Certificate for #467 ⟨a, b | abaaab=ba⟩

Completion settings:

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

Axiom: abaaab=ba.

Referenced by [3].

Axiom: aaab=c.

Defines rule #2.

Referenced by [3], [4], [5], [6], [7], [8].

Overlap of [1] abaaab=ba with [2] aaab=c:

Critical pair: abc=ba.

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

Overlap of [2] aaab=c with [3] abc=ba:

Critical pair: aaba=cc.

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

Overlap of [2] aaab=c with [4] aaba=cc:

Critical pair: acc=ca.

Defines rule #1.

Overlap of [4] aaba=cc with [2] aaab=c:

Critical pair: aabc=ccaab.

Reduce LHS:

Referenced by [7], [8].

Overlap of [6] aba=ccaab with [2] aaab=c:

Critical pair: abc=ccaabaab.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [8].

Overlap of [7] ba=ccccab with [2] aaab=c:

Critical pair: bc=ccccabaab.

Reduce RHS:

Defines rule #4.