Certificate for #19831 ⟨a, b | aaa=a, baab=abb⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #1.

Referenced by [5].

Axiom: baab=abb.

Referenced by [4].

Axiom: abb=c.

Defines rule #8.

Referenced by [4], [5], [7], [8], [10].

Simplify [2] baab=abb.

Reduce RHS:

Defines rule #9.

Referenced by [6], [7], [8], [9].

Overlap of [1] aaa=a with [3] abb=c:

Critical pair: aac=abb.

Reduce RHS:

Defines rule #2.

Referenced by [6], [9].

Overlap of [4] baab=c with [4] baab=c:

Critical pair: baac=caab.

Reduce LHS:

Defines rule #6.

Referenced by [8].

Overlap of [4] baab=c with [3] abb=c:

Critical pair: bac=cb.

Defines rule #7.

Overlap of [3] abb=c with [4] baab=c:

Critical pair: abc=caab.

Reduce LHS:

Defines rule #5.

Referenced by [9], [10].

Overlap of [8] acaab=caab with [4] baab=c:

Critical pair: acaac=caabaab.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Overlap of [8] acaab=caab with [3] abb=c:

Critical pair: acac=caabb.

Reduce RHS:

Defines rule #4.