Certificate for #12162 ⟨a, b | aaaa=aa, babb=a⟩

Completion settings:

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

Axiom: aaaa=aa.

Defines rule #1.

Referenced by [6], [11].

Axiom: babb=a.

Defines rule #7.

Referenced by [3], [4], [7], [9], [10].

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

Critical pair: baba=aabb.

Defines rule #4.

Referenced by [4], [5], [7], [9].

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

Critical pair: baa=aabbbb.

Flip LHS and RHS.

Defines rule #10.

Referenced by [6], [8], [11].

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

Critical pair: baaabb=aabbba.

Flip LHS and RHS.

Referenced by [11], [13].

Overlap of [1] aaaa=aa with [4] aabbbb=baa:

Critical pair: aabaa=aabbbb.

Reduce RHS:

Defines rule #2.

Referenced by [7], [8], [12].

Overlap of [3] baba=aabb with [6] aabaa=baa:

Critical pair: babbaa=aabbabaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [9], [10], [11].

Overlap of [6] aabaa=baa with [4] aabbbb=baa:

Critical pair: aabbaa=baabbbb.

Reduce RHS:

Referenced by [9], [11].

Overlap of [2] babb=a with [7] baabba=aaa:

Critical pair: babaaa=aaabba.

Reduce LHS:

Defines rule #6.

Referenced by [11].

Overlap of [7] baabba=aaa with [2] babb=a:

Critical pair: baaba=aaabb.

Defines rule #5.

Overlap of [7] baabba=aaa with [4] aabbbb=baa:

Critical pair: baabbbaa=aaaabbbb.

Reduce LHS:

Reduce RHS:

Referenced by [12].

Overlap of [6] aabaa=baa with [11] abaaa=baa:

Critical pair: abaa=baaa.

Flip LHS and RHS.

Defines rule #3.

Referenced by [13].

Simplify [5] aabbba=baaabb.

Reduce RHS:

Defines rule #8.