Certificate for #18952 ⟨a, b | aab=a, bbbbaa=a⟩

Completion settings:

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

Axiom: aab=a.

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

Axiom: bbbbaa=a.

Referenced by [3], [4].

Overlap of [2] bbbbaa=a with [1] aab=a:

Critical pair: bbbba=ab.

Referenced by [4], [5], [6], [7], [10].

Overlap of [2] bbbbaa=a with [1] aab=a:

Critical pair: bbbbaa=aab.

Reduce LHS:

Reduce RHS:

Referenced by [6], [8], [9].

Overlap of [1] aab=a with [3] bbbba=ab:

Critical pair: aaab=abbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [3] bbbba=ab with [4] aba=a:

Critical pair: bbbba=abba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7], [8].

Overlap of [3] bbbba=ab with [6] abba=ab:

Critical pair: bbbbab=abbba.

Reduce LHS:

Reduce RHS:

Referenced by [8].

Overlap of [4] aba=a with [6] abba=ab:

Critical pair: abab=abba.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Referenced by [9], [10].

Overlap of [4] aba=a with [8] ab=aaa:

Critical pair: aaaa=a.

Defines rule #1.

Simplify [3] bbbba=ab.

Reduce RHS:

Defines rule #3.