Certificate for #18954 ⟨a, b | aab=a, bbbbab=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].

Axiom: bbbbab=a.

Referenced by [3], [4].

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

Critical pair: aaa=abbbab.

Flip LHS and RHS.

Referenced by [4].

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

Critical pair: bbbbaa=abbbab.

Reduce RHS:

Referenced by [5].

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

Critical pair: bbbba=aaab.

Reduce RHS:

Defines rule #3.

Referenced by [6].

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

Critical pair: aaaa=abbba.

Flip LHS and RHS.

Referenced by [7].

Overlap of [6] abbba=aaaa with [6] abbba=aaaa:

Critical pair: abbbaaaa=aaaabbba.

Reduce LHS:

Reduce RHS:

Referenced by [8].

Overlap of [7] aaaaaaa=aa with [1] aab=a:

Critical pair: aaaaaa=aab.

Reduce RHS:

Defines rule #1.

Referenced by [9].

Overlap of [8] aaaaaa=a with [1] aab=a:

Critical pair: aaaaa=ab.

Flip LHS and RHS.

Defines rule #2.