Certificate for #3865 ⟨a, b | aaaaabaaa=ab⟩

Completion settings:

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

Axiom: aaaaabaaa=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #6.

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

Simplify [1] aaaaabaaa=ab.

Reduce RHS:

Referenced by [4].

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

Critical pair: aaaacaaa=c.

Defines rule #4.

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

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

Critical pair: aaaacaac=cb.

Flip LHS and RHS.

Referenced by [9].

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

Critical pair: aaaacc=cacaaa.

Defines rule #1.

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

Critical pair: aaaacac=caacaaa.

Defines rule #2.

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

Critical pair: aaaacaac=caaacaaa.

Defines rule #3.

Referenced by [9].

Simplify [5] cb=aaaacaac.

Reduce RHS:

Defines rule #5.