Certificate for #14465 ⟨a, b | aaab=a, bbbaa=a⟩

Completion settings:

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

Axiom: aaab=a.

Referenced by [3], [4], [6], [10].

Axiom: bbbaa=a.

Referenced by [3], [4], [5], [7].

Overlap of [2] bbbaa=a with [1] aaab=a:

Critical pair: bbba=aab.

Referenced by [4], [5], [7], [9].

Overlap of [2] bbbaa=a with [1] aaab=a:

Critical pair: bbbaa=aaab.

Reduce LHS:

Reduce RHS:

Referenced by [5], [6].

Overlap of [2] bbbaa=a with [4] aaba=a:

Critical pair: bbba=aba.

Reduce LHS:

Referenced by [6], [7], [9], [11].

Overlap of [4] aaba=a with [1] aaab=a:

Critical pair: aaba=aaab.

Reduce LHS:

Reduce RHS:

Referenced by [11], [12].

Overlap of [2] bbbaa=a with [5] aab=aba:

Critical pair: bbbaba=ab.

Reduce LHS:

Referenced by [8].

Overlap of [7] ababa=ab with [7] ababa=ab:

Critical pair: abab=abba.

Referenced by [11].

Simplify [3] bbba=aab.

Reduce RHS:

Referenced by [10], [11], [13].

Overlap of [1] aaab=a with [9] bbba=aba:

Critical pair: aaaaba=abba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [9] bbba=aba with [5] aab=aba:

Critical pair: bbbaba=abaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [12], [13].

Overlap of [6] abaa=a with [11] ab=aaaa:

Critical pair: aaaaaa=a.

Defines rule #1.

Simplify [9] bbba=aba.

Reduce RHS:

Defines rule #3.