Certificate for #972 ⟨a, b | abaaaba=ab⟩

Completion settings:

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

Axiom: abaaaba=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #5.

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

Simplify [1] abaaaba=ab.

Reduce RHS:

Referenced by [4].

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

Critical pair: caaaba=c.

Reduce LHS:

Referenced by [5], [6], [8], [9].

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

Critical pair: caacc=cb.

Flip LHS and RHS.

Referenced by [7].

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

Critical pair: caac=caca.

Referenced by [7], [8], [9], [11], [12].

Simplify [5] cb=caacc.

Reduce RHS:

Referenced by [11].

Overlap of [4] caaca=c with [6] caac=caca:

Critical pair: cacaa=c.

Referenced by [9], [10].

Overlap of [4] caaca=c with [6] caac=caca:

Critical pair: caacaca=cac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [10], [11], [12].

Simplify [8] cacaa=c.

Reduce LHS:

Defines rule #3.

Simplify [7] cb=cacac.

Reduce RHS:

Defines rule #4.

Simplify [6] caac=caca.

Reduce RHS:

Defines rule #2.