Certificate for #12982 ⟨a, b | abb=aaa, baab=a⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with a < b

Axiom: abb=aaa.

Defines rule #2.

Referenced by [4], [5], [6], [8], [10].

Axiom: baab=a.

Referenced by [3], [4], [6], [10].

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

Critical pair: baaa=aaab.

Referenced by [4], [9].

Overlap of [2] baab=a with [1] abb=aaa:

Critical pair: baaaa=ab.

Reduce LHS:

Referenced by [5], [7], [8], [9].

Overlap of [4] aaaba=ab with [1] abb=aaa:

Critical pair: aaabaaa=abbb.

Reduce LHS:

Reduce RHS:

Referenced by [6].

Overlap of [5] abaa=aaab with [2] baab=a:

Critical pair: aa=aaabb.

Reduce RHS:

Flip LHS and RHS.

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

Overlap of [6] aaaaa=aa with [4] aaaba=ab:

Critical pair: aaab=aaba.

Flip LHS and RHS.

Referenced by [8].

Overlap of [7] aaba=aaab with [1] abb=aaa:

Critical pair: aabaaa=aaabbb.

Reduce LHS:

Reduce RHS:

Referenced by [9], [11].

Overlap of [3] baaa=aaab with [6] aaaaa=aa:

Critical pair: baa=aaabaa.

Reduce RHS:

Referenced by [10], [11].

Overlap of [2] baab=a with [9] baa=aab:

Critical pair: aabb=a.

Reduce LHS:

Defines rule #3.

Referenced by [11].

Overlap of [9] baa=aab with [10] aaaa=a:

Critical pair: ba=aabaa.

Reduce RHS:

Defines rule #1.