Certificate for #5356 ⟨a, b | abababa=aaab⟩

Completion settings:

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

Axiom: abababa=aaab.

Referenced by [3].

Axiom: aaab=c.

Defines rule #2.

Referenced by [3], [5], [6], [8], [10], [11].

Simplify [1] abababa=aaab.

Reduce RHS:

Defines rule #9.

Referenced by [4], [5], [6], [7], [9].

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

Critical pair: abc=cba.

Flip LHS and RHS.

Defines rule #1.

Referenced by [7], [8], [13].

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

Critical pair: abababc=caab.

Defines rule #10.

Referenced by [7], [9], [12], [13].

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

Critical pair: aac=cababa.

Flip LHS and RHS.

Defines rule #6.

Referenced by [11].

Overlap of [4] cba=abc with [3] abababa=c:

Critical pair: cbc=abcbababa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [13].

Overlap of [4] cba=abc with [2] aaab=c:

Critical pair: cbc=abcaab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [9], [10], [12].

Overlap of [3] abababa=c with [8] abcaab=cbc:

Critical pair: abababcbc=cbcaab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Overlap of [2] aaab=c with [8] abcaab=cbc:

Critical pair: aacbc=ccaab.

Flip LHS and RHS.

Defines rule #3.

Overlap of [6] cababa=aac with [2] aaab=c:

Critical pair: cababc=aacaab.

Defines rule #7.

Overlap of [5] abababc=caab with [8] abcaab=cbc:

Critical pair: ababcbc=caabaab.

Flip LHS and RHS.

Defines rule #11.

Overlap of [7] caabba=cbc with [5] abababc=caab:

Critical pair: caabbcaab=cbcbababc.

Reduce RHS:

Defines rule #12.