Certificate for #3928 ⟨a, b | aaaabbaaa=ab⟩

Completion settings:

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

Axiom: aaaabbaaa=ab.

Referenced by [3].

Axiom: abb=c.

Referenced by [3], [4].

Overlap of [1] aaaabbaaa=ab with [2] abb=c:

Critical pair: aaacaaa=ab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [4], [5].

Overlap of [2] abb=c with [3] ab=aaacaaa:

Critical pair: aaacaaab=c.

Reduce LHS:

Defines rule #4.

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

Overlap of [4] aaacaaaaacaaa=c with [3] ab=aaacaaa:

Critical pair: aaacaaaaacaaaaacaaa=cb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

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

Critical pair: aaacaac=caacaaa.

Flip LHS and RHS.

Defines rule #1.

Referenced by [9].

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

Critical pair: aaacaaaaacc=ccaaaaacaaa.

Flip LHS and RHS.

Defines rule #2.

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

Critical pair: aaacaaaaacac=cacaaaaacaaa.

Flip LHS and RHS.

Defines rule #3.

Simplify [5] cb=caacaaa.

Reduce RHS:

Defines rule #6.