Certificate for #4711 ⟨a, b | aaba=a, babb=b⟩

Completion settings:

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

Axiom: aaba=a.

Defines rule #2.

Referenced by [3], [6], [8].

Axiom: babb=b.

Referenced by [3], [4].

Overlap of [1] aaba=a with [2] babb=b:

Critical pair: aab=abb.

Flip LHS and RHS.

Defines rule #6.

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

Overlap of [2] babb=b with [3] abb=aab:

Critical pair: baab=b.

Defines rule #4.

Referenced by [5].

Overlap of [4] baab=b with [3] abb=aab:

Critical pair: baaab=bb.

Defines rule #5.

Referenced by [6], [7].

Overlap of [5] baaab=bb with [1] aaba=a:

Critical pair: baa=bba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [8].

Overlap of [5] baaab=bb with [3] abb=aab:

Critical pair: baaaab=bbb.

Flip LHS and RHS.

Defines rule #7.

Overlap of [3] abb=aab with [6] bba=baa:

Critical pair: abaa=aaba.

Reduce RHS:

Defines rule #1.