Certificate for #12633 ⟨a, b | babb=aa, bbbb=b⟩

Completion settings:

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

Axiom: babb=aa.

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

Axiom: bbbb=b.

Defines rule #13.

Referenced by [4], [5].

Overlap of [1] babb=aa with [1] babb=aa:

Critical pair: babaa=aaabb.

Referenced by [7].

Overlap of [1] babb=aa with [2] bbbb=b:

Critical pair: bab=aabb.

Defines rule #4.

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

Overlap of [2] bbbb=b with [1] babb=aa:

Critical pair: bbbaa=babb.

Reduce RHS:

Referenced by [10].

Overlap of [1] babb=aa with [4] bab=aabb:

Critical pair: aabbb=aa.

Defines rule #9.

Referenced by [8], [9], [10], [19].

Simplify [3] babaa=aaabb.

Reduce LHS:

Defines rule #7.

Referenced by [8], [9], [12], [17].

Overlap of [7] aabbaa=aaabb with [7] aabbaa=aaabb:

Critical pair: aabbaaaabb=aaabbabbaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [14].

Overlap of [7] aabbaa=aaabb with [6] aabbb=aa:

Critical pair: aabbaaa=aaabbabbb.

Reduce LHS:

Reduce RHS:

Defines rule #5.

Referenced by [12], [17], [18].

Simplify [5] bbbaa=aabbb.

Reduce RHS:

Defines rule #11.

Referenced by [11], [13].

Overlap of [1] babb=aa with [10] bbbaa=aa:

Critical pair: baaa=aabaa.

Defines rule #3.

Referenced by [12], [13], [14], [15], [18].

Overlap of [7] aabbaa=aaabb with [11] baaa=aabaa:

Critical pair: aabaabaa=aaabba.

Reduce RHS:

Defines rule #8.

Referenced by [18].

Overlap of [10] bbbaa=aa with [11] baaa=aabaa:

Critical pair: bbaabaa=aaa.

Defines rule #12.

Simplify [8] aaabaaaa=aaaab.

Reduce LHS:

Referenced by [15], [16].

Overlap of [14] aaaaaaabaa=aaaab with [11] baaa=aabaa:

Critical pair: aaaaaaaaabaa=aaaaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [16].

Overlap of [14] aaaaaaabaa=aaaab with [15] aaaaba=aaaaaab:

Critical pair: aaaaaaaaaba=aaaab.

Reduce LHS:

Referenced by [19].

Overlap of [9] aaabba=aaabaab with [7] aabbaa=aaabb:

Critical pair: aaaabb=aaabaaba.

Flip LHS and RHS.

Defines rule #6.

Overlap of [11] baaa=aabaa with [9] aaabba=aaabaab:

Critical pair: baaabaab=aabaabba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Overlap of [16] aaaaaaaaaaab=aaaab with [6] aabbb=aa:

Critical pair: aaaaaaaaaaa=aaaabbb.

Reduce RHS:

Defines rule #1.