Certificate for #18756 ⟨a, b | aaa=a, bbabbb=a⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #4.

Referenced by [5], [9], [10].

Axiom: bbabbb=a.

Referenced by [3], [4], [5], [7], [8], [11], [12], [14], [15].

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

Critical pair: bbaba=aabbb.

Referenced by [5], [6], [8], [9], [13].

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

Critical pair: bbabba=ababbb.

Referenced by [5], [15].

Overlap of [4] bbabba=ababbb with [3] bbaba=aabbb:

Critical pair: bbaaabbb=ababbbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [3] bbaba=aabbb with [5] ababbbba=a:

Critical pair: bba=aabbbbbbba.

Flip LHS and RHS.

Referenced by [15], [16].

Overlap of [5] ababbbba=a with [2] bbabbb=a:

Critical pair: ababba=abbb.

Referenced by [8], [9].

Overlap of [3] bbaba=aabbb with [7] ababba=abbb:

Critical pair: bbabbb=aabbbbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10], [11].

Overlap of [7] ababba=abbb with [3] bbaba=aabbb:

Critical pair: abaaabbb=abbbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [15].

Overlap of [1] aaa=a with [8] aabbbbba=a:

Critical pair: aa=abbbbba.

Flip LHS and RHS.

Referenced by [12].

Overlap of [8] aabbbbba=a with [2] bbabbb=a:

Critical pair: aabbba=abbb.

Referenced by [13].

Overlap of [10] abbbbba=aa with [2] bbabbb=a:

Critical pair: abbba=aabbb.

Referenced by [13], [14], [15].

Overlap of [3] bbaba=aabbb with [12] abbba=aabbb:

Critical pair: bbabaabbb=aabbbbbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [15], [16].

Overlap of [12] abbba=aabbb with [2] bbabbb=a:

Critical pair: aba=aabbbbbb.

Defines rule #3.

Referenced by [15], [16].

Overlap of [4] bbabba=ababbb with [14] aba=aabbbbbb:

Critical pair: bbabbaabbbbbb=ababbbba.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Overlap of [14] aba=aabbbbbb with [14] aba=aabbbbbb:

Critical pair: abaabbbbbb=aabbbbbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.