Certificate for #19287 ⟨a, b | aaa=a, baabb=aa⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #1.

Referenced by [3], [4], [5], [6], [7], [8], [9], [10], [13].

Axiom: baabb=aa.

Referenced by [3], [4], [6], [8], [10], [11], [13].

Overlap of [2] baabb=aa with [2] baabb=aa:

Critical pair: baabaa=aaaabb.

Reduce RHS:

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

Overlap of [2] baabb=aa with [3] baabaa=aabb:

Critical pair: baabaabb=aaaabaa.

Reduce LHS:

Reduce RHS:

Referenced by [6].

Overlap of [3] baabaa=aabb with [1] aaa=a:

Critical pair: baaba=aabba.

Flip LHS and RHS.

Referenced by [12].

Overlap of [3] baabaa=aabb with [2] baabb=aa:

Critical pair: baaaa=aabbbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [6] aabaa=baa with [1] aaa=a:

Critical pair: aaba=baaa.

Reduce RHS:

Defines rule #4.

Referenced by [8], [12].

Overlap of [3] baabaa=aabb with [7] aaba=ba:

Critical pair: baabba=aabbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [1] aaa=a with [8] aabbba=a:

Critical pair: aa=abbba.

Flip LHS and RHS.

Referenced by [10].

Overlap of [9] abbba=aa with [2] baabb=aa:

Critical pair: abbaa=aaabb.

Reduce RHS:

Defines rule #6.

Referenced by [11], [14].

Overlap of [10] abbaa=abb with [2] baabb=aa:

Critical pair: abaa=abbbb.

Flip LHS and RHS.

Defines rule #5.

Simplify [5] aabba=baaba.

Reduce RHS:

Referenced by [13], [14].

Overlap of [2] baabb=aa with [12] aabba=bba:

Critical pair: bbba=aaa.

Reduce RHS:

Defines rule #2.

Overlap of [12] aabba=bba with [10] abbaa=abb:

Critical pair: aabb=bbaa.

Defines rule #3.