Certificate for #5865 ⟨a, b | ababab=aabaa⟩

Completion settings:

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

Axiom: ababab=aabaa.

Referenced by [3].

Axiom: aba=c.

Defines rule #1.

Referenced by [3], [4], [5], [7], [8], [10].

Simplify [1] ababab=aabaa.

Reduce RHS:

Referenced by [4].

Overlap of [3] ababab=aca with [2] aba=c:

Critical pair: cbab=aca.

Referenced by [6].

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

Critical pair: abc=cba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [6], [8], [9].

Simplify [4] cbab=aca.

Reduce LHS:

Defines rule #3.

Referenced by [7], [8], [9], [10], [11].

Overlap of [2] aba=c with [6] abcb=aca:

Critical pair: abaca=cbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [11].

Overlap of [6] abcb=aca with [5] cba=abc:

Critical pair: ababc=acaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [10], [11].

Overlap of [5] cba=abc with [6] abcb=aca:

Critical pair: cbaca=abcbcb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [2] aba=c with [8] acaa=cbc:

Critical pair: abcbc=ccaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [8] acaa=cbc with [6] abcb=aca:

Critical pair: acaaca=cbcbcb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.