Certificate for #1126 ⟨a, b | ababba=bab⟩

Completion settings:

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

Axiom: ababba=bab.

Referenced by [3].

Axiom: bba=c.

Defines rule #8.

Referenced by [3], [4], [5], [9], [13].

Overlap of [1] ababba=bab with [2] bba=c:

Critical pair: abac=bab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5], [6], [7], [8], [10], [12], [14], [16], [17], [22], [23], [24], [32].

Overlap of [2] bba=c with [3] bab=abac:

Critical pair: babac=cb.

Reduce LHS:

Defines rule #1.

Referenced by [7], [13], [24].

Overlap of [3] bab=abac with [2] bba=c:

Critical pair: bac=abacba.

Flip LHS and RHS.

Defines rule #9.

Referenced by [12], [14], [18], [22].

Overlap of [3] bab=abac with [3] bab=abac:

Critical pair: baabac=abacab.

Defines rule #13.

Overlap of [3] bab=abac with [4] abacac=cb:

Critical pair: bcb=abacacac.

Reduce RHS:

Defines rule #5.

Referenced by [8], [9], [10], [11], [15], [20], [21], [24], [25], [26], [27], [33].

Overlap of [3] bab=abac with [7] bcb=cbac:

Critical pair: bacbac=abaccb.

Defines rule #15.

Referenced by [18], [19], [26].

Overlap of [7] bcb=cbac with [2] bba=c:

Critical pair: bcc=cbacba.

Flip LHS and RHS.

Defines rule #10.

Referenced by [13], [14], [15], [16], [17], [19], [23], [28], [34].

Overlap of [7] bcb=cbac with [3] bab=abac:

Critical pair: bcabac=cbacab.

Defines rule #14.

Overlap of [7] bcb=cbac with [7] bcb=cbac:

Critical pair: bccbac=cbaccb.

Defines rule #16.

Referenced by [27].

Overlap of [5] abacba=bac with [3] bab=abac:

Critical pair: abacabac=bacb.

Defines rule #17.

Overlap of [4] abacac=cb with [9] cbacba=bcc:

Critical pair: abacabcc=cbbacba.

Reduce RHS:

Defines rule #26.

Overlap of [5] abacba=bac with [9] cbacba=bcc:

Critical pair: ababcc=baccba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #11.

Referenced by [24], [25], [26], [27], [28], [29], [30], [31], [35], [38].

Overlap of [7] bcb=cbac with [9] cbacba=bcc:

Critical pair: bbcc=cbacacba.

Defines rule #23.

Overlap of [9] cbacba=bcc with [3] bab=abac:

Critical pair: cbacabac=bccb.

Defines rule #18.

Referenced by [22], [23].

Overlap of [9] cbacba=bcc with [9] cbacba=bcc:

Critical pair: cbabcc=bcccba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #12.

Referenced by [32], [33], [34], [35], [36], [37], [39].

Overlap of [5] abacba=bac with [8] bacbac=abaccb:

Critical pair: aabaccb=bacc.

Defines rule #6.

Referenced by [20], [30], [36].

Overlap of [9] cbacba=bcc with [8] bacbac=abaccb:

Critical pair: cabaccb=bccc.

Defines rule #7.

Referenced by [21], [31], [37].

Overlap of [18] aabaccb=bacc with [7] bcb=cbac:

Critical pair: aabacccbac=bacccb.

Defines rule #21.

Overlap of [19] cabaccb=bccc with [7] bcb=cbac:

Critical pair: cabacccbac=bccccb.

Defines rule #22.

Overlap of [5] abacba=bac with [16] cbacabac=bccb:

Critical pair: ababccb=baccabac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #19.

Overlap of [9] cbacba=bcc with [16] cbacabac=bccb:

Critical pair: cbabccb=bcccabac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #20.

Overlap of [3] bab=abac with [14] baccba=aabaccc:

Critical pair: baaabaccc=abacaccba.

Reduce RHS:

Defines rule #27.

Referenced by [38], [39].

Overlap of [7] bcb=cbac with [14] baccba=aabaccc:

Critical pair: bcaabaccc=cbacaccba.

Defines rule #28.

Overlap of [8] bacbac=abaccb with [14] baccba=aabaccc:

Critical pair: bacaabaccc=abaccbcba.

Reduce RHS:

Defines rule #31.

Overlap of [11] bccbac=cbaccb with [14] baccba=aabaccc:

Critical pair: bccaabaccc=cbaccbcba.

Reduce RHS:

Defines rule #32.

Overlap of [14] baccba=aabaccc with [9] cbacba=bcc:

Critical pair: bacbcc=aabaccccba.

Defines rule #24.

Overlap of [14] baccba=aabaccc with [14] baccba=aabaccc:

Critical pair: baccaabaccc=aabacccccba.

Defines rule #33.

Overlap of [18] aabaccb=bacc with [14] baccba=aabaccc:

Critical pair: aaaabaccc=bacca.

Defines rule #2.

Overlap of [19] cabaccb=bccc with [14] baccba=aabaccc:

Critical pair: caaabaccc=bccca.

Defines rule #3.

Overlap of [3] bab=abac with [17] bcccba=cabaccc:

Critical pair: bacabaccc=abaccccba.

Defines rule #29.

Overlap of [7] bcb=cbac with [17] bcccba=cabaccc:

Critical pair: bccabaccc=cbaccccba.

Defines rule #30.

Overlap of [17] bcccba=cabaccc with [9] cbacba=bcc:

Critical pair: bccbcc=cabaccccba.

Defines rule #25.

Overlap of [17] bcccba=cabaccc with [14] baccba=aabaccc:

Critical pair: bcccaabaccc=cabacccccba.

Defines rule #34.

Overlap of [18] aabaccb=bacc with [17] bcccba=cabaccc:

Critical pair: aabacccabaccc=bacccccba.

Defines rule #35.

Overlap of [19] cabaccb=bccc with [17] bcccba=cabaccc:

Critical pair: cabacccabaccc=bccccccba.

Defines rule #36.

Overlap of [14] baccba=aabaccc with [24] baaabaccc=ccbaca:

Critical pair: baccccbaca=aabacccaabaccc.

Flip LHS and RHS.

Defines rule #37.

Overlap of [17] bcccba=cabaccc with [24] baaabaccc=ccbaca:

Critical pair: bcccccbaca=cabacccaabaccc.

Flip LHS and RHS.

Defines rule #38.