Certificate for #15908 ⟨a, b | aba=bb, aaaab=b⟩

Completion settings:

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

Axiom: aba=bb.

Defines rule #5.

Referenced by [3], [4], [5], [6], [8], [11], [12], [13], [15], [16].

Axiom: aaaab=b.

Defines rule #10.

Referenced by [4], [5].

Overlap of [1] aba=bb with [1] aba=bb:

Critical pair: abbb=bbba.

Defines rule #4.

Referenced by [7], [8], [9], [10], [12], [13], [15], [16].

Overlap of [1] aba=bb with [2] aaaab=b:

Critical pair: abb=bbaaab.

Flip LHS and RHS.

Referenced by [11], [13], [14].

Overlap of [2] aaaab=b with [1] aba=bb:

Critical pair: aaabb=ba.

Referenced by [6], [7], [9], [12], [15].

Overlap of [1] aba=bb with [5] aaabb=ba:

Critical pair: abba=bbaabb.

Flip LHS and RHS.

Referenced by [9], [10], [11], [12], [13].

Overlap of [5] aaabb=ba with [3] abbb=bbba:

Critical pair: aabbba=bab.

Reduce LHS:

Referenced by [8], [17].

Overlap of [3] abbb=bbba with [7] bbbaaa=bab:

Critical pair: abbab=bbbabaaa.

Reduce RHS:

Defines rule #6.

Referenced by [9], [10], [11], [13].

Overlap of [5] aaabb=ba with [8] abbab=bbbbbaa:

Critical pair: aabbbbbaa=baab.

Reduce LHS:

Referenced by [12].

Overlap of [6] bbaabb=abba with [8] abbab=bbbbbaa:

Critical pair: bbabbbbbaa=abbaab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [11], [12], [13].

Overlap of [8] abbab=bbbbbaa with [4] bbaaab=abb:

Critical pair: abbaabb=bbbbbaabaaab.

Reduce LHS:

Reduce RHS:

Referenced by [12].

Overlap of [5] aaabb=ba with [10] abbaab=bbbbbabbaa:

Critical pair: aabbbbbabbaa=baaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [14].

Overlap of [6] bbaabb=abba with [10] abbaab=bbbbbabbaa:

Critical pair: bbabbbbbabbaa=abbaaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [15].

Overlap of [4] bbaaab=abb with [12] baaab=bbbbbbbbbbbabb:

Critical pair: bbbbbbbbbbbbabb=abb.

Defines rule #3.

Overlap of [5] aaabb=ba with [13] aabb=bbbbbbbbbbabba:

Critical pair: abbbbbbbbbbabba=ba.

Reduce LHS:

Defines rule #2.

Referenced by [16], [17].

Overlap of [3] abbb=bbba with [15] bbbbbbbbbbbbba=ba:

Critical pair: aba=bbbabbbbbbbbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [15] bbbbbbbbbbbbba=ba with [7] bbbaaa=bab:

Critical pair: bbbbbbbbbbbab=baaa.

Flip LHS and RHS.

Defines rule #8.