Certificate for #19021 ⟨a, b | aab=b, abbbba=b⟩

Completion settings:

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

Axiom: aab=b.

Defines rule #3.

Referenced by [3], [4], [5], [8], [9], [10].

Axiom: abbbba=b.

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

Overlap of [1] aab=b with [2] abbbba=b:

Critical pair: ab=bbbba.

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [2] abbbba=b with [1] aab=b:

Critical pair: abbbbb=bab.

Flip LHS and RHS.

Referenced by [5], [6], [7], [9].

Overlap of [2] abbbba=b with [4] bab=abbbbb:

Critical pair: abbbabbbbb=bb.

Reduce LHS:

Referenced by [6].

Overlap of [5] bbbbbbbbbbbbbbbbb=bb with [3] bbbba=ab:

Critical pair: bbbbbbbbbbbbbab=bba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7], [9].

Overlap of [3] bbbba=ab with [6] bba=abbbbbbbb:

Critical pair: bbabbbbbbbb=ab.

Reduce LHS:

Referenced by [8], [9].

Overlap of [1] aab=b with [7] abbbbbbbbbbbbbbbb=ab:

Critical pair: aab=bbbbbbbbbbbbbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [9].

Overlap of [7] abbbbbbbbbbbbbbbb=ab with [6] bba=abbbbbbbb:

Critical pair: abbbbbbbbbbbbbbabbbbbbbb=aba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [1] aab=b with [9] aba=bbbb:

Critical pair: abbbb=ba.

Flip LHS and RHS.

Defines rule #2.