Certificate for #18942 ⟨a, b | aab=a, bbabbb=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], [7], [8], [9], [11].

Axiom: bbabbb=a.

Referenced by [3], [4], [6], [8].

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

Critical pair: bbaba=aabbb.

Reduce RHS:

Referenced by [4], [7].

Overlap of [2] bbabbb=a with [3] bbaba=abb:

Critical pair: bbababb=aaba.

Reduce LHS:

Reduce RHS:

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

Overlap of [1] aab=a with [4] abbbb=aa:

Critical pair: aaa=abbb.

Flip LHS and RHS.

Referenced by [7], [8].

Overlap of [2] bbabbb=a with [4] abbbb=aa:

Critical pair: bbaa=ab.

Referenced by [9], [11].

Overlap of [3] bbaba=abb with [4] abbbb=aa:

Critical pair: bbabaa=abbbbbb.

Reduce LHS:

Reduce RHS:

Referenced by [10].

Overlap of [4] abbbb=aa with [2] bbabbb=a:

Critical pair: abbba=aababbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [9], [10].

Overlap of [6] bbaa=ab with [1] aab=a:

Critical pair: bba=abb.

Reduce RHS:

Defines rule #3.

Simplify [7] abba=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [11].

Overlap of [10] ab=aaaaa with [6] bbaa=ab:

Critical pair: aab=aaaaabaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.