Certificate for #2068 ⟨a, b | ababbbba=ab⟩

Completion settings:

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

Axiom: ababbbba=ab.

Referenced by [3].

Axiom: abbbb=c.

Defines rule #6.

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

Overlap of [1] ababbbba=ab with [2] abbbb=c:

Critical pair: abca=ab.

Defines rule #2.

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

Overlap of [3] abca=ab with [3] abca=ab:

Critical pair: abcab=abbca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [6], [7].

Overlap of [3] abca=ab with [2] abbbb=c:

Critical pair: abcc=abbbbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [3] abca=ab with [4] abbca=abb:

Critical pair: abcabb=abbbca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [4] abbca=abb with [4] abbca=abb:

Critical pair: abbcabb=abbbbca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.