Certificate for #16293 ⟨a, b | aab=bb, abab=aa⟩

Completion settings:

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

Axiom: aab=bb.

Flip LHS and RHS.

Referenced by [3], [4], [14].

Axiom: abab=aa.

Defines rule #6.

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

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

Critical pair: baab=aabb.

Reduce RHS:

Referenced by [10], [12].

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

Critical pair: abaaab=aab.

Referenced by [6].

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

Critical pair: abaa=aaab.

Flip LHS and RHS.

Referenced by [6], [7], [10], [12], [13].

Overlap of [5] aaab=abaa with [2] abab=aa:

Critical pair: aaaa=abaaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [7], [9], [12], [14].

Overlap of [6] aab=aaaa with [2] abab=aa:

Critical pair: aaa=aaaaab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [8], [9], [10], [11].

Overlap of [2] abab=aa with [7] abaaaa=aaa:

Critical pair: abaaa=aaaaaa.

Referenced by [10].

Overlap of [6] aab=aaaa with [7] abaaaa=aaa:

Critical pair: aaaa=aaaaaaaa.

Flip LHS and RHS.

Referenced by [10].

Overlap of [7] abaaaa=aaa with [5] aaab=abaa:

Critical pair: abaabaa=aaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [11], [13].

Overlap of [7] abaaaa=aaa with [10] abaa=aaaaa:

Critical pair: aaaaaaa=aaa.

Defines rule #1.

Referenced by [13].

Simplify [3] baab=aaaab.

Reduce LHS:

Reduce RHS:

Referenced by [13].

Overlap of [12] baaaa=aaaaaa with [5] aaab=abaa:

Critical pair: baaabaa=aaaaaaab.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Simplify [1] bb=aab.

Reduce RHS:

Defines rule #5.