Certificate for #1307 ⟨a, b | bab=aaa, bbb=1⟩

Completion settings:

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

Axiom: bab=aaa.

Defines rule #5.

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

Axiom: bbb=1.

Defines rule #9.

Referenced by [4], [8].

Overlap of [1] bab=aaa with [1] bab=aaa:

Critical pair: baaaa=aaaab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [6], [7], [10], [11].

Overlap of [2] bbb=1 with [1] bab=aaa:

Critical pair: bbaaa=ab.

Referenced by [5], [6], [7], [8], [9].

Overlap of [1] bab=aaa with [4] bbaaa=ab:

Critical pair: baab=aaabaaa.

Defines rule #6.

Referenced by [6], [7].

Overlap of [4] bbaaa=ab with [3] aaaab=baaaa:

Critical pair: bbaabaaaa=abaaab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [7].

Overlap of [4] bbaaa=ab with [6] abaaab=baaabaaaaaaa:

Critical pair: bbaabaaabaaaaaaa=abbaaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [4] bbaaa=ab with [7] aabb=aaabaaaaaaaaaaaaaaaaaaaaa:

Critical pair: bbaaaabaaaaaaaaaaaaaaaaaaaaa=abbb.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [9], [10].

Overlap of [4] bbaaa=ab with [8] aaaaaaaaaaaaaaaaaaaaaaaaa=a:

Critical pair: bba=abaaaaaaaaaaaaaaaaaaaaaa.

Defines rule #4.

Referenced by [11].

Overlap of [8] aaaaaaaaaaaaaaaaaaaaaaaaa=a with [3] aaaab=baaaa:

Critical pair: aaaaaaaaaaaaaaaaaaaaabaaaa=ab.

Reduce LHS:

Defines rule #2.

Referenced by [11].

Overlap of [10] abaaaaaaaaaaaaaaaaaaaaaaaa=ab with [3] aaaab=baaaa:

Critical pair: abaaaaaaaaaaaaaaaaaaaabaaaa=abb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.