Certificate for #18926 ⟨a, b | aab=a, babbbb=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], [8], [9], [10].

Axiom: babbbb=a.

Referenced by [3], [4].

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

Critical pair: aaa=aabbbb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [4], [5].

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

Critical pair: babbba=aabbbb.

Reduce LHS:

Reduce RHS:

Referenced by [7].

Overlap of [1] aab=a with [3] abbb=aaa:

Critical pair: aaaa=abb.

Flip LHS and RHS.

Referenced by [6].

Overlap of [1] aab=a with [5] abb=aaaa:

Critical pair: aaaaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [9], [10].

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

Critical pair: baaa=aaab.

Reduce RHS:

Referenced by [8], [9].

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

Critical pair: baa=aab.

Reduce RHS:

Referenced by [9], [10].

Overlap of [7] baaa=aa with [6] ab=aaaaa:

Critical pair: baaaaaaa=aab.

Reduce LHS:

Reduce RHS:

Defines rule #1.

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

Critical pair: ba=ab.

Reduce RHS:

Defines rule #2.