Certificate for #2606 ⟨a, b, c | aba=b, acbb=1⟩

Completion settings:

• Auxiliary generators:
  1. d = bb
• Reduction order:
  • Left-to-right recursive path with deg(c) = 0; deg(d) = deg(a) = deg(b) = 1, d < a < b

Axiom: aba=b.

Referenced by [6], [7], [9], [11].

Axiom: acbb=1.

Referenced by [4].

Axiom: bb=d.

Defines rule #8.

Referenced by [4], [5], [6], [8], [9], [12].

Overlap of [2] acbb=1 with [3] bb=d:

Critical pair: acd=1.

Defines rule #4.

Referenced by [7], [10].

Overlap of [3] bb=d with [3] bb=d:

Critical pair: bd=db.

Defines rule #5.

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

Critical pair: abb=bba.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Overlap of [1] aba=b with [4] acd=1:

Critical pair: ab=bcd.

Flip LHS and RHS.

Defines rule #6.

Referenced by [8].

Overlap of [3] bb=d with [7] bcd=ab:

Critical pair: bab=dcd.

Referenced by [9], [12].

Overlap of [8] bab=dcd with [1] aba=b:

Critical pair: bb=dcda.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [4] acd=1 with [9] dcda=d:

Critical pair: acd=cda.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [11].

Overlap of [10] cda=1 with [1] aba=b:

Critical pair: cdb=ba.

Flip LHS and RHS.

Defines rule #7.

Referenced by [12].

Overlap of [8] bab=dcd with [11] ba=cdb:

Critical pair: cdbb=dcd.

Reduce LHS:

Defines rule #1.