Certificate for #3248 ⟨a, b, c | bb=aa, abac=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], [5], [9].

Axiom: abac=1.

Referenced by [4], [11].

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

Critical pair: baa=aab.

Flip LHS and RHS.

Referenced by [4], [6], [7], [9].

Overlap of [3] aab=baa with [2] abac=1:

Critical pair: a=baaac.

Flip LHS and RHS.

Referenced by [5], [6], [8].

Overlap of [1] bb=aa with [4] baaac=a:

Critical pair: ba=aaaaac.

Referenced by [6], [7], [8], [9], [10], [11], [12], [13].

Overlap of [3] aab=baa with [4] baaac=a:

Critical pair: aaa=baaaaac.

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [3] aab=baa with [5] ba=aaaaac:

Critical pair: aaaaaaac=baaa.

Reduce RHS:

Defines rule #2.

Overlap of [4] baaac=a with [5] ba=aaaaac:

Critical pair: aaaaacaac=a.

Defines rule #3.

Overlap of [5] ba=aaaaac with [3] aab=baa:

Critical pair: bbaa=aaaaacab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [9] aaaaacab=aaaa with [5] ba=aaaaac:

Critical pair: aaaaacaaaaaac=aaaaa.

Defines rule #5.

Overlap of [2] abac=1 with [5] ba=aaaaac:

Critical pair: aaaaaacc=1.

Defines rule #1.

Referenced by [12].

Overlap of [5] ba=aaaaac with [11] aaaaaacc=1:

Critical pair: b=aaaaacaaaaacc.

Defines rule #7.

Referenced by [13].

Overlap of [5] ba=aaaaac with [12] b=aaaaacaaaaacc:

Critical pair: aaaaacaaaaacca=aaaaac.

Defines rule #6.