Certificate for #12597 ⟨a, b | abba=bb, baab=b⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with a < b

Axiom: abba=bb.

Referenced by [3], [4], [5], [6], [10], [11].

Axiom: baab=b.

Defines rule #4.

Referenced by [3], [4], [8].

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

Critical pair: abb=bbab.

Flip LHS and RHS.

Referenced by [7], [9].

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

Critical pair: babb=bba.

Referenced by [5], [7], [9], [12].

Overlap of [4] babb=bba with [1] abba=bb:

Critical pair: bbb=bbaa.

Flip LHS and RHS.

Referenced by [6], [7], [8], [10].

Overlap of [1] abba=bb with [5] bbaa=bbb:

Critical pair: abbb=bba.

Referenced by [9].

Overlap of [4] babb=bba with [5] bbaa=bbb:

Critical pair: babbb=bbaaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [5] bbaa=bbb with [2] baab=b:

Critical pair: bb=bbbb.

Flip LHS and RHS.

Referenced by [9], [10].

Overlap of [8] bbbb=bb with [4] babb=bba:

Critical pair: bbbbba=bbabb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [10], [11], [12].

Overlap of [8] bbbb=bb with [5] bbaa=bbb:

Critical pair: bbbbb=bbaa.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Overlap of [1] abba=bb with [9] bba=abb:

Critical pair: aabb=bb.

Defines rule #3.

Simplify [4] babb=bba.

Reduce RHS:

Defines rule #5.