Certificate for #12157 ⟨a, b | aaaa=aa, abba=b⟩

Completion settings:

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

Axiom: aaaa=aa.

Defines rule #4.

Referenced by [4], [5].

Axiom: abba=b.

Referenced by [3], [4], [5], [6], [7], [8], [9], [10].

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

Critical pair: abbb=bbba.

Flip LHS and RHS.

Referenced by [10], [11].

Overlap of [1] aaaa=aa with [2] abba=b:

Critical pair: aaab=aabba.

Reduce RHS:

Referenced by [6].

Overlap of [2] abba=b with [1] aaaa=aa:

Critical pair: abbaa=baaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [4] aaab=ab with [2] abba=b:

Critical pair: aab=abba.

Reduce RHS:

Defines rule #3.

Referenced by [7], [10], [12].

Overlap of [6] aab=b with [2] abba=b:

Critical pair: ab=bba.

Flip LHS and RHS.

Referenced by [11].

Overlap of [2] abba=b with [5] baaa=ba:

Critical pair: abba=baa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [2] abba=b with [8] baa=b:

Critical pair: abb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [10].

Overlap of [9] ba=abb with [2] abba=b:

Critical pair: bb=abbbba.

Reduce RHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [10] bbbbb=bb with [7] bba=ab:

Critical pair: bbbab=bba.

Reduce LHS:

Reduce RHS:

Referenced by [12].

Overlap of [6] aab=b with [11] abbbb=ab:

Critical pair: aab=bbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.