Certificate for #1835 ⟨a, b | aaaaabaa=ab⟩

Completion settings:

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

Axiom: aaaaabaa=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #5.

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

Simplify [1] aaaaabaa=ab.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaaaabaa=c with [2] ab=c:

Critical pair: aaaacaa=c.

Defines rule #3.

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

Overlap of [4] aaaacaa=c with [2] ab=c:

Critical pair: aaaacac=cb.

Flip LHS and RHS.

Referenced by [8].

Overlap of [4] aaaacaa=c with [4] aaaacaa=c:

Critical pair: aaaacc=caacaa.

Defines rule #1.

Overlap of [4] aaaacaa=c with [4] aaaacaa=c:

Critical pair: aaaacac=caaacaa.

Defines rule #2.

Referenced by [8].

Simplify [5] cb=aaaacac.

Reduce RHS:

Defines rule #4.