Certificate for #13092 ⟨a, b | bab=aaa, abbb=a⟩

Completion settings:

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

Axiom: bab=aaa.

Defines rule #5.

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

Axiom: abbb=a.

Defines rule #9.

Referenced by [4], [9].

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

Critical pair: baaaa=aaaab.

Defines rule #3.

Referenced by [6], [7], [8], [12].

Overlap of [1] bab=aaa with [2] abbb=a:

Critical pair: ba=aaabb.

Flip LHS and RHS.

Referenced by [5], [6], [7], [8], [10], [11].

Overlap of [4] aaabb=ba with [1] bab=aaa:

Critical pair: aaabaaa=baab.

Flip LHS and RHS.

Defines rule #6.

Referenced by [6], [7].

Overlap of [3] baaaa=aaaab with [4] aaabb=ba:

Critical pair: baaaba=aaaabaabb.

Reduce RHS:

Defines rule #8.

Referenced by [7].

Overlap of [6] baaaba=aaaaaaabaaab with [4] aaabb=ba:

Critical pair: baaabba=aaaaaaabaaabaabb.

Reduce LHS:

Reduce RHS:

Referenced by [8].

Overlap of [7] bbaa=aaaaaaaaaaaaaaaaaaaaabaaa with [4] aaabb=ba:

Critical pair: bbba=aaaaaaaaaaaaaaaaaaaaabaaaabb.

Reduce RHS:

Referenced by [9].

Overlap of [2] abbb=a with [8] bbba=aaaaaaaaaaaaaaaaaaaaaaaaa:

Critical pair: aaaaaaaaaaaaaaaaaaaaaaaaaa=aa.

Defines rule #1.

Referenced by [10], [12].

Overlap of [9] aaaaaaaaaaaaaaaaaaaaaaaaaa=aa with [4] aaabb=ba:

Critical pair: aaaaaaaaaaaaaaaaaaaaaaaba=aabb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [11], [12].

Overlap of [4] aaabb=ba with [10] aabb=aaaaaaaaaaaaaaaaaaaaaaaba:

Critical pair: aaaaaaaaaaaaaaaaaaaaaaaaba=ba.

Defines rule #2.

Referenced by [12].

Overlap of [3] baaaa=aaaab with [11] aaaaaaaaaaaaaaaaaaaaaaaaba=ba:

Critical pair: bba=aaaabaaaaaaaaaaaaaaaaaaaaba.

Reduce RHS:

Defines rule #7.