Certificate for #18956 ⟨a, b | aab=a, bbbbba=a⟩

Completion settings:

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

Axiom: aab=a.

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

Axiom: bbbbba=a.

Defines rule #3.

Referenced by [3].

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

Critical pair: aaa=abbbba.

Flip LHS and RHS.

Referenced by [4], [5].

Overlap of [3] abbbba=aaa with [3] abbbba=aaa:

Critical pair: abbbbaaa=aaabbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [5].

Overlap of [3] abbbba=aaa with [4] abba=aaaaa:

Critical pair: abbbbaaaaa=aaabba.

Reduce LHS:

Reduce RHS:

Referenced by [6].

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

Critical pair: aaaaaa=aab.

Reduce RHS:

Defines rule #1.

Referenced by [7].

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

Critical pair: aaaaa=ab.

Flip LHS and RHS.

Defines rule #2.