Certificate for #16104 ⟨a, b | aab=aa, abab=bb⟩

Completion settings:

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

Axiom: aab=aa.

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

Axiom: abab=bb.

Defines rule #5.

Referenced by [3], [4], [7].

Overlap of [1] aab=aa with [2] abab=bb:

Critical pair: abb=aaab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [5], [6], [9], [10], [11].

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

Critical pair: abbb=bbab.

Referenced by [5].

Overlap of [3] aaa=abb with [1] aab=aa:

Critical pair: aaa=abbb.

Reduce LHS:

Reduce RHS:

Referenced by [6], [7], [9], [10], [11], [12].

Overlap of [3] aaa=abb with [3] aaa=abb:

Critical pair: aabb=abba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [7], [10].

Overlap of [2] abab=bb with [5] abb=bbab:

Critical pair: abbbab=bbb.

Reduce LHS:

Referenced by [8], [9], [10].

Overlap of [7] bbaa=bbb with [1] aab=aa:

Critical pair: bbaa=bbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [9], [10].

Overlap of [7] bbaa=bbb with [3] aaa=abb:

Critical pair: bbabb=bbba.

Reduce LHS:

Referenced by [10].

Overlap of [1] aab=aa with [6] bbaba=aa:

Critical pair: aaaa=aababa.

Reduce LHS:

Reduce RHS:

Defines rule #4.

Referenced by [11].

Overlap of [3] aaa=abb with [10] aa=bbb:

Critical pair: bbba=abb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [12].

Simplify [5] abb=bbab.

Reduce RHS:

Defines rule #3.