Certificate for #1463 ⟨a, b | aabbbababa=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. bbbabab=d

Axiom: aabbbababa=1.

Referenced by [4].

Axiom: aaa=c.

Defines rule #5.

Referenced by [5], [6], [10], [20], [25], [29], [30], [31], [32], [34], [37], [42], [43], [46].

Axiom: bbbabab=d.

Referenced by [4], [11], [13].

Overlap of [1] aabbbababa=1 with [3] bbbabab=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 [23], [28].

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], [24], [31], [32], [37], [42], [43], [46].

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], [21], [26], [27], [32], [33], [38], [39], [41], [44], [45], [47].

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

Critical pair: dc=adaa.

Reduce RHS:

Defines rule #1.

Referenced by [12], [21], [26], [33], [39].

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

Critical pair: bbbabad=dbbabab.

Referenced by [12].

Overlap of [11] bbbabad=dbbabab with [10] dc=1:

Critical pair: bbbaba=dbbababc.

Referenced by [13].

Overlap of [3] bbbabab=d with [12] bbbaba=dbbababc:

Critical pair: dbbababcb=d.

Referenced by [14].

Overlap of [8] cd=1 with [13] dbbababcb=d:

Critical pair: cd=bbababcb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [15], [16], [17], [22].

Overlap of [14] bbababcb=1 with [14] bbababcb=1:

Critical pair: bbababc=bababcb.

Referenced by [16], [17], [18].

Overlap of [14] bbababcb=1 with [15] bbababc=bababcb:

Critical pair: bababcbb=1.

Referenced by [17], [19].

Overlap of [14] bbababcb=1 with [15] bbababc=bababcb:

Critical pair: bbababcbababcb=bababc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [18], [19], [23], [24], [30].

Overlap of [15] bbababc=bababcb with [8] cd=1:

Critical pair: bbabab=bababcbd.

Reduce RHS:

Flip LHS and RHS.

Referenced by [29].

Simplify [16] bababcbb=1.

Reduce LHS:

Referenced by [20].

Overlap of [2] aaa=c with [19] ababcbbb=1:

Critical pair: aa=cbabcbbb.

Flip LHS and RHS.

Referenced by [21], [22].

Overlap of [10] dc=1 with [20] cbabcbbb=aa:

Critical pair: daa=babcbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #17.

Referenced by [31], [35].

Overlap of [14] bbababcb=1 with [20] cbabcbbb=aa:

Critical pair: bbababaa=abcbbb.

Defines rule #16.

Referenced by [30].

Overlap of [17] bababc=ababcb with [5] ca=ac:

Critical pair: bababac=ababcba.

Defines rule #9.

Referenced by [28].

Overlap of [17] bababc=ababcb with [8] cd=1:

Critical pair: babab=ababcbd.

Flip LHS and RHS.

Referenced by [25].

Overlap of [2] aaa=c with [24] ababcbd=babab:

Critical pair: aababab=cbabcbd.

Flip LHS and RHS.

Referenced by [26].

Overlap of [10] dc=1 with [25] cbabcbd=aababab:

Critical pair: daababab=babcbd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [27], [36].

Overlap of [26] babcbd=aadbabab with [9] da=ad:

Critical pair: babcbad=aadbababa.

Defines rule #10.

Referenced by [38].

Overlap of [23] bababac=ababcba with [5] ca=ac:

Critical pair: bababaac=ababcbaa.

Defines rule #12.

Overlap of [2] aaa=c with [18] ababcbbd=bbabab:

Critical pair: aabbabab=cbabcbbd.

Flip LHS and RHS.

Referenced by [39].

Overlap of [22] bbababaa=abcbbb with [2] aaa=c:

Critical pair: bbababc=abcbbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [31].

Overlap of [30] abcbbba=ababcbb with [21] babcbbb=aad:

Critical pair: abcbbaad=ababcbbbcbbb.

Reduce RHS:

Referenced by [32].

Overlap of [31] abcbbaad=cbbb with [9] da=ad:

Critical pair: abcbbaaad=cbbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [33].

Overlap of [10] dc=1 with [32] cbbba=abcbb:

Critical pair: dabcbb=bbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [34], [35], [36], [40].

Overlap of [33] bbba=adbcbb with [2] aaa=c:

Critical pair: bbbc=adbcbbaa.

Flip LHS and RHS.

Referenced by [37].

Overlap of [33] bbba=adbcbb with [21] babcbbb=aad:

Critical pair: bbaad=adbcbbbcbbb.

Flip LHS and RHS.

Referenced by [42].

Overlap of [33] bbba=adbcbb with [26] babcbd=aadbabab:

Critical pair: bbaadbabab=adbcbbbcbd.

Flip LHS and RHS.

Referenced by [43].

Overlap of [2] aaa=c with [34] adbcbbaa=bbbc:

Critical pair: aabbbc=cdbcbbaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #11.

Overlap of [27] babcbad=aadbababa with [9] da=ad:

Critical pair: babcbaad=aadbababaa.

Defines rule #13.

Overlap of [10] dc=1 with [29] cbabcbbd=aabbabab:

Critical pair: daabbabab=babcbbd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #14.

Referenced by [40], [41].

Overlap of [33] bbba=adbcbb with [39] babcbbd=aadbbabab:

Critical pair: bbaadbbabab=adbcbbbcbbd.

Flip LHS and RHS.

Referenced by [46].

Overlap of [39] babcbbd=aadbbabab with [9] da=ad:

Critical pair: babcbbad=aadbbababa.

Defines rule #15.

Overlap of [2] aaa=c with [35] adbcbbbcbbb=bbaad:

Critical pair: aabbaad=cdbcbbbcbbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #23.

Overlap of [2] aaa=c with [36] adbcbbbcbd=bbaadbabab:

Critical pair: aabbaadbabab=cdbcbbbcbd.

Reduce RHS:

Flip LHS and RHS.

Defines rule #18.

Referenced by [44].

Overlap of [43] bcbbbcbd=aabbaadbabab with [9] da=ad:

Critical pair: bcbbbcbad=aabbaadbababa.

Defines rule #19.

Referenced by [45].

Overlap of [44] bcbbbcbad=aabbaadbababa with [9] da=ad:

Critical pair: bcbbbcbaad=aabbaadbababaa.

Defines rule #20.

Overlap of [2] aaa=c with [40] adbcbbbcbbd=bbaadbbabab:

Critical pair: aabbaadbbabab=cdbcbbbcbbd.

Reduce RHS:

Flip LHS and RHS.

Defines rule #21.

Referenced by [47].

Overlap of [46] bcbbbcbbd=aabbaadbbabab with [9] da=ad:

Critical pair: bcbbbcbbad=aabbaadbbababa.

Defines rule #22.