Certificate for #2633 ⟨a, b | abbbba=babb

Completion settings:

[1] abbbba=babb

Axiom: abbbba=babb.

Referenced by [3].

[2] babb=c

Axiom: babb=c.

Defines rule #2.

Referenced by [3], [4], [5], [6], [7].

[3] abbbba=c

Simplify [1] abbbba=babb.

Reduce RHS:

[2](babb)
c

Defines rule #11.

Referenced by [5], [6].

[4] babc=cabb

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

bab b babb

Critical pair: babc=cabb.

Defines rule #3.

Referenced by [10], [21].

[5] abbbc=cbb

Overlap of [3] abbbba=c with [2] babb=c:

abbb ba babb

Critical pair: abbbc=cbb.

Defines rule #6.

Referenced by [11], [12], [13], [19].

[6] cbba=bc

Overlap of [2] babb=c with [3] abbbba=c:

b abb abbbba

Critical pair: bc=cbba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [7], [8].

[7] bcbb=cbc

Overlap of [6] cbba=bc with [2] babb=c:

cb ba babb

Critical pair: cbc=bcbb.

Flip LHS and RHS.

Defines rule #1.

Referenced by [8], [9], [10], [11], [13], [14], [15], [17], [25], [26], [29], [30], [35], [40], [47], [54], [58], [59], [60], [63], [66], [67].

[8] cbca=bbc

Overlap of [7] bcbb=cbc with [6] cbba=bc:

b cbb cbba

Critical pair: bbc=cbca.

Flip LHS and RHS.

Defines rule #5.

Referenced by [12], [14], [16], [17], [23], [26], [27], [39], [48].

[9] bcbcbc=cbccbb

Overlap of [7] bcbb=cbc with [7] bcbb=cbc:

bcb b bcbb

Critical pair: bcbcbc=cbccbb.

Defines rule #9.

Referenced by [17], [18], [19], [20], [28], [42], [45], [49], [55], [56], [64], [65].

[10] cabbbb=bacbc

Overlap of [4] babc=cabb with [7] bcbb=cbc:

ba bc bcbb

Critical pair: bacbc=cabbbb.

Flip LHS and RHS.

Defines rule #7.

Referenced by [13], [19], [22], [24].

[11] abbcbc=cbbbb

Overlap of [5] abbbc=cbb with [7] bcbb=cbc:

abb bc bcbb

Critical pair: abbcbc=cbbbb.

Defines rule #8.

Referenced by [14], [15], [16], [17], [20], [29], [36], [67].

[12] abbbbbc=cbbbca

Overlap of [5] abbbc=cbb with [8] cbca=bbc:

abbb c cbca

Critical pair: abbbbbc=cbbbca.

Defines rule #12.

Referenced by [22], [23], [24], [33], [37], [48], [49], [50], [51], [55], [58].

[13] bacbccbb=ccbbbc

Overlap of [10] cabbbb=bacbc with [7] bcbb=cbc:

cabbb b bcbb

Critical pair: cabbbcbc=bacbccbb.

Reduce LHS:

[5]c(abbbc)bc
ccbbbc

Flip LHS and RHS.

Defines rule #17.

Referenced by [31], [32].

[14] cbccbbbb=bcbccbc

Overlap of [8] cbca=bbc with [11] abbcbc=cbbbb:

cbc a abbcbc

Critical pair: cbccbbbb=bbcbbcbc.

Reduce RHS:

[7]b(bcbb)cbc
bcbccbc

Defines rule #15.

Referenced by [33], [34], [36], [50].

[15] abbccbc=cbbbbbb

Overlap of [11] abbcbc=cbbbb with [7] bcbb=cbc:

abbc bc bcbb

Critical pair: abbccbc=cbbbbbb.

Defines rule #13.

Referenced by [25], [26], [27], [28], [30], [34], [38], [40], [59].

[16] cbbbba=abbbbc

Overlap of [11] abbcbc=cbbbb with [8] cbca=bbc:

abb cbc cbca

Critical pair: abbbbc=cbbbba.

Flip LHS and RHS.

Defines rule #10.

Referenced by [21], [31], [41], [44], [52], [62].

[17] cbbbbbca=acbccbb

Overlap of [11] abbcbc=cbbbb with [8] cbca=bbc:

abbcb c cbca

Critical pair: abbcbbbc=cbbbbbca.

Reduce LHS:

[7]ab(bcbb)bc
[9]a(bcbcbc)
acbccbb

Flip LHS and RHS.

Defines rule #21.

Referenced by [36].

[18] cbccbbbc=bccbccbb

Overlap of [9] bcbcbc=cbccbb with [9] bcbcbc=cbccbb:

bc bcbc bcbcbc

Critical pair: bccbccbb=cbccbbbc.

