Certificate for #19638 ⟨a, b | aba=a, aaaab=bb⟩

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].

Axiom: aaaab=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3].

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

Critical pair: baaaab=aaaabb.

Reduce RHS:

Referenced by [4].

Overlap of [3] baaaab=aaaaaaaab with [1] aba=a:

Critical pair: baaaa=aaaaaaaaba.

Reduce RHS:

Defines rule #2.

Referenced by [5].

Overlap of [1] aba=a with [4] baaaa=aaaaaaaa:

Critical pair: aaaaaaaaa=aaaa.

Defines rule #1.