Certificate for #14467 ⟨a, b | aaab=a, bbbab=a⟩

Completion settings:

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

Axiom: aaab=a.

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

Axiom: bbbab=a.

Referenced by [3], [4].

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

Critical pair: aaaa=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=aaaa with [1] aaab=a:

Critical pair: bbba=aaaaab.

Reduce RHS:

Defines rule #3.

Referenced by [6].

Overlap of [1] aaab=a with [5] bbba=aaa:

Critical pair: aaaaaa=abba.

Flip LHS and RHS.

Referenced by [7].

Overlap of [1] aaab=a with [6] abba=aaaaaa:

Critical pair: aaaaaaaa=aba.

Flip LHS and RHS.

Referenced by [8], [9].

Overlap of [1] aaab=a with [7] aba=aaaaaaaa:

Critical pair: aaaaaaaaaa=aa.

Referenced by [9].

Overlap of [7] aba=aaaaaaaa with [1] aaab=a:

Critical pair: aba=aaaaaaaaaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [10], [11].

Overlap of [1] aaab=a with [9] aab=aaaaaaaa:

Critical pair: aaaaaaaaa=a.

Defines rule #1.

Referenced by [11].

Overlap of [10] aaaaaaaaa=a with [9] aab=aaaaaaaa:

Critical pair: aaaaaaaaaaaaaaa=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.