Certificate for #5071 ⟨a, b | aaabbaa=aaba⟩

Completion settings:

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

Axiom: aaabbaa=aaba.

Referenced by [3].

Axiom: aaba=c.

Defines rule #1.

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

Simplify [1] aaabbaa=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] aaabbaa=c with [3] aaabbaa=c:

Critical pair: aaabbc=cabbaa.

Flip LHS and RHS.

Referenced by [13], [15].

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

Critical pair: aaabbac=caabbaa.

Flip LHS and RHS.

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

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

Critical pair: aaabbc=cba.

Defines rule #4.

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

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

Critical pair: aaabbac=caba.

Reduce RHS:

Defines rule #9.

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

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

Critical pair: cabc=aabcaabbaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #11.

Overlap of [3] aaabbaa=c with [7] aaabbc=cba:

Critical pair: aaabbcba=cabbc.

Reduce LHS:

Defines rule #3.

Referenced by [12], [13].

Overlap of [3] aaabbaa=c with [7] aaabbc=cba:

Critical pair: aaabbacba=caabbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [7] aaabbc=cba with [10] cbaba=cabbc:

Critical pair: aaabbcabbc=cbababa.

Reduce LHS:

Reduce RHS:

Defines rule #12.

Overlap of [10] cbaba=cabbc with [3] aaabbaa=c:

Critical pair: cbabc=cabbcaabbaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #14.

Overlap of [3] aaabbaa=c with [8] aaabbac=aabc:

Critical pair: aaabbaabc=cabbac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Simplify [5] cabbaa=aaabbc.

Reduce RHS:

Defines rule #6.

Referenced by [16].

Overlap of [15] cabbaa=cba with [3] aaabbaa=c:

Critical pair: cabbc=cbaabbaa.

Flip LHS and RHS.

Defines rule #13.

Simplify [6] caabbaa=aaabbac.

Reduce RHS:

Defines rule #10.