Certificate for #3607 ⟨a, b | aababbabaa=a⟩

Completion settings:

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

Axiom: aababbabaa=a.

Referenced by [3].

Axiom: ba=c.

Defines rule #1.

Referenced by [3], [4].

Overlap of [1] aababbabaa=a with [2] ba=c:

Critical pair: aacbbabaa=a.

Reduce LHS:

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

Overlap of [2] ba=c with [3] aacbcca=a:

Critical pair: ba=cacbcca.

Reduce LHS:

Flip LHS and RHS.

Referenced by [5], [6], [7], [11].

Overlap of [3] aacbcca=a with [4] cacbcca=c:

Critical pair: aacbcc=acbcca.

Defines rule #4.

Referenced by [8], [9].

Overlap of [4] cacbcca=c with [4] cacbcca=c:

Critical pair: cacbcc=ccbcca.

Defines rule #2.

Referenced by [7].

Overlap of [4] cacbcca=c with [6] cacbcc=ccbcca:

Critical pair: ccbccaa=c.

Referenced by [9], [12].

Overlap of [3] aacbcca=a with [5] aacbcc=acbcca:

Critical pair: acbccaa=a.

Referenced by [13].

Overlap of [5] aacbcc=acbcca with [7] ccbccaa=c:

Critical pair: aacbc=acbccabccaa.

Flip LHS and RHS.

Referenced by [10], [11].

Overlap of [3] aacbcca=a with [9] acbccabccaa=aacbc:

Critical pair: aaacbc=abccaa.

Flip LHS and RHS.

Defines rule #5.

Overlap of [4] cacbcca=c with [9] acbccabccaa=aacbc:

Critical pair: caacbc=cbccaa.

Flip LHS and RHS.

Defines rule #3.

Referenced by [12], [13].

Overlap of [7] ccbccaa=c with [11] cbccaa=caacbc:

Critical pair: ccaacbc=c.

Defines rule #6.

Overlap of [8] acbccaa=a with [11] cbccaa=caacbc:

Critical pair: acaacbc=a.

Defines rule #7.