Certificate for #2967 ⟨a, b | aaabbabaaab=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. bbabaaab=d

Axiom: aaabbabaaab=1.

Referenced by [4].

Axiom: aaa=c.

Defines rule #5.

Referenced by [3], [4], [5], [15], [20], [27], [32].

Axiom: bbabaaab=d.

Reduce LHS:

Referenced by [4], [6], [7], [9], [10], [14].

Overlap of [1] aaabbabaaab=1 with [2] aaa=c:

Critical pair: cbbabaaab=1.

Reduce LHS:

Defines rule #2.

Referenced by [6], [8], [16], [19], [22], [23], [24], [32].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [15], [18], [25], [30].

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

Critical pair: bbabcd=dbabcb.

Reduce LHS:

Referenced by [7], [10], [11].

Overlap of [3] bbabcb=d with [6] bbab=dbabcb:

Critical pair: dbabcbcb=d.

Referenced by [8].

Overlap of [4] cd=1 with [7] dbabcbcb=d:

Critical pair: cd=babcbcb.

Reduce LHS:

Flip LHS and RHS.

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

Overlap of [3] bbabcb=d with [8] babcbcb=1:

Critical pair: b=dcb.

Flip LHS and RHS.

Referenced by [13].

Overlap of [3] bbabcb=d with [8] babcbcb=1:

Critical pair: bbabc=dabcbcb.

Reduce LHS:

Referenced by [14].

Overlap of [6] bbab=dbabcb with [8] babcbcb=1:

Critical pair: bba=dbabcbabcbcb.

Reduce RHS:

Defines rule #6.

Referenced by [14], [15].

Overlap of [8] babcbcb=1 with [8] babcbcb=1:

Critical pair: babcbc=abcbcb.

Defines rule #8.

Referenced by [13], [24], [25], [26].

Overlap of [9] dcb=b with [8] babcbcb=1:

Critical pair: dc=babcbcb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [14], [17].

Overlap of [3] bbabcb=d with [11] bba=dbabc:

Critical pair: dbabcbcb=d.

Reduce LHS:

Referenced by [16].

Overlap of [11] bba=dbabc with [2] aaa=c:

Critical pair: bbc=dbabcaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [22].

Overlap of [4] cd=1 with [14] ddc=d:

Critical pair: cd=dc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [17], [18], [21], [28], [31].

Simplify [13] abcbcbb=dc.

Reduce RHS:

Referenced by [20], [26].

Overlap of [16] dc=1 with [5] ca=ac:

Critical pair: dac=a.

Referenced by [19].

Overlap of [18] dac=a with [4] cd=1:

Critical pair: da=ad.

Defines rule #4.

Referenced by [21], [28], [29], [31].

Overlap of [2] aaa=c with [17] abcbcbb=1:

Critical pair: aa=cbcbcbb.

Flip LHS and RHS.

Referenced by [21], [26].

Overlap of [16] dc=1 with [20] cbcbcbb=aa:

Critical pair: daa=bcbcbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #14.

Overlap of [15] dbabaac=bbc with [4] cd=1:

Critical pair: dbabaa=bbcd.

Reduce RHS:

Referenced by [23].

Overlap of [4] cd=1 with [22] dbabaa=bb:

Critical pair: cbb=babaa.

Flip LHS and RHS.

Defines rule #7.

Overlap of [12] babcbc=abcbcb with [4] cd=1:

Critical pair: babcb=abcbcbd.

Flip LHS and RHS.

Referenced by [27].

Overlap of [12] babcbc=abcbcb with [5] ca=ac:

Critical pair: babcbac=abcbcba.

Defines rule #10.

Referenced by [30].

Overlap of [12] babcbc=abcbcb with [20] cbcbcbb=aa:

Critical pair: babcbaa=abcbcbbcbcbb.

Reduce RHS:

Defines rule #13.

Referenced by [30].

Overlap of [2] aaa=c with [24] abcbcbd=babcb:

Critical pair: aababcb=cbcbcbd.

Flip LHS and RHS.

Referenced by [28].

Overlap of [16] dc=1 with [27] cbcbcbd=aababcb:

Critical pair: daababcb=bcbcbd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [29].

Overlap of [28] bcbcbd=aadbabcb with [19] da=ad:

Critical pair: bcbcbad=aadbabcba.

Defines rule #11.

Overlap of [25] babcbac=abcbcba with [5] ca=ac:

Critical pair: babcbaac=abcbcbaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [31].

Overlap of [19] da=ad with [30] abcbcbaa=cbcbbc:

Critical pair: dcbcbbc=adbcbcbaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [32].

Overlap of [2] aaa=c with [31] adbcbcbaa=bcbbc:

Critical pair: aabcbbc=cdbcbcbaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #12.