Flip LHS and RHS.

Defines rule #18.

Referenced by [37], [38], [51].

[19] bacbccbcbc=ccbbbccbb

Overlap of [10] cabbbb=bacbc with [9] bcbcbc=cbccbb:

cabbb b bcbcbc

Critical pair: cabbbcbccbb=bacbccbcbc.

Reduce LHS:

[5]c(abbbc)bccbb
ccbbbccbb

Flip LHS and RHS.

Defines rule #26.

Referenced by [41], [42], [43].

[20] abcbccbb=cbbbbbc

Overlap of [11] abbcbc=cbbbb with [9] bcbcbc=cbccbb:

ab bcbc bcbcbc

Critical pair: abcbccbb=cbbbbbc.

Defines rule #16.

Referenced by [35].

[21] abbbbcbc=cbbbcabb

Overlap of [16] cbbbba=abbbbc with [4] babc=cabb:

cbbb ba babc

Critical pair: cbbbcabb=abbbbcbc.

Flip LHS and RHS.

Defines rule #19.

Referenced by [39].

[22] ccbbbca=bacbcbc

Overlap of [10] cabbbb=bacbc with [12] abbbbbc=cbbbca:

c abbbb abbbbbc

Critical pair: ccbbbca=bacbcbc.

Defines rule #14.

Referenced by [29], [30].

[23] cbbbcabca=abbbbbbbc

Overlap of [12] abbbbbc=cbbbca with [8] cbca=bbc:

abbbbb c cbca

Critical pair: abbbbbbbc=cbbbcabca.

Flip LHS and RHS.

Defines rule #24.

Referenced by [40].

[24] abbbbbbacbc=cbbbcaabbbb

Overlap of [12] abbbbbc=cbbbca with [10] cabbbb=bacbc:

abbbbb c cabbbb

Critical pair: abbbbbbacbc=cbbbcaabbbb.

Defines rule #30.

Referenced by [47], [48], [49], [50], [51].

[25] cbbbbbbbb=abbcccbc

Overlap of [15] abbccbc=cbbbbbb with [7] bcbb=cbc:

abbcc bc bcbb

Critical pair: abbcccbc=cbbbbbbbb.

Flip LHS and RHS.

Defines rule #22.

[26] cbbbbbba=abcbcc

Overlap of [15] abbccbc=cbbbbbb with [8] cbca=bbc:

abbc cbc cbca

Critical pair: abbcbbc=cbbbbbba.

Reduce LHS:

[7]ab(bcbb)c
abcbcc

Flip LHS and RHS.

Defines rule #20.

Referenced by [32].

[27] cbbbbbbbca=abbccbbbc

Overlap of [15] abbccbc=cbbbbbb with [8] cbca=bbc:

abbccb c cbca

Critical pair: abbccbbbc=cbbbbbbbca.

Flip LHS and RHS.

Defines rule #27.

[28] cbbbbbbbcbc=abbcccbccbb

Overlap of [15] abbccbc=cbbbbbb with [9] bcbcbc=cbccbb:

abbcc bc bcbcbc

Critical pair: abbcccbccbb=cbbbbbbbcbc.

Flip LHS and RHS.

Defines rule #28.

[29] bacbccbccbc=ccbbbccbbbb

Overlap of [22] ccbbbca=bacbcbc with [11] abbcbc=cbbbb:

ccbbbc a abbcbc

Critical pair: ccbbbccbbbb=bacbcbcbbcbc.

Reduce RHS:

[7]bacbc(bcbb)cbc
bacbccbccbc

Flip LHS and RHS.

Defines rule #29.

Referenced by [44], [45], [46].

[30] ccbbbccbbbbbb=bacbccbcccbc

Overlap of [22] ccbbbca=bacbcbc with [15] abbccbc=cbbbbbb:

ccbbbc a abbccbc

Critical pair: ccbbbccbbbbbb=bacbcbcbbccbc.

Reduce RHS:

[7]bacbc(bcbb)ccbc
bacbccbcccbc

Defines rule #35.

[31] abbbbccbccbb=cbbbccbbbc

Overlap of [16] cbbbba=abbbbc with [13] bacbccbb=ccbbbc:

cbbb ba bacbccbb

Critical pair: cbbbccbbbc=abbbbccbccbb.

Flip LHS and RHS.

Defines rule #32.

Referenced by [60].

[32] cbbbbbccbbbc=abcbcccbccbb

Overlap of [26] cbbbbbba=abcbcc with [13] bacbccbb=ccbbbc:

cbbbbb ba bacbccbb

Critical pair: cbbbbbccbbbc=abcbcccbccbb.

Defines rule #34.

