Certificate for #6376 ⟨a, b | aab=a, bbbab=a⟩

Completion settings:

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

Axiom: aab=a.

Referenced by [3], [5], [6], [7], [8], [9], [10].

Axiom: bbbab=a.

Referenced by [3], [4].

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

Critical pair: aaa=abbab.

Flip LHS and RHS.

Referenced by [4].

Overlap of [2] bbbab=a with [2] bbbab=a:

Critical pair: bbbaa=abbab.

Reduce RHS:

Referenced by [5].

Overlap of [4] bbbaa=aaa with [1] aab=a:

Critical pair: bbba=aaab.

Reduce RHS:

Defines rule #3.

Referenced by [6].

Overlap of [1] aab=a with [5] bbba=aa:

Critical pair: aaaa=abba.

Flip LHS and RHS.

Referenced by [7].

Overlap of [1] aab=a with [6] abba=aaaa:

Critical pair: aaaaa=aba.

Flip LHS and RHS.

Referenced by [8], [9].

Overlap of [1] aab=a with [7] aba=aaaaa:

Critical pair: aaaaaa=aa.

Referenced by [9].

Overlap of [7] aba=aaaaa with [1] aab=a:

Critical pair: aba=aaaaaab.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [10].

Overlap of [9] aaaaa=a with [1] aab=a:

Critical pair: aaaa=ab.

Flip LHS and RHS.

Defines rule #2.