Certificate for #12571 ⟨a, b | abba=ab, baaa=b⟩

Completion settings:

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

Axiom: abba=ab.

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

Axiom: baaa=b.

Defines rule #5.

Referenced by [3], [4].

Overlap of [2] baaa=b with [1] abba=ab:

Critical pair: baaab=bbba.

Reduce LHS:

Flip LHS and RHS.

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

Overlap of [3] bbba=bb with [2] baaa=b:

Critical pair: bbb=bbaa.

Flip LHS and RHS.

Referenced by [5], [6].

Overlap of [1] abba=ab with [4] bbaa=bbb:

Critical pair: abbb=aba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [7], [8].

Overlap of [3] bbba=bb with [4] bbaa=bbb:

Critical pair: bbbb=bba.

Flip LHS and RHS.

Defines rule #3.

Overlap of [1] abba=ab with [5] aba=abbb:

Critical pair: abbabbb=abba.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Overlap of [3] bbba=bb with [5] aba=abbb:

Critical pair: bbbabbb=bbba.

Reduce LHS:

Reduce RHS:

Defines rule #1.