Certificate for #1996 ⟨a, b | aaa=a, babb=a⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #3.

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

Axiom: babb=a.

Referenced by [3], [4], [5], [7], [8], [10].

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

Critical pair: baba=aabb.

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

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

Critical pair: baa=aabbbb.

Referenced by [7].

Overlap of [3] baba=aabb with [3] baba=aabb:

Critical pair: baaabb=aabbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [9].

Overlap of [1] aaa=a with [5] aabbba=a:

Critical pair: aa=abbba.

Flip LHS and RHS.

Referenced by [7], [8].

Overlap of [2] babb=a with [6] abbba=aa:

Critical pair: baa=aba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [6] abbba=aa with [2] babb=a:

Critical pair: abba=aabb.

Referenced by [9].

Overlap of [3] baba=aabb with [7] aba=aabbbb:

Critical pair: babaabbbb=aabbba.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [10].

Overlap of [2] babb=a with [9] abbbbbb=a:

Critical pair: ba=abbbb.

Defines rule #2.