Certificate for #19299 ⟨a, b | aaa=a, bbabb=ab⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #1.

Referenced by [5], [6], [9].

Axiom: bbabb=ab.

Referenced by [3], [4], [5], [8], [11].

Overlap of [2] bbabb=ab with [2] bbabb=ab:

Critical pair: bbaab=ababb.

Referenced by [12].

Overlap of [2] bbabb=ab with [2] bbabb=ab:

Critical pair: bbabab=abbabb.

Reduce RHS:

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

Overlap of [2] bbabb=ab with [4] bbabab=aab:

Critical pair: bbaaab=ababab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [1] aaa=a with [5] ababab=bbab:

Critical pair: aabbab=ababab.

Reduce RHS:

Referenced by [10].

Overlap of [5] ababab=bbab with [5] ababab=bbab:

Critical pair: abbbab=bbabab.

Reduce RHS:

Referenced by [8], [9].

Overlap of [7] abbbab=aab with [2] bbabb=ab:

Critical pair: abab=aabb.

Defines rule #2.

Referenced by [9], [10], [12].

Overlap of [7] abbbab=aab with [4] bbabab=aab:

Critical pair: abaab=aabab.

Reduce RHS:

Defines rule #4.

Referenced by [10].

Overlap of [8] abab=aabb with [8] abab=aabb:

Critical pair: abaabb=aabbab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [11].

Overlap of [2] bbabb=ab with [10] bbab=abbb:

Critical pair: abbbb=ab.

Defines rule #5.

Simplify [3] bbaab=ababb.

Reduce RHS:

Defines rule #6.