Certificate for #15941 ⟨a, b | aba=bb, bbabb=a⟩

Completion settings:

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

Axiom: aba=bb.

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

Axiom: bbabb=a.

Referenced by [4], [5], [6], [7], [9].

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

Critical pair: abbb=bbba.

Flip LHS and RHS.

Referenced by [5], [6].

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

Critical pair: bbaa=aabb.

Referenced by [5].

Overlap of [2] bbabb=a with [3] bbba=abbb:

Critical pair: bbaabbb=aba.

Reduce LHS:

Reduce RHS:

Referenced by [8].

Overlap of [3] bbba=abbb with [2] bbabb=a:

Critical pair: ba=abbbbb.

Defines rule #3.

Referenced by [7].

Overlap of [2] bbabb=a with [6] ba=abbbbb:

Critical pair: bbababbbbb=aa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [8].

Simplify [5] aabbbbb=bb.

Reduce LHS:

Defines rule #1.

Referenced by [9].

Overlap of [2] bbabb=a with [8] bbbbbbbbbbbbbb=bb:

Critical pair: bbabb=abbbbbbbbbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.