Certificate for #22836 ⟨a, b | aaa=1, baabb=bba⟩

Completion settings:

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

Axiom: aaa=1.

Defines rule #9.

Referenced by [3], [6], [13].

Axiom: baabb=bba.

Defines rule #8.

Referenced by [3], [4], [5], [7], [8], [10], [11], [12].

Overlap of [2] baabb=bba with [2] baabb=bba:

Critical pair: baabbba=bbaaabb.

Reduce LHS:

Reduce RHS:

Defines rule #5.

Referenced by [4], [5], [6], [7], [12], [13].

Overlap of [2] baabb=bba with [3] bbaba=bbbb:

Critical pair: baabbbb=bbaaba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [2] baabb=bba with [3] bbaba=bbbb:

Critical pair: baabbbbb=bbababa.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [10], [11], [12].

Overlap of [3] bbaba=bbbb with [1] aaa=1:

Critical pair: bbab=bbbbaa.

Flip LHS and RHS.

Referenced by [8], [10], [14].

Overlap of [3] bbaba=bbbb with [2] baabb=bba:

Critical pair: bbabba=bbbbabb.

Defines rule #6.

Referenced by [8], [9], [11].

Overlap of [2] baabb=bba with [6] bbbbaa=bbab:

Critical pair: baabbab=bbabbaa.

Reduce LHS:

Reduce RHS:

Defines rule #7.

Referenced by [9].

Simplify [4] bbaaba=bbabb.

Reduce LHS:

Referenced by [10].

Overlap of [2] baabb=bba with [9] bbbbbbbbabb=bbabb:

Critical pair: baabbabb=bbabbbbbbabb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [12].

Overlap of [2] baabb=bba with [7] bbabba=bbbbabb:

Critical pair: baabbbbabb=bbaabba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [13], [14].

Overlap of [2] baabb=bba with [10] bbbbbbbbba=bbba:

Critical pair: baabbba=bbabbbbbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [14].

Overlap of [11] bbbaa=bbbbbbbab with [1] aaa=1:

Critical pair: bbb=bbbbbbbaba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [14].

Overlap of [12] bbbbbbbbbb=bbbb with [11] bbbaa=bbbbbbbab:

Critical pair: bbbbbbbbbbbbbbab=bbbbaa.

Reduce LHS:

Reduce RHS:

Defines rule #2.