Certificate for #1434 ⟨a, b | baab=a, bbbb=1⟩

Completion settings:

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

Axiom: baab=a.

Defines rule #4.

Referenced by [3], [4], [5], [6], [7], [8], [11].

Axiom: bbbb=1.

Defines rule #9.

Referenced by [4], [5], [13].

Overlap of [1] baab=a with [1] baab=a:

Critical pair: baaa=aaab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [9], [11].

Overlap of [1] baab=a with [2] bbbb=1:

Critical pair: baa=abbb.

Flip LHS and RHS.

Referenced by [7].

Overlap of [2] bbbb=1 with [1] baab=a:

Critical pair: bbba=aab.

Defines rule #7.

Referenced by [6], [9].

Overlap of [5] bbba=aab with [1] baab=a:

Critical pair: bba=aabab.

Flip LHS and RHS.

Defines rule #6.

Referenced by [11].

Overlap of [1] baab=a with [4] abbb=baa:

Critical pair: babaa=abb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [8], [9].

Overlap of [1] baab=a with [7] abb=babaa:

Critical pair: bababaa=ab.

Referenced by [9], [10], [12].

Overlap of [7] abb=babaa with [8] bababaa=ab:

Critical pair: abab=babaaababaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [8] bababaa=ab with [9] ababaaaaaaaaaaaa=abab:

Critical pair: babab=abaaaaaaaaaa.

Defines rule #8.

Referenced by [11], [12].

Overlap of [6] aabab=bba with [10] babab=abaaaaaaaaaa:

Critical pair: aaabaaaaaaaaaa=bbaab.

Reduce LHS:

Reduce RHS:

Referenced by [13].

Overlap of [8] bababaa=ab with [10] babab=abaaaaaaaaaa:

Critical pair: abaaaaaaaaaaaa=ab.

Defines rule #2.

Overlap of [2] bbbb=1 with [11] baaaaaaaaaaaaa=ba:

Critical pair: bbbba=aaaaaaaaaaaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.