Certificate for #7548 ⟨a, b | aaa=1, bbabbb=a⟩

Completion settings:

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

Axiom: aaa=1.

Defines rule #3.

Referenced by [5], [6], [9], [12], [14], [15], [16], [21], [23], [25].

Axiom: bbabbb=a.

Referenced by [3], [4], [7], [11], [13], [14], [15], [16], [17], [20], [22].

Overlap of [2] bbabbb=a with [2] bbabbb=a:

Critical pair: bbaba=aabbb.

Flip LHS and RHS.

Referenced by [5], [8], [10].

Overlap of [2] bbabbb=a with [2] bbabbb=a:

Critical pair: bbabba=ababbb.

Flip LHS and RHS.

Referenced by [16], [18].

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

Critical pair: abbaba=bbb.

Referenced by [6], [11].

Overlap of [5] abbaba=bbb with [1] aaa=1:

Critical pair: abbab=bbbaa.

Referenced by [7], [11], [16].

Overlap of [6] abbab=bbbaa with [2] bbabbb=a:

Critical pair: aa=bbbaabb.

Flip LHS and RHS.

Referenced by [8], [11].

Overlap of [7] bbbaabb=aa with [3] aabbb=bbaba:

Critical pair: bbbbbaba=aab.

Flip LHS and RHS.

Referenced by [9], [10], [11], [13], [14], [15], [16], [22].

Overlap of [1] aaa=1 with [8] aab=bbbbbaba:

Critical pair: abbbbbaba=b.

Referenced by [12].

Overlap of [3] aabbb=bbaba with [8] aab=bbbbbaba:

Critical pair: bbbbbababb=bbaba.

Referenced by [11], [14], [15], [22].

Overlap of [5] abbaba=bbb with [8] aab=bbbbbaba:

Critical pair: abbabbbbbbaba=bbbab.

Reduce LHS:

Referenced by [14], [15], [16], [21].

Overlap of [9] abbbbbaba=b with [1] aaa=1:

Critical pair: abbbbbab=baa.

Referenced by [13].

Overlap of [12] abbbbbab=baa with [2] bbabbb=a:

Critical pair: abbba=baabb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [19].

Overlap of [1] aaa=1 with [11] abbbabaa=bbbab:

Critical pair: aabbbab=bbbabaa.

Reduce LHS:

Referenced by [15].

Overlap of [8] aab=bbbbbaba with [11] abbbabaa=bbbab:

Critical pair: abbbab=bbbbbababbabaa.

Reduce RHS:

Referenced by [16], [17].

Overlap of [11] abbbabaa=bbbab with [8] aab=bbbbbaba:

Critical pair: abbbabbbbbbaba=bbbabb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [18].

Overlap of [15] abbbab=bbbaba with [2] bbabbb=a:

Critical pair: aba=bbbababb.

Flip LHS and RHS.

Referenced by [18].

Overlap of [17] bbbababb=aba with [4] ababbb=bbabba:

Critical pair: bbbbbabba=abab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [19], [21].

Simplify [13] bbbbbbabab=abbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [20], [21], [22].

Overlap of [2] bbabbb=a with [19] abbba=bbbbbbbbbbbbbbbbbbbbbbaba:

Critical pair: bbbbbbbbbbbbbbbbbbbbbbbbaba=aa.

Referenced by [21], [22], [24].

Overlap of [11] abbbabaa=bbbab with [19] abbba=bbbbbbbbbbbbbbbbbbbbbbaba:

Critical pair: bbbbbbbbbbbbbbbbbbbbbbababaa=bbbab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [22].

Overlap of [19] abbba=bbbbbbbbbbbbbbbbbbbbbbaba with [2] bbabbb=a:

Critical pair: aba=bbbbbbbbbbbbbbbbbbbbbbababbb.

Reduce RHS:

Referenced by [23].

Overlap of [22] aba=bbbbbbbbbbbaa with [1] aaa=1:

Critical pair: ab=bbbbbbbbbbbaaaa.

Reduce RHS:

Defines rule #2.

Referenced by [24].

Simplify [20] bbbbbbbbbbbbbbbbbbbbbbbbaba=aa.

Reduce LHS:

Referenced by [25].

Overlap of [24] bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbaa=aa with [1] aaa=1:

Critical pair: bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=aaa.

Reduce RHS:

Defines rule #1.