Certificate for #10963 ⟨a, b | abab=aaa, bbbb=1⟩

Completion settings:

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

Axiom: abab=aaa.

Defines rule #5.

Referenced by [3], [4], [5], [7], [17].

Axiom: bbbb=1.

Defines rule #12.

Referenced by [4].

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

Critical pair: abaaa=aaaab.

Defines rule #4.

Referenced by [5], [6], [7], [8], [9], [10], [15].

Overlap of [1] abab=aaa with [2] bbbb=1:

Critical pair: aba=aaabbb.

Flip LHS and RHS.

Defines rule #9.

Referenced by [7], [8], [16].

Overlap of [3] abaaa=aaaab with [1] abab=aaa:

Critical pair: abaaaaa=aaaabbab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Referenced by [10], [11], [14].

Overlap of [3] abaaa=aaaab with [3] abaaa=aaaab:

Critical pair: abaaaaaab=aaaabbaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [3] abaaa=aaaab with [4] aaabbb=aba:

Critical pair: abaaba=aaaababbb.

Reduce RHS:

Defines rule #7.

Referenced by [9], [10].

Overlap of [3] abaaa=aaaab with [4] aaabbb=aba:

Critical pair: abaaaba=aaaabaabbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.

Referenced by [10], [11], [13].

Overlap of [7] abaaba=aaaaaabb with [3] abaaa=aaaab:

Critical pair: abaaaaab=aaaaaabbaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11], [12].

Overlap of [3] abaaa=aaaab with [8] aaaabaabbb=aaaabba:

Critical pair: abaaaaabba=aaaabaabaabbb.

Reduce LHS:

Reduce RHS:

Defines rule #11.

Referenced by [11].

Overlap of [6] aaaabbaaa=aaaaaaabb with [8] aaaabaabbb=aaaabba:

Critical pair: aaaabbaaaaabba=aaaaaaabbaabaabbb.

Reduce LHS:

Reduce RHS:

Referenced by [12], [18].

Overlap of [9] aaaaaabbaa=aaaabaab with [11] aaaaabbaa=aaaaaaaaaaaaaaabaab:

Critical pair: aaaaaaaaaaaaaaaabaab=aaaabaab.

Referenced by [13].

Overlap of [12] aaaaaaaaaaaaaaaabaab=aaaabaab with [8] aaaabaabbb=aaaabba:

Critical pair: aaaaaaaaaaaaaaaabba=aaaabaabbb.

Reduce RHS:

Defines rule #6.

Referenced by [14], [18].

Overlap of [13] aaaaaaaaaaaaaaaabba=aaaabba with [5] aaaabbab=aaaabaa:

Critical pair: aaaaaaaaaaaaaaaabaa=aaaabbab.

Reduce RHS:

Defines rule #3.

Referenced by [15].

Overlap of [14] aaaaaaaaaaaaaaaabaa=aaaabaa with [3] abaaa=aaaab:

Critical pair: aaaaaaaaaaaaaaaaaaab=aaaabaaa.

Reduce RHS:

Referenced by [16].

Overlap of [15] aaaaaaaaaaaaaaaaaaab=aaaaaaab with [4] aaabbb=aba:

Critical pair: aaaaaaaaaaaaaaaaaba=aaaaaaabbb.

Reduce RHS:

Defines rule #2.

Referenced by [17].

Overlap of [16] aaaaaaaaaaaaaaaaaba=aaaaaba with [1] abab=aaa:

Critical pair: aaaaaaaaaaaaaaaaaaa=aaaaabab.

Reduce RHS:

Defines rule #1.

Referenced by [18].

Overlap of [13] aaaaaaaaaaaaaaaabba=aaaabba with [11] aaaaabbaa=aaaaaaaaaaaaaaabaab:

Critical pair: aaaaaaaaaaaaaaaaaaaaaaaaaabaab=aaaabbaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.