Certificate for #5241 ⟨a, b | aabbbaa=aaba⟩

Completion settings:

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

Axiom: aabbbaa=aaba.

Referenced by [3].

Axiom: aaba=c.

Defines rule #1.

Referenced by [3], [4], [7], [8], [9].

Simplify [1] aabbbaa=aaba.

Reduce RHS:

Defines rule #8.

Referenced by [5], [6], [7], [8], [9], [10], [11], [13], [14], [16].

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

Critical pair: aabc=caba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [8], [9].

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

Critical pair: aabbbc=cbbbaa.

Flip LHS and RHS.

Referenced by [13], [15].

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

Critical pair: aabbbac=cabbbaa.

Flip LHS and RHS.

Referenced by [9], [13], [17].

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

Critical pair: aabbbc=cba.

Defines rule #4.

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

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

Critical pair: aabbbac=caba.

Reduce RHS:

Defines rule #9.

Referenced by [11], [14], [17].

Overlap of [4] caba=aabc with [3] aabbbaa=c:

Critical pair: cabc=aabcabbbaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #12.

Overlap of [3] aabbbaa=c with [7] aabbbc=cba:

Critical pair: aabbbcba=cbbbc.

Reduce LHS:

Defines rule #3.

Referenced by [12], [13].

Overlap of [3] aabbbaa=c with [7] aabbbc=cba:

Critical pair: aabbbacba=cabbbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [7] aabbbc=cba with [10] cbaba=cbbbc:

Critical pair: aabbbcbbbc=cbababa.

Reduce LHS:

Reduce RHS:

Defines rule #10.

Overlap of [10] cbaba=cbbbc with [3] aabbbaa=c:

Critical pair: cbabc=cbbbcabbbaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #14.

Overlap of [3] aabbbaa=c with [8] aabbbac=aabc:

Critical pair: aabbbaabc=cbbbac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Simplify [5] cbbbaa=aabbbc.

Reduce RHS:

Defines rule #5.

Referenced by [16].

Overlap of [15] cbbbaa=cba with [3] aabbbaa=c:

Critical pair: cbbbc=cbabbbaa.

Flip LHS and RHS.

Defines rule #13.

Simplify [6] cabbbaa=aabbbac.

Reduce RHS:

Defines rule #11.