Certificate for #4749 ⟨a, b | abba=b, baab=a⟩

Completion settings:

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

Axiom: abba=b.

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

Axiom: baab=a.

Defines rule #6.

Referenced by [3], [5], [7].

Overlap of [2] baab=a with [2] baab=a:

Critical pair: baaa=aaab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [7].

Overlap of [1] abba=b with [1] abba=b:

Critical pair: abbb=bbba.

Referenced by [7].

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

Critical pair: aba=bab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [6].

Overlap of [1] abba=b with [5] bab=aba:

Critical pair: ababa=bb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [7].

Overlap of [1] abba=b with [3] aaab=baaa:

Critical pair: abbbaaa=baab.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [8].

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

Critical pair: abba=baaaaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.