Certificate for #1672 ⟨a, b | aba=ab, bba=a⟩

Completion settings:

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

Axiom: aba=ab.

Defines rule #4.

Referenced by [3], [4].

Axiom: bba=a.

Defines rule #2.

Referenced by [3].

Overlap of [1] aba=ab with [1] aba=ab:

Critical pair: abab=abba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

Overlap of [1] aba=ab with [3] aa=abb:

Critical pair: ababb=aba.

Reduce LHS:

Reduce RHS:

Defines rule #1.