[33] abbbbbbcbccbc=cbbbcabccbbbb

Overlap of [12] abbbbbc=cbbbca with [14] cbccbbbb=bcbccbc:

abbbbb c cbccbbbb

Critical pair: abbbbbbcbccbc=cbbbcabccbbbb.

Defines rule #37.

Referenced by [56], [57].

[34] cbbbbbbbccbbbb=abbccbbcbccbc

Overlap of [15] abbccbc=cbbbbbb with [14] cbccbbbb=bcbccbc:

abbccb c cbccbbbb

Critical pair: abbccbbcbccbc=cbbbbbbbccbbbb.

Flip LHS and RHS.

Defines rule #39.

[35] abcbccbcbc=cbbbbbccbb

Overlap of [20] abcbccbb=cbbbbbc with [7] bcbb=cbc:

abcbccb b bcbb

Critical pair: abcbccbcbc=cbbbbbccbb.

Defines rule #25.

[36] cbbbbbccbbbb=abcbccbccbc

Overlap of [17] cbbbbbca=acbccbb with [11] abbcbc=cbbbb:

cbbbbbc a abbcbc

Critical pair: cbbbbbccbbbb=acbccbbbbcbc.

Reduce RHS:

[14]a(cbccbbbb)cbc
abcbccbccbc

Defines rule #31.

[37] abbbbbbccbccbb=cbbbcabccbbbc

Overlap of [12] abbbbbc=cbbbca with [18] cbccbbbc=bccbccbb:

abbbbb c cbccbbbc

Critical pair: abbbbbbccbccbb=cbbbcabccbbbc.

Defines rule #40.

Referenced by [61].

[38] cbbbbbbbccbbbc=abbccbbccbccbb

Overlap of [15] abbccbc=cbbbbbb with [18] cbccbbbc=bccbccbb:

abbccb c cbccbbbc

Critical pair: abbccbbccbccbb=cbbbbbbbccbbbc.

Flip LHS and RHS.

Defines rule #41.

[39] cbbbcabba=abbbbbbc

Overlap of [21] abbbbcbc=cbbbcabb with [8] cbca=bbc:

abbbb cbc cbca

Critical pair: abbbbbbc=cbbbcabba.

Flip LHS and RHS.

Defines rule #23.

Referenced by [43], [46], [53].

[40] cbbbcabccbbbbbb=abbbbbbcbcccbc

Overlap of [23] cbbbcabca=abbbbbbbc with [15] abbccbc=cbbbbbb:

cbbbcabc a abbccbc

Critical pair: cbbbcabccbbbbbb=abbbbbbbcbbccbc.

Reduce RHS:

[7]abbbbbb(bcbb)ccbc
abbbbbbcbcccbc

Defines rule #44.

[41] abbbbccbccbcbc=cbbbccbbbccbb

Overlap of [16] cbbbba=abbbbc with [19] bacbccbcbc=ccbbbccbb:

cbbb ba bacbccbcbc

Critical pair: cbbbccbbbccbb=abbbbccbccbcbc.

Flip LHS and RHS.

Defines rule #42.

[42] bacbcccbccbb=ccbbbccbbbc

Overlap of [19] bacbccbcbc=ccbbbccbb with [9] bcbcbc=cbccbb:

bacbcc bcbc bcbcbc

Critical pair: bacbcccbccbb=ccbbbccbbbc.

Defines rule #33.

Referenced by [52], [53], [54].

[43] abbbbbbccbccbcbc=cbbbcabccbbbccbb

Overlap of [39] cbbbcabba=abbbbbbc with [19] bacbccbcbc=ccbbbccbb:

cbbbcab ba bacbccbcbc

Critical pair: cbbbcabccbbbccbb=abbbbbbccbccbcbc.

Flip LHS and RHS.

Defines rule #51.

[44] abbbbccbccbccbc=cbbbccbbbccbbbb

Overlap of [16] cbbbba=abbbbc with [29] bacbccbccbc=ccbbbccbbbb:

cbbb ba bacbccbccbc

Critical pair: cbbbccbbbccbbbb=abbbbccbccbccbc.

Flip LHS and RHS.

Defines rule #47.

[45] ccbbbccbbbbbcbc=bacbccbcccbccbb

Overlap of [29] bacbccbccbc=ccbbbccbbbb with [9] bcbcbc=cbccbb:

bacbccbcc bc bcbcbc

Critical pair: bacbccbcccbccbb=ccbbbccbbbbbcbc.

Flip LHS and RHS.

Defines rule #46.

[46] cbbbcabccbbbccbbbb=abbbbbbccbccbccbc

Overlap of [39] cbbbcabba=abbbbbbc with [29] bacbccbccbc=ccbbbccbbbb:

cbbbcab ba bacbccbccbc

Critical pair: cbbbcabccbbbccbbbb=abbbbbbccbccbccbc.

