Certificate for #4673 ⟨a, b | aaab=a, bbba=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].

Axiom: bbba=a.

Defines rule #3.

Referenced by [3].

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

Critical pair: aaaa=abba.

Flip LHS and RHS.

Referenced by [4].

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

Critical pair: aaaaaa=aba.

Flip LHS and RHS.

Referenced by [5], [6].

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

Critical pair: aaaaaaaa=aa.

Referenced by [6].

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

Critical pair: aba=aaaaaaaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [7], [8].

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

Critical pair: aaaaaaa=a.

Defines rule #1.

Referenced by [8].

Overlap of [7] aaaaaaa=a with [6] aab=aaaaaa:

Critical pair: aaaaaaaaaaa=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.