Certificate for #16540 ⟨a, b | aba=ab, bba=aaa⟩

Completion settings:

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

Axiom: aba=ab.

Defines rule #2.

Referenced by [3], [4].

Axiom: bba=aaa.

Defines rule #4.

Referenced by [3], [5].

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

Critical pair: abab=abba.

Reduce LHS:

Reduce RHS:

Defines rule #5.

Referenced by [4], [5].

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

Critical pair: abaaaa=abbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [6].

Overlap of [3] abb=aaaa with [2] bba=aaa:

Critical pair: aaaa=aaaaa.

Flip LHS and RHS.

Defines rule #1.

Referenced by [6].

Overlap of [5] aaaaa=aaaa with [4] aaaab=ab:

Critical pair: aab=aaaab.

Reduce RHS:

Defines rule #3.