Certificate for #6272 ⟨a, b | aaa=a, babbb=a⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #3.

Referenced by [4], [7], [8], [10], [11], [13], [15], [16], [17].

Axiom: babbb=a.

Referenced by [3], [5], [6], [7], [9], [11], [12], [13], [14].

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

Critical pair: babba=aabbb.

Referenced by [4], [5], [7], [11], [13], [15].

Overlap of [3] babba=aabbb with [1] aaa=a:

Critical pair: babba=aabbbaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [3] babba=aabbb with [2] babbb=a:

Critical pair: baba=aabbbbbb.

Referenced by [6], [7], [15].

Overlap of [5] baba=aabbbbbb with [2] babbb=a:

Critical pair: baa=aabbbbbbbbb.

Referenced by [10], [13], [15], [16], [17].

Overlap of [5] baba=aabbbbbb with [3] babba=aabbb:

Critical pair: baaabbb=aabbbbbbbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8], [16].

Overlap of [1] aaa=a with [7] aabbbbbbbba=a:

Critical pair: aa=abbbbbbbba.

Flip LHS and RHS.

Referenced by [9], [17].

Overlap of [8] abbbbbbbba=aa with [2] babbb=a:

Critical pair: abbbbbbba=aabbb.

Referenced by [14], [17].

Simplify [4] aabbbaa=aabbb.

Reduce LHS:

Referenced by [11], [12], [13].

Overlap of [3] babba=aabbb with [10] aabbbbbbbbbbbbbbbbbbbbbbbbbbb=aabbb:

Critical pair: babbaabbb=aabbbabbbbbbbbbbbbbbbbbbbbbbbbbbb.

Reduce LHS:

Reduce RHS:

Referenced by [12].

Overlap of [10] aabbbbbbbbbbbbbbbbbbbbbbbbbbb=aabbb with [2] babbb=a:

Critical pair: aabbbbbbbbbbbbbbbbbbbbbbbbbba=aabbbabbb.

Reduce RHS:

Referenced by [13].

Overlap of [10] aabbbbbbbbbbbbbbbbbbbbbbbbbbb=aabbb with [3] babba=aabbb:

Critical pair: aabbbbbbbbbbbbbbbbbbbbbbbbbbaabbb=aabbbabba.

Reduce LHS:

Reduce RHS:

Referenced by [16].

Overlap of [9] abbbbbbba=aabbb with [2] babbb=a:

Critical pair: abbbbbba=aabbbbbb.

Referenced by [15].

Overlap of [3] babba=aabbb with [6] baa=aabbbbbbbbb:

Critical pair: babaabbbbbbbbb=aabbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [17].

Overlap of [6] baa=aabbbbbbbbb with [7] aabbbbbbbba=a:

Critical pair: ba=aabbbbbbbbbbbbbbbbba.

Reduce RHS:

Defines rule #2.

Overlap of [8] abbbbbbbba=aa with [6] baa=aabbbbbbbbb:

Critical pair: abbbbbbbaabbbbbbbbb=aaa.

Reduce LHS:

Reduce RHS:

Defines rule #1.