Certificate for #1654 ⟨a, b | aab=bb, bba=a⟩

Completion settings:

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

Axiom: aab=bb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2], [3], [5].

Axiom: bba=a.

Reduce LHS:

Referenced by [4], [5].

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

Critical pair: baab=aabb.

Reduce RHS:

Referenced by [4].

Overlap of [3] baab=aaaab with [2] aaba=a:

Critical pair: ba=aaaaba.

Reduce RHS:

Defines rule #2.

Referenced by [5].

Overlap of [1] bb=aab with [4] ba=aaa:

Critical pair: baaa=aaba.

Reduce LHS:

Reduce RHS:

Defines rule #1.