Certificate for #16358 ⟨a, b | aba=aa, abba=bb⟩

Completion settings:

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

Axiom: aba=aa.

Defines rule #1.

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

Axiom: abba=bb.

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

Overlap of [1] aba=aa with [2] abba=bb:

Critical pair: abbb=aabba.

Reduce RHS:

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

Overlap of [2] abba=bb with [1] aba=aa:

Critical pair: abbaa=bbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [5].

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

Critical pair: abbbb=bbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [6], [8], [9].

Overlap of [5] bba=abb with [2] abba=bb:

Critical pair: bbbb=abbbba.

Reduce RHS:

Referenced by [7].

Overlap of [2] abba=bb with [3] abbb=abb:

Critical pair: abbabb=bbbbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [9].

Overlap of [3] abbb=abb with [5] bba=abb:

Critical pair: ababb=abba.

Reduce LHS:

Reduce RHS:

Defines rule #4.

Overlap of [7] bbb=bb with [5] bba=abb:

Critical pair: babb=bba.

Reduce RHS:

Defines rule #5.