Certificate for #20096 ⟨a, b | aab=b, abba=aaa⟩

Completion settings:

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

Axiom: aab=b.

Referenced by [3], [4], [5], [6], [7], [8], [9].

Axiom: abba=aaa.

Flip LHS and RHS.

Referenced by [3], [4], [9], [12].

Overlap of [2] aaa=abba with [1] aab=b:

Critical pair: ab=abbab.

Flip LHS and RHS.

Referenced by [5].

Overlap of [2] aaa=abba with [2] aaa=abba:

Critical pair: aabba=abbaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [1] aab=b with [3] abbab=ab:

Critical pair: aab=bbab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7], [9].

Overlap of [1] aab=b with [4] abbaa=bba:

Critical pair: abba=bbaa.

Flip LHS and RHS.

Referenced by [10].

Overlap of [4] abbaa=bba with [1] aab=b:

Critical pair: abbb=bbab.

Reduce RHS:

Referenced by [8], [9], [11].

Overlap of [1] aab=b with [7] abbb=b:

Critical pair: ab=bbb.

Defines rule #2.

Referenced by [9], [10], [11], [12].

Overlap of [2] aaa=abba with [7] abbb=b:

Critical pair: aab=abbabbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [11].

Simplify [6] bbaa=abba.

Reduce RHS:

Referenced by [11].

Overlap of [7] abbb=b with [10] bbaa=bbbba:

Critical pair: abbbbba=baa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Simplify [2] aaa=abba.

Reduce RHS:

Defines rule #4.