Certificate for #6682 ⟨a, b, c | aa=1, abcba=b⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #3.

Referenced by [3], [4], [6].

Axiom: abcba=b.

Referenced by [3], [4].

Overlap of [1] aa=1 with [2] abcba=b:

Critical pair: ab=bcba.

Flip LHS and RHS.

Referenced by [5].

Overlap of [2] abcba=b with [1] aa=1:

Critical pair: abcb=ba.

Flip LHS and RHS.

Defines rule #1.

Referenced by [5].

Simplify [3] bcba=ab.

Reduce LHS:

Defines rule #2.

Referenced by [6].

Overlap of [5] bcabcb=ab with [5] bcabcb=ab:

Critical pair: bcabcab=abcabcb.

Reduce RHS:

Defines rule #4.