Certificate for #5073 ⟨a, b | aaabbaa=abaa⟩

Completion settings:

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

Axiom: aaabbaa=abaa.

Referenced by [3].

Axiom: abaa=c.

Defines rule #1.

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

Simplify [1] aaabbaa=abaa.

Reduce RHS:

Defines rule #8.

Referenced by [5], [6], [7], [8], [9], [10], [12], [13], [16].

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

Critical pair: abac=cbaa.

Defines rule #2.

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

Critical pair: aaabbc=cabbaa.

Referenced by [15].

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

Critical pair: aaabbac=caabbaa.

Referenced by [7], [17].

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

Critical pair: aaabbac=cbaa.

Reduce LHS:

Defines rule #9.

Referenced by [10], [12], [13], [17].

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

Critical pair: abc=cabbaa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [9], [10], [11], [14], [15].

Overlap of [8] cabbaa=abc with [3] aaabbaa=c:

Critical pair: cabbc=abcabbaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [11].

Overlap of [8] cabbaa=abc with [3] aaabbaa=c:

Critical pair: cabbac=abcaabbaa.

Reduce RHS:

Defines rule #7.

Overlap of [9] ababc=cabbc with [8] cabbaa=abc:

Critical pair: abababc=cabbcabbaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #10.

Overlap of [7] caabbaa=cbaa with [3] aaabbaa=c:

Critical pair: caabbc=cbaaabbaa.

Reduce RHS:

Defines rule #6.

Referenced by [14].

Overlap of [7] caabbaa=cbaa with [3] aaabbaa=c:

Critical pair: caabbac=cbaaaabbaa.

Reduce RHS:

Defines rule #12.

Overlap of [12] caabbc=cbc with [8] cabbaa=abc:

Critical pair: caabbabc=cbcabbaa.

Reduce RHS:

Defines rule #14.

Simplify [5] aaabbc=cabbaa.

Reduce RHS:

Defines rule #5.

Referenced by [16].

Overlap of [3] aaabbaa=c with [15] aaabbc=abc:

Critical pair: aaabbabc=cabbc.

Defines rule #13.

Simplify [6] aaabbac=caabbaa.

Reduce RHS:

Defines rule #11.