Certificate for #16197 ⟨a, b | aab=ab, bbab=aa⟩

Completion settings:

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

Axiom: aab=ab.

Referenced by [3].

Axiom: bbab=aa.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4], [5], [6], [7].

Overlap of [1] aab=ab with [2] aa=bbab:

Critical pair: bbabb=ab.

Referenced by [5], [6], [7], [8], [9], [10], [11].

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

Critical pair: abbab=bbaba.

Referenced by [6], [8].

Overlap of [3] bbabb=ab with [3] bbabb=ab:

Critical pair: bbaab=ababb.

Reduce LHS:

Flip LHS and RHS.

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

Overlap of [2] aa=bbab with [5] ababb=bbab:

Critical pair: abbab=bbabbabb.

Reduce LHS:

Reduce RHS:

Referenced by [7], [8], [10].

Overlap of [5] ababb=bbab with [3] bbabb=ab:

Critical pair: abaab=bbababb.

Reduce LHS:

Reduce RHS:

Referenced by [8].

Overlap of [5] ababb=bbab with [3] bbabb=ab:

Critical pair: ababab=bbabbabb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [9], [10].

Overlap of [3] bbabb=ab with [8] abbb=bbab:

Critical pair: bbbbab=abb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [10], [11].

Overlap of [8] abbb=bbab with [6] bbaba=bbab:

Critical pair: abbbab=bbababa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [3] bbabb=ab with [9] abb=bbbbab:

Critical pair: bbbbbbab=ab.

Defines rule #1.