Certificate for #19826 ⟨a, b | aaa=a, abbb=bba⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(b) = 0; deg(a) = 1

Axiom: aaa=a.

Defines rule #4.

Referenced by [3], [7], [9].

Axiom: abbb=bba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4], [5], [6], [8], [9].

Overlap of [2] bba=abbb with [1] aaa=a:

Critical pair: bba=abbbaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

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

Overlap of [2] bba=abbb with [3] abababbb=abbb:

Critical pair: bbabbb=abbbbababbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [3] abababbb=abbb with [2] bba=abbb:

Critical pair: abababbabbb=abbbba.

Reduce LHS:

Reduce RHS:

Referenced by [6].

Overlap of [2] bba=abbb with [5] ababaabbbbbb=aabbbbbb:

Critical pair: bbaabbbbbb=abbbbabaabbbbbb.

Reduce LHS:

Reduce RHS:

Referenced by [7], [8].

Simplify [4] aababbbbbbbbbbbb=abbbbbb.

Reduce LHS:

Defines rule #1.

Referenced by [8], [9], [10].

Overlap of [2] bba=abbb with [6] ababbbbbbbbb=aabbbbbbbbbbbbbbbbbb:

Critical pair: bbaabbbbbbbbbbbbbbbbbb=abbbbabbbbbbbbb.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [9].

Overlap of [8] ababbbbbb=aabbbbbbbbbbbbbbb with [2] bba=abbb:

Critical pair: ababbbbabbb=aabbbbbbbbbbbbbbba.

Reduce LHS:

Reduce RHS:

Referenced by [10].

Overlap of [9] abaabbbbbbbbb=abbbbbbbbbbbbbbb with [7] abbbbbbbbbbbbbbbbbbbbb=abbbbbb:

Critical pair: abaabbbbbb=abbbbbbbbbbbbbbbbbbbbbbbbbbb.

Reduce RHS:

Defines rule #5.