Certificate for #16448 ⟨a, b | aba=bb, aabb=aa⟩

Completion settings:

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

Axiom: aba=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [2], [3], [5], [7], [9], [14].

Axiom: aabb=aa.

Reduce LHS:

Referenced by [4], [7], [8].

Overlap of [1] bb=aba with [1] bb=aba:

Critical pair: baba=abab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [4], [6], [10].

Overlap of [2] aaaba=aa with [3] abab=baba:

Critical pair: aababa=aab.

Reduce LHS:

Referenced by [5], [6], [7], [9], [13].

Overlap of [1] bb=aba with [4] babaaa=aab:

Critical pair: baab=abaabaaa.

Flip LHS and RHS.

Referenced by [9].

Overlap of [3] abab=baba with [4] babaaa=aab:

Critical pair: aaab=babaaaa.

Reduce RHS:

Referenced by [7], [8], [9], [10].

Overlap of [4] babaaa=aab with [2] aaaba=aa:

Critical pair: babaa=aabba.

Reduce RHS:

Referenced by [10].

Overlap of [2] aaaba=aa with [6] aaab=aaba:

Critical pair: aabaa=aa.

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

Overlap of [4] babaaa=aab with [6] aaab=aaba:

Critical pair: babaaaaba=aabaab.

Reduce LHS:

Reduce RHS:

Referenced by [12].

Overlap of [6] aaab=aaba with [3] abab=baba:

Critical pair: aababa=aabaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [11], [12], [13].

Simplify [8] aabaa=aa.

Reduce LHS:

Defines rule #1.

Referenced by [13].

Simplify [9] abaaba=aab.

Reduce LHS:

Reduce RHS:

Referenced by [13].

Overlap of [4] babaaa=aab with [12] abaaaaa=aaaa:

Critical pair: baaaa=aabaa.

Reduce RHS:

Referenced by [14].

Overlap of [1] bb=aba with [13] baaaa=aa:

Critical pair: baa=abaaaaa.

Reduce RHS:

Defines rule #2.