Certificate for #4587 ⟨a, b, c | abc=1, bcba=b⟩

Completion settings:

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

Axiom: abc=1.

Defines rule #2.

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

Axiom: bcba=b.

Referenced by [3], [4], [5].

Overlap of [1] abc=1 with [2] bcba=b:

Critical pair: ab=ba.

Flip LHS and RHS.

Defines rule #1.

Referenced by [5], [6].

Overlap of [2] bcba=b with [1] abc=1:

Critical pair: bcb=bbc.

Flip LHS and RHS.

Defines rule #4.

Overlap of [2] bcba=b with [3] ba=ab:

Critical pair: bcab=b.

Referenced by [6].

Overlap of [5] bcab=b with [3] ba=ab:

Critical pair: bcaab=ba.

Reduce RHS:

Referenced by [7].

Overlap of [6] bcaab=ab with [1] abc=1:

Critical pair: bca=abc.

Reduce RHS:

Defines rule #3.