Certificate for #2581 ⟨a, b | abaaba=aaba⟩

Completion settings:

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

Axiom: abaaba=aaba.

Referenced by [3].

Axiom: aaba=c.

Defines rule #6.

Referenced by [3], [4], [5], [6], [7].

Simplify [1] abaaba=aaba.

Reduce RHS:

Referenced by [4].

Overlap of [3] abaaba=c with [2] aaba=c:

Critical pair: abc=c.

Defines rule #4.

Referenced by [5], [6], [7], [9].

Overlap of [2] aaba=c with [2] aaba=c:

Critical pair: aabc=caba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [2] aaba=c with [4] abc=c:

Critical pair: aabc=cbc.

Reduce LHS:

Defines rule #3.

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

Overlap of [2] aaba=c with [6] ac=cbc:

Critical pair: aabcbc=cc.

Reduce LHS:

Defines rule #2.

Simplify [5] caba=ac.

Reduce RHS:

Defines rule #5.

Referenced by [9].

Overlap of [8] caba=cbc with [6] ac=cbc:

Critical pair: cabcbc=cbcc.

Reduce LHS:

Defines rule #1.