Certificate for #3070 ⟨a, b | aabababbaba=1⟩

Completion settings:

• Reduction order:
  • Right-to-left recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
• Auxiliary generators:
  1. aaa=c
  2. bababbab=d

Axiom: aabababbaba=1.

Referenced by [4].

Axiom: aaa=c.

Defines rule #5.

Referenced by [5], [6], [10], [14], [15], [20], [21], [26].

Axiom: bababbab=d.

Referenced by [4], [11], [15], [17].

Overlap of [1] aabababbaba=1 with [3] bababbab=d:

Critical pair: aada=1.

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

Overlap of [2] aaa=c with [2] aaa=c:

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [16], [18].

Overlap of [2] aaa=c with [4] aada=1:

Critical pair: a=cda.

Flip LHS and RHS.

Referenced by [8].

Overlap of [4] aada=1 with [4] aada=1:

Critical pair: aad=ada.

Flip LHS and RHS.

Referenced by [9], [10].

Overlap of [6] cda=a with [4] aada=1:

Critical pair: cd=aada.

Reduce RHS:

Defines rule #2.

Referenced by [14], [18], [20], [25], [26].

Overlap of [4] aada=1 with [7] ada=aad:

Critical pair: aadaad=da.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [10], [11], [12], [17], [23].

Overlap of [9] da=ad with [2] aaa=c:

Critical pair: dc=adaa.

Reduce RHS:

Defines rule #1.

Referenced by [13], [15], [24], [27].

Overlap of [3] bababbab=d with [3] bababbab=d:

Critical pair: bababd=dabbab.

Reduce RHS:

Defines rule #7.

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

Overlap of [11] bababd=adbbab with [9] da=ad:

Critical pair: bababad=adbbaba.

Defines rule #10.

Referenced by [23].

Overlap of [11] bababd=adbbab with [10] dc=1:

Critical pair: babab=adbbabc.

Flip LHS and RHS.

Referenced by [14].

Overlap of [2] aaa=c with [13] adbbabc=babab:

Critical pair: aababab=cdbbabc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [15], [16].

Overlap of [3] bababbab=d with [14] bbabc=aababab:

Critical pair: babaaababab=dc.

Reduce LHS:

Reduce RHS:

Referenced by [17], [18], [19].

Overlap of [14] bbabc=aababab with [5] ca=ac:

Critical pair: bbabac=aabababa.

Defines rule #9.

Overlap of [3] bababbab=d with [15] babcbabab=1:

Critical pair: bababba=dabcbabab.

Reduce RHS:

Defines rule #13.

Referenced by [18].

Overlap of [15] babcbabab=1 with [11] bababd=adbbab:

Critical pair: babcadbbab=d.

Reduce LHS:

Referenced by [20].

Overlap of [15] babcbabab=1 with [15] babcbabab=1:

Critical pair: babcba=cbabab.

Defines rule #8.

Referenced by [21], [22].

Overlap of [2] aaa=c with [18] adbcbababb=d:

Critical pair: aad=cdbcbababb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #14.

Overlap of [19] babcba=cbabab with [2] aaa=c:

Critical pair: babcbc=cbababaa.

Flip LHS and RHS.

Referenced by [24].

Overlap of [19] babcba=cbabab with [19] babcba=cbabab:

Critical pair: babccbabab=cbababbcba.

Flip LHS and RHS.

Referenced by [27].

Overlap of [12] bababad=adbbaba with [9] da=ad:

Critical pair: bababaad=adbbabaa.

Referenced by [25].

Overlap of [10] dc=1 with [21] cbababaa=babcbc:

Critical pair: dbabcbc=bababaa.

Flip LHS and RHS.

Defines rule #12.

Referenced by [25].

Overlap of [23] bababaad=adbbabaa with [24] bababaa=dbabcbc:

Critical pair: dbabcbcd=adbbabaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [26].

Overlap of [2] aaa=c with [25] adbbabaa=dbabcb:

Critical pair: aadbabcb=cdbbabaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #11.

Overlap of [10] dc=1 with [22] cbababbcba=babccbabab:

Critical pair: dbabccbabab=bababbcba.

Flip LHS and RHS.

Defines rule #15.