Certificate for #20318 ⟨a, b | aba=b, bbbb=bab⟩

Completion settings:

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

Axiom: aba=b.

Defines rule #5.

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

Axiom: bbbb=bab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5].

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

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [5], [8].

Overlap of [1] aba=b with [2] bab=bbbb:

Critical pair: abbbb=bb.

Referenced by [6].

Overlap of [3] bba=abb with [2] bab=bbbb:

Critical pair: bbbbb=abbb.

Flip LHS and RHS.

Referenced by [6], [7].

Simplify [4] abbbb=bb.

Reduce LHS:

Defines rule #1.

Referenced by [7].

Overlap of [1] aba=b with [5] abbb=bbbbb:

Critical pair: abbbbbb=bbbb.

Reduce LHS:

Defines rule #2.

Referenced by [8].

Simplify [3] bba=abb.

Reduce RHS:

Defines rule #4.