Certificate for #4626 ⟨a, b | aaaa=a, baab=a⟩

Completion settings:

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

Axiom: aaaa=a.

Defines rule #2.

Referenced by [8], [9].

Axiom: baab=a.

Referenced by [4].

Axiom: ab=c.

Defines rule #7.

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

Overlap of [2] baab=a with [3] ab=c:

Critical pair: bac=a.

Referenced by [5], [6].

Overlap of [3] ab=c with [4] bac=a:

Critical pair: aa=cac.

Flip LHS and RHS.

Defines rule #1.

Referenced by [6], [7].

Overlap of [4] bac=a with [5] cac=aa:

Critical pair: baaa=aac.

Referenced by [9], [10].

Overlap of [5] cac=aa with [5] cac=aa:

Critical pair: caaa=aaac.

Referenced by [11].

Overlap of [1] aaaa=a with [3] ab=c:

Critical pair: aaac=ab.

Reduce RHS:

Defines rule #3.

Referenced by [10], [11].

Overlap of [6] baaa=aac with [1] aaaa=a:

Critical pair: ba=aaca.

Defines rule #5.

Overlap of [6] baaa=aac with [8] aaac=c:

Critical pair: bc=aacc.

Defines rule #6.

Simplify [7] caaa=aaac.

Reduce RHS:

Defines rule #4.

Referenced by [12].

Overlap of [11] caaa=c with [3] ab=c:

Critical pair: caac=cb.

Flip LHS and RHS.

Defines rule #8.