Certificate for #19054 ⟨a, b | aab=b, babbbb=a⟩

Completion settings:

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

Axiom: aab=b.

Referenced by [3], [4], [5], [11].

Axiom: babbbb=a.

Referenced by [3], [4], [5], [6], [7], [8], [9], [13].

Overlap of [1] aab=b with [2] babbbb=a:

Critical pair: aaa=babbbb.

Reduce RHS:

Referenced by [12].

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

Critical pair: babbba=aabbbb.

Reduce RHS:

Referenced by [5], [6].

Overlap of [2] babbbb=a with [4] babbba=bbbb:

Critical pair: babbbbbbb=aabbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [7], [8], [9], [12].

Overlap of [4] babbba=bbbb with [2] babbbb=a:

Critical pair: babba=bbbbbbbb.

Referenced by [8].

Overlap of [2] babbbb=a with [5] bbba=abbb:

Critical pair: bababbb=aa.

Referenced by [10].

Overlap of [2] babbbb=a with [5] bbba=abbb:

Critical pair: babbabbb=aba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [5] bbba=abbb with [2] babbbb=a:

Critical pair: bba=abbbbbbb.

Referenced by [13].

Simplify [7] bababbb=aa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [11], [12].

Overlap of [1] aab=b with [10] aa=bbbbbbbbbbbbbbb:

Critical pair: bbbbbbbbbbbbbbbb=b.

Defines rule #1.

Overlap of [3] aaa=a with [10] aa=bbbbbbbbbbbbbbb:

Critical pair: bbbbbbbbbbbbbbba=a.

Reduce LHS:

Defines rule #2.

Overlap of [9] bba=abbbbbbb with [2] babbbb=a:

Critical pair: ba=abbbbbbbbbbb.

Defines rule #3.