Certificate for #16465 ⟨a, b | aba=bb, baab=bb⟩

Completion settings:

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

Axiom: aba=bb.

Defines rule #6.

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

Axiom: baab=bb.

Defines rule #7.

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

Overlap of [1] aba=bb with [2] baab=bb:

Critical pair: abb=bbab.

Flip LHS and RHS.

Referenced by [6].

Overlap of [2] baab=bb with [1] aba=bb:

Critical pair: babb=bba.

Flip LHS and RHS.

Referenced by [5], [6], [8], [10].

Overlap of [4] bba=babb with [2] baab=bb:

Critical pair: bbb=babbab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Simplify [3] bbab=abb.

Reduce LHS:

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

Overlap of [1] aba=bb with [6] babbb=abb:

Critical pair: aabb=bbbbb.

Defines rule #5.

Overlap of [4] bba=babb with [6] babbb=abb:

Critical pair: babb=babbbbb.

Reduce RHS:

Defines rule #3.

Referenced by [9], [10].

Overlap of [6] babbb=abb with [8] babb=abbbb:

Critical pair: abbbbb=abb.

Defines rule #2.

Simplify [4] bba=babb.

Reduce RHS:

Defines rule #4.