Certificate for #16333 ⟨a, b | aab=bb, bbbb=aa⟩

Completion settings:

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

Axiom: aab=bb.

Referenced by [3].

Axiom: bbbb=aa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4].

Overlap of [1] aab=bb with [2] aa=bbbb:

Critical pair: bbbbb=bb.

Defines rule #1.

Referenced by [5], [6], [7], [8].

Overlap of [2] aa=bbbb with [2] aa=bbbb:

Critical pair: abbbb=bbbba.

Flip LHS and RHS.

Referenced by [5], [6].

Overlap of [3] bbbbb=bb with [4] bbbba=abbbb:

Critical pair: babbbb=bba.

Flip LHS and RHS.

Referenced by [6], [7], [8].

Overlap of [3] bbbbb=bb with [5] bba=babbbb:

Critical pair: bbbbabbbb=bba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [5] bba=babbbb with [6] babbbb=abb:

Critical pair: babb=babbbbbbbb.

Reduce RHS:

Defines rule #2.

Referenced by [8].

Simplify [5] bba=babbbb.

Reduce RHS:

Defines rule #3.