Certificate for #1851 ⟨a, b | aaaabaaa=ab⟩

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: aaaabaaa=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #5.

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

Simplify [1] aaaabaaa=ab.

Reduce RHS:

Referenced by [4].

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

Critical pair: aaacaaa=c.

Defines rule #3.

Referenced by [5], [6], [7], [8].

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

Critical pair: aaacaac=cb.

Flip LHS and RHS.

Defines rule #6.

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

Critical pair: aaacc=ccaaa.

Flip LHS and RHS.

Defines rule #1.

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

Critical pair: aaacac=cacaaa.

Flip LHS and RHS.

Defines rule #2.

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

Critical pair: aaacaac=caacaaa.

Flip LHS and RHS.

Defines rule #4.