Certificate for #3039 ⟨a, b, c | aba=b, bcb=a⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with c < b < a

Axiom: aba=b.

Defines rule #4.

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

Axiom: bcb=a.

Defines rule #1.

Referenced by [3], [5], [7], [8], [9], [10].

Overlap of [2] bcb=a with [2] bcb=a:

Critical pair: bca=acb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5], [8], [9].

Overlap of [1] aba=b with [1] aba=b:

Critical pair: abb=bba.

Defines rule #3.

Referenced by [5], [6].

Overlap of [4] abb=bba with [2] bcb=a:

Critical pair: aba=bbacb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [6].

Overlap of [4] abb=bba with [5] bbbca=b:

Critical pair: ab=bbabca.

Flip LHS and RHS.

Referenced by [7], [8].

Overlap of [2] bcb=a with [6] bbabca=ab:

Critical pair: bcab=ababca.

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [9].

Overlap of [3] acb=bca with [6] bbabca=ab:

Critical pair: acab=bcababca.

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [7] bbca=bcab with [3] acb=bca:

Critical pair: bbcbca=bcabcb.

Reduce LHS:

Reduce RHS:

Defines rule #6.

Referenced by [10].

Overlap of [2] bcb=a with [9] baca=bcaa:

Critical pair: bcbcaa=aaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.