Certificate for #4667 ⟨a, b | aaab=a, babb=a⟩

Completion settings:

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

Axiom: aaab=a.

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

Axiom: babb=a.

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

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

Critical pair: aaaa=aabb.

Flip LHS and RHS.

Referenced by [4].

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

Critical pair: baba=aabb.

Reduce RHS:

Referenced by [5].

Overlap of [4] baba=aaaa with [2] babb=a:

Critical pair: baa=aaaabb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [6], [7], [8], [9].

Overlap of [5] aab=baa with [2] babb=a:

Critical pair: aaa=baaabb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [5] aab=baa with [6] bab=aaa:

Critical pair: aaaaa=baaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [8], [9].

Overlap of [1] aaab=a with [5] aab=baa:

Critical pair: abaa=a.

Reduce LHS:

Defines rule #1.

Referenced by [10].

Simplify [5] aab=baa.

Reduce RHS:

Referenced by [10].

Overlap of [8] aaaaaaa=a with [9] aab=aaaaaa:

Critical pair: aaaaaaaaaaa=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.