Certificate for #1983 ⟨a, b | aabbaaab=ba⟩

Completion settings:

• Auxiliary generators:
  1. c = ba
  2. d = ab
• Reduction order:
  • Right-to-left recursive path with deg(c) = deg(d) = 0, c < d; deg(a) = deg(b) = 1, a < b

Axiom: aabbaaab=ba.

Referenced by [4].

Axiom: ba=c.

Defines rule #6.

Referenced by [4], [5], [6], [7], [8].

Axiom: ab=d.

Defines rule #7.

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

Simplify [1] aabbaaab=ba.

Reduce RHS:

Referenced by [5].

Overlap of [4] aabbaaab=c with [3] ab=d:

Critical pair: adbaaab=c.

Reduce LHS:

Defines rule #5.

Referenced by [8], [9].

Overlap of [2] ba=c with [3] ab=d:

Critical pair: bd=cb.

Defines rule #4.

Overlap of [3] ab=d with [2] ba=c:

Critical pair: ac=da.

Defines rule #1.

Overlap of [2] ba=c with [5] adcad=c:

Critical pair: bc=cdcad.

Defines rule #3.

Overlap of [5] adcad=c with [5] adcad=c:

Critical pair: adcc=ccad.

Defines rule #2.