Certificate for #16298 ⟨a, b | aab=bb, abba=ab⟩

Completion settings:

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

Axiom: aab=bb.

Defines rule #4.

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

Axiom: abba=ab.

Referenced by [3], [4], [7], [9].

Overlap of [1] aab=bb with [2] abba=ab:

Critical pair: aab=bbba.

Reduce LHS:

Flip LHS and RHS.

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

Overlap of [2] abba=ab with [1] aab=bb:

Critical pair: abbbb=abab.

Flip LHS and RHS.

Referenced by [9].

Overlap of [3] bbba=bb with [1] aab=bb:

Critical pair: bbbbb=bbab.

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [1] aab=bb with [5] bbab=bbbbb:

Critical pair: aabbbbb=bbbab.

Reduce LHS:

Reduce RHS:

Referenced by [7].

Overlap of [5] bbab=bbbbb with [2] abba=ab:

Critical pair: bbab=bbbbbba.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [8], [9].

Overlap of [7] bbbbb=bb with [3] bbba=bb:

Critical pair: bbbb=bba.

Flip LHS and RHS.

Defines rule #3.

Overlap of [4] abab=abbbb with [2] abba=ab:

Critical pair: abab=abbbbba.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Referenced by [10].

Overlap of [9] abbbb=ab with [3] bbba=bb:

Critical pair: abbb=aba.

Flip LHS and RHS.

Defines rule #5.