Certificate for #14843 ⟨a, b | abba=b, aabab=a⟩

Completion settings:

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

Axiom: abba=b.

Referenced by [3], [4], [6], [9], [10], [11].

Axiom: aabab=a.

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

Overlap of [1] abba=b with [2] aabab=a:

Critical pair: abba=babab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [5].

Overlap of [2] aabab=a with [1] abba=b:

Critical pair: aabb=aba.

Flip LHS and RHS.

Referenced by [5], [6], [11], [12].

Simplify [3] babab=b.

Reduce LHS:

Referenced by [6], [8].

Overlap of [4] aba=aabb with [5] baabbb=b:

Critical pair: ab=aabbabbb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [7], [8].

Overlap of [2] aabab=a with [6] abbbb=ab:

Critical pair: aabab=abbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [9], [10], [13].

Overlap of [5] baabbb=b with [6] abbbb=ab:

Critical pair: baab=bb.

Referenced by [10].

Overlap of [1] abba=b with [7] abbb=a:

Critical pair: abba=bbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [1] abba=b with [8] baab=bb:

Critical pair: abbb=bab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11], [12], [13].

Overlap of [1] abba=b with [10] bab=a:

Critical pair: aba=bb.

Reduce LHS:

Referenced by [12].

Overlap of [4] aba=aabb with [10] bab=a:

Critical pair: aa=aabbb.

Reduce RHS:

Defines rule #4.

Overlap of [10] bab=a with [7] abbb=a:

Critical pair: ba=abb.

Defines rule #3.