Certificate for #47 ⟨a, b, c | bb=aa, bc=1⟩

Completion settings:

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

Axiom: bb=aa.

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

Axiom: bc=1.

Referenced by [4], [6].

Overlap of [1] bb=aa with [1] bb=aa:

Critical pair: baa=aab.

Flip LHS and RHS.

Referenced by [7].

Overlap of [1] bb=aa with [2] bc=1:

Critical pair: b=aac.

Defines rule #4.

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

Overlap of [1] bb=aa with [4] b=aac:

Critical pair: aacb=aa.

Reduce LHS:

Defines rule #3.

Overlap of [2] bc=1 with [4] b=aac:

Critical pair: aacc=1.

Defines rule #1.

Simplify [3] aab=baa.

Reduce LHS:

Reduce RHS:

Defines rule #2.