Certificate for #16189 ⟨a, b | aab=ab, babb=aa⟩

Completion settings:

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

Axiom: aab=ab.

Referenced by [3].

Axiom: babb=aa.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4], [5], [6], [8], [9].

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

Critical pair: babbb=ab.

Referenced by [5], [6], [7], [8], [9], [10], [11], [12], [14].

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

Critical pair: ababb=babba.

Referenced by [5], [6], [8], [13].

Overlap of [4] ababb=babba with [3] babbb=ab:

Critical pair: aab=babbab.

Reduce LHS:

Flip LHS and RHS.

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

Overlap of [4] ababb=babba with [3] babbb=ab:

Critical pair: ababab=babbaabbb.

Reduce RHS:

Referenced by [8].

Overlap of [5] babbab=ab with [3] babbb=ab:

Critical pair: babab=abbb.

Referenced by [8], [9].

Overlap of [4] ababb=babba with [7] babab=abbb:

Critical pair: abababbb=babbaabab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [10], [12].

Overlap of [7] babab=abbb with [7] babab=abbb:

Critical pair: baabbb=abbbab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [3] babbb=ab with [9] abbbab=ab:

Critical pair: bab=abab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [3] babbb=ab with [10] abbbbb=bab:

Critical pair: bbab=abbb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [12], [14], [15].

Simplify [8] abab=abbbbb.

Reduce RHS:

Defines rule #5.

Referenced by [13], [15].

Overlap of [4] ababb=babba with [12] abab=bab:

Critical pair: babb=babba.

Flip LHS and RHS.

Referenced by [15].

Overlap of [3] babbb=ab with [11] abbb=bbab:

Critical pair: bbbab=ab.

Defines rule #1.

Referenced by [15].

Overlap of [11] abbb=bbab with [13] babba=babb:

Critical pair: abbbabb=bbababba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.