Certificate for #4408 ⟨a, b | aaaaabba=aab⟩

Completion settings:

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

Axiom: aaaaabba=aab.

Referenced by [3].

Axiom: aab=c.

Defines rule #1.

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

Simplify [1] aaaaabba=aab.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaaaabba=c with [2] aab=c:

Critical pair: aaacba=c.

Defines rule #6.

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

Overlap of [4] aaacba=c with [2] aab=c:

Critical pair: aaacbc=cab.

Defines rule #3.

Referenced by [6], [7], [8], [9].

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

Critical pair: aaacbc=caacba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [8], [9].

Overlap of [4] aaacba=c with [5] aaacbc=cab:

Critical pair: aaacbcab=caacbc.

Reduce LHS:

Defines rule #2.

Referenced by [8].

Overlap of [5] aaacbc=cab with [6] caacba=cab:

Critical pair: aaacbcab=cabaacba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [6] caacba=cab with [5] aaacbc=cab:

Critical pair: caacbcab=cabaacbc.

Flip LHS and RHS.

Defines rule #5.