Certificate for #3304 ⟨a, b, c | bb=ac, cbaa=1⟩

Completion settings:

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

Axiom: bb=ac.

Defines rule #5.

Referenced by [3], [6], [10].

Axiom: cbaa=1.

Referenced by [4], [5], [12].

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

Critical pair: bac=acb.

Flip LHS and RHS.

Referenced by [4], [5], [7], [10].

Overlap of [2] cbaa=1 with [3] acb=bac:

Critical pair: cbabac=cb.

Referenced by [9].

Overlap of [3] acb=bac with [2] cbaa=1:

Critical pair: a=bacaa.

Flip LHS and RHS.

Referenced by [6], [8].

Overlap of [1] bb=ac with [5] bacaa=a:

Critical pair: ba=acacaa.

Defines rule #3.

Referenced by [7], [8], [9], [10], [11], [12].

Overlap of [3] acb=bac with [6] ba=acacaa:

Critical pair: acacacaa=baca.

Reduce RHS:

Flip LHS and RHS.

Referenced by [8], [10].

Overlap of [5] bacaa=a with [6] ba=acacaa:

Critical pair: acacaacaa=a.

Reduce LHS:

Referenced by [10].

Simplify [4] cbabac=cb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10], [11], [13].

Overlap of [9] cb=cacacaaacacaac with [1] bb=ac:

Critical pair: cac=cacacaaacacaacb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [9] cb=cacacaaacacaac with [6] ba=acacaa:

Critical pair: cacacaa=cacacaaacacaaca.

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [2] cbaa=1 with [6] ba=acacaa:

Critical pair: cacacaaa=1.

Defines rule #2.

Referenced by [13].

Simplify [9] cb=cacacaaacacaac.

Reduce RHS:

Defines rule #4.