Certificate for #2036 ⟨a, b | abaabaab=ba⟩

Completion settings:

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

Axiom: abaabaab=ba.

Referenced by [3].

Axiom: aab=c.

Defines rule #2.

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

Overlap of [1] abaabaab=ba with [2] aab=c:

Critical pair: abcaab=ba.

Reduce LHS:

Referenced by [4], [7].

Overlap of [2] aab=c with [3] abcc=ba:

Critical pair: aba=ccc.

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

Overlap of [2] aab=c with [4] aba=ccc:

Critical pair: accc=ca.

Defines rule #1.

Overlap of [4] aba=ccc with [2] aab=c:

Critical pair: abc=cccab.

Referenced by [7].

Overlap of [3] abcc=ba with [6] abc=cccab:

Critical pair: cccabc=ba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [8].

Overlap of [7] ba=ccccccab with [2] aab=c:

Critical pair: bc=ccccccabab.

Reduce RHS:

Defines rule #4.