Certificate for #14469 ⟨a, b | aaab=a, bbbba=a⟩

Completion settings:

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

Axiom: aaab=a.

Referenced by [3], [4], [5], [6], [7], [8].

Axiom: bbbba=a.

Defines rule #3.

Referenced by [3].

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

Critical pair: aaaa=abbba.

Flip LHS and RHS.

Referenced by [4].

Overlap of [1] aaab=a with [3] abbba=aaaa:

Critical pair: aaaaaa=abba.

Flip LHS and RHS.

Referenced by [5].

Overlap of [1] aaab=a with [4] abba=aaaaaa:

Critical pair: aaaaaaaa=aba.

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [1] aaab=a with [5] aba=aaaaaaaa:

Critical pair: aaaaaaaaaa=aa.

Referenced by [7].

Overlap of [5] aba=aaaaaaaa with [1] aaab=a:

Critical pair: aba=aaaaaaaaaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [8], [9].

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

Critical pair: aaaaaaaaa=a.

Defines rule #1.

Referenced by [9].

Overlap of [8] aaaaaaaaa=a with [7] aab=aaaaaaaa:

Critical pair: aaaaaaaaaaaaaaa=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.