Certificate for #4691 ⟨a, b | aaab=b, babb=a⟩

Completion settings:

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

Axiom: aaab=b.

Referenced by [4], [5], [8], [10].

Axiom: babb=a.

Referenced by [3], [4], [5], [6], [9].

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

Critical pair: baba=aabb.

Referenced by [5], [6].

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

Critical pair: aaaa=babb.

Reduce RHS:

Referenced by [7].

Overlap of [3] baba=aabb with [1] aaab=b:

Critical pair: babb=aabbaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [3] baba=aabb with [2] babb=a:

Critical pair: baa=aabbbb.

Referenced by [7].

Simplify [5] aabbaab=a.

Reduce LHS:

Defines rule #2.

Referenced by [8], [9].

Overlap of [1] aaab=b with [7] abbbbbbbbb=a:

Critical pair: aaa=bbbbbbbbb.

Defines rule #4.

Referenced by [10].

Overlap of [2] babb=a with [7] abbbbbbbbb=a:

Critical pair: ba=abbbbbbb.

Defines rule #3.

Overlap of [1] aaab=b with [8] aaa=bbbbbbbbb:

Critical pair: bbbbbbbbbb=b.

Defines rule #1.