Certificate for #4555 ⟨a, b | aaabbaba=bba⟩

Completion settings:

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

Axiom: aaabbaba=bba.

Referenced by [3].

Axiom: bba=c.

Defines rule #3.

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

Simplify [1] aaabbaba=bba.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaabbaba=c with [2] bba=c:

Critical pair: aaacba=c.

Defines rule #1.

Referenced by [5], [6].

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

Critical pair: bbc=caacba.

Referenced by [7].

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

Critical pair: aaacbc=caacba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

Simplify [5] bbc=caacba.

Reduce RHS:

Defines rule #4.