Certificate for #1682 ⟨a, b | aba=bb, bab=a⟩

Completion settings:

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

Axiom: aba=bb.

Referenced by [3], [4], [5].

Axiom: bab=a.

Referenced by [3], [5], [6], [7].

Overlap of [1] aba=bb with [2] bab=a:

Critical pair: aa=bbb.

Defines rule #4.

Referenced by [4], [5].

Overlap of [1] aba=bb with [3] aa=bbb:

Critical pair: abbbb=bba.

Flip LHS and RHS.

Referenced by [5], [6].

Overlap of [2] bab=a with [4] bba=abbbb:

Critical pair: baabbbb=aba.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Overlap of [4] bba=abbbb with [2] bab=a:

Critical pair: ba=abbbbb.

Defines rule #3.

Referenced by [7].

Overlap of [2] bab=a with [6] ba=abbbbb:

Critical pair: abbbbbb=a.

Defines rule #2.