Certificate for #24142 ⟨a, b | aa=a, abbbbab=a⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with a < b

Axiom: aa=a.

Defines rule #1.

Referenced by [8], [11].

Axiom: abbbbab=a.

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

Overlap of [2] abbbbab=a with [2] abbbbab=a:

Critical pair: abbbba=abbbab.

Referenced by [4], [5], [7], [9], [11], [13].

Overlap of [2] abbbbab=a with [3] abbbba=abbbab:

Critical pair: abbbabb=a.

Referenced by [5], [6].

Overlap of [2] abbbbab=a with [3] abbbba=abbbab:

Critical pair: abbbbabbbab=abbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [7], [8], [9], [13], [14].

Simplify [4] abbbabb=a.

Reduce LHS:

Referenced by [7], [8], [9], [10].

Overlap of [2] abbbbab=a with [6] abbabbb=a:

Critical pair: abbbba=ababbb.

Reduce LHS:

Referenced by [8], [9].

Overlap of [6] abbabbb=a with [5] abbba=abbab:

Critical pair: abbabbab=aa.

Reduce LHS:

Reduce RHS:

Referenced by [9].

Overlap of [5] abbba=abbab with [6] abbabbb=a:

Critical pair: abbba=abbabbbabbb.

Reduce LHS:

Reduce RHS:

Referenced by [10], [11].

Overlap of [6] abbabbb=a with [9] abbab=abbb:

Critical pair: abbbbb=a.

Defines rule #6.

Referenced by [11].

Overlap of [9] abbab=abbb with [3] abbbba=abbbab:

Critical pair: abbabbbab=abbbbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [12].

Overlap of [11] aba=ab with [11] aba=ab:

Critical pair: abab=abba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [13], [14].

Simplify [3] abbbba=abbbab.

Reduce RHS:

Defines rule #5.

Simplify [5] abbba=abbab.

Reduce RHS:

Defines rule #4.