Certificate for #20243 ⟨a, b | aba=a, bbbb=aab⟩

Completion settings:

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

Axiom: aba=a.

Defines rule #3.

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

Axiom: bbbb=aab.

Defines rule #5.

Referenced by [3], [7].

Overlap of [2] bbbb=aab with [2] bbbb=aab:

Critical pair: baab=aabb.

Flip LHS and RHS.

Referenced by [4], [5], [8], [10].

Overlap of [1] aba=a with [3] aabb=baab:

Critical pair: abbaab=aabb.

Reduce RHS:

Referenced by [5].

Overlap of [3] aabb=baab with [4] abbaab=baab:

Critical pair: abaab=baabaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [6].

Overlap of [5] baaab=aab with [1] aba=a:

Critical pair: baaa=aaba.

Reduce RHS:

Referenced by [7], [8].

Overlap of [2] bbbb=aab with [6] baaa=aa:

Critical pair: bbbaa=aabaaa.

Reduce RHS:

Referenced by [8].

Overlap of [3] aabb=baab with [7] bbbaa=aaaa:

Critical pair: aaaaaa=baabbaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [9], [10].

Overlap of [1] aba=a with [8] baa=aaaaaa:

Critical pair: aaaaaaa=aa.

Defines rule #1.

Simplify [3] aabb=baab.

Reduce RHS:

Defines rule #4.