Certificate for #12932 ⟨a, b | aba=aab, aaaa=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: aba=aab.

Flip LHS and RHS.

Referenced by [4].

Axiom: aaaa=a.

Defines rule #2.

Referenced by [7].

Axiom: ab=c.

Defines rule #4.

Referenced by [4], [5], [6], [7].

Simplify [1] aab=aba.

Reduce RHS:

Referenced by [5].

Overlap of [4] aab=ca with [3] ab=c:

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [6].

Overlap of [5] ca=ac with [3] ab=c:

Critical pair: cc=acb.

Flip LHS and RHS.

Referenced by [8].

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

Critical pair: aaac=ab.

Reduce RHS:

Defines rule #3.

Referenced by [8].

Overlap of [7] aaac=c with [6] acb=cc:

Critical pair: aacc=cb.

Flip LHS and RHS.

Defines rule #5.