Certificate for #19810 ⟨a, b | aaa=a, abab=baa⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #1.

Referenced by [3], [4], [5], [8].

Axiom: abab=baa.

Referenced by [3], [4], [6], [7].

Overlap of [1] aaa=a with [2] abab=baa:

Critical pair: aabaa=abab.

Reduce RHS:

Referenced by [5], [6].

Overlap of [2] abab=baa with [2] abab=baa:

Critical pair: abbaa=baaab.

Reduce RHS:

Referenced by [6].

Overlap of [3] aabaa=baa with [1] aaa=a:

Critical pair: aaba=baaa.

Reduce RHS:

Defines rule #2.

Referenced by [6], [7].

Overlap of [3] aabaa=baa with [3] aabaa=baa:

Critical pair: aabbaa=baabaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [5] aaba=ba with [2] abab=baa:

Critical pair: abaa=bab.

Flip LHS and RHS.

Defines rule #4.

Overlap of [6] bbaa=baa with [1] aaa=a:

Critical pair: bba=baaa.

Reduce RHS:

Defines rule #3.