenced by [20], [21].

Overlap of [19] cbbbaa=cab with [3] aabbbaa=c:

Critical pair: cbbbc=cabbbbaa.

Flip LHS and RHS.

Defines rule #15.

Overlap of [19] cbbbaa=cab with [6] aabbbac=caab:

Critical pair: cbbbcaab=cabbbbac.

Flip LHS and RHS.

Defines rule #16.