Defines rule #55.

[47] cbbbcaabbbbbb=abbbbbbaccbc

Overlap of [24] abbbbbbacbc=cbbbcaabbbb with [7] bcbb=cbc:

abbbbbbac bc bcbb

Critical pair: abbbbbbaccbc=cbbbcaabbbbbb.

Flip LHS and RHS.

Defines rule #36.

Referenced by [55], [57], [61].

[48] cbbbcacbbbcaa=abbbbbbacbbbc

Overlap of [24] abbbbbbacbc=cbbbcaabbbb with [8] cbca=bbc:

abbbbbbacb c cbca

Critical pair: abbbbbbacbbbc=cbbbcaabbbbbca.

Reduce RHS:

[12]cbbbca(abbbbbc)a
cbbbcacbbbcaa

Flip LHS and RHS.

Defines rule #38.

Referenced by [58], [59], [60].

[49] abbbbbbaccbccbb=cbbbcacbbbcabc

Overlap of [24] abbbbbbacbc=cbbbcaabbbb with [9] bcbcbc=cbccbb:

abbbbbbac bc bcbcbc

Critical pair: abbbbbbaccbccbb=cbbbcaabbbbbcbc.

Reduce RHS:

[12]cbbbca(abbbbbc)bc
cbbbcacbbbcabc

Defines rule #45.

[50] abbbbbbacbbcbccbc=cbbbcacbbbcacbbbb

Overlap of [24] abbbbbbacbc=cbbbcaabbbb with [14] cbccbbbb=bcbccbc:

abbbbbbacb c cbccbbbb

Critical pair: abbbbbbacbbcbccbc=cbbbcaabbbbbccbbbb.

Reduce RHS:

[12]cbbbca(abbbbbc)cbbbb
cbbbcacbbbcacbbbb

Defines rule #54.

Referenced by [65].

[51] abbbbbbacbbccbccbb=cbbbcacbbbcacbbbc

Overlap of [24] abbbbbbacbc=cbbbcaabbbb with [18] cbccbbbc=bccbccbb:

abbbbbbacb c cbccbbbc

Critical pair: abbbbbbacbbccbccbb=cbbbcaabbbbbccbbbc.

Reduce RHS:

[12]cbbbca(abbbbbc)cbbbc
cbbbcacbbbcacbbbc

Defines rule #56.

Referenced by [66].

[52] abbbbccbcccbccbb=cbbbccbbbccbbbc

Overlap of [16] cbbbba=abbbbc with [42] bacbcccbccbb=ccbbbccbbbc:

cbbb ba bacbcccbccbb

Critical pair: cbbbccbbbccbbbc=abbbbccbcccbccbb.

Flip LHS and RHS.

Defines rule #49.

[53] cbbbcabccbbbccbbbc=abbbbbbccbcccbccbb

Overlap of [39] cbbbcabba=abbbbbbc with [42] bacbcccbccbb=ccbbbccbbbc:

cbbbcab ba bacbcccbccbb

Critical pair: cbbbcabccbbbccbbbc=abbbbbbccbcccbccbb.

Defines rule #57.

[54] bacbcccbccbcbc=ccbbbccbbbccbb

Overlap of [42] bacbcccbccbb=ccbbbccbbbc with [7] bcbb=cbc:

bacbcccbccb b bcbb

Critical pair: bacbcccbccbcbc=ccbbbccbbbccbb.

Defines rule #43.

Referenced by [62], [63], [64].

[55] abbbbbbaccbccbcbc=cbbbcacbbbcabccbb

Overlap of [47] cbbbcaabbbbbb=abbbbbbaccbc with [9] bcbcbc=cbccbb:

cbbbcaabbbbb b bcbcbc

Critical pair: cbbbcaabbbbbcbccbb=abbbbbbaccbccbcbc.

Reduce LHS:

[12]cbbbca(abbbbbc)bccbb
cbbbcacbbbcabccbb

Flip LHS and RHS.

Defines rule #53.

[56] cbbbcabccbbbbbcbc=abbbbbbcbcccbccbb

Overlap of [33] abbbbbbcbccbc=cbbbcabccbbbb with [9] bcbcbc=cbccbb:

abbbbbbcbcc bc bcbcbc

Critical pair: abbbbbbcbcccbccbb=cbbbcabccbbbbbcbc.

Flip LHS and RHS.

Defines rule #52.

[57] cbbbcacbbbcabccbbbb=abbbbbbaccbccbccbc

Overlap of [47] cbbbcaabbbbbb=abbbbbbaccbc with [33] abbbbbbcbccbc=cbbbcabccbbbb:

cbbbca abbbbbb abbbbbbcbccbc

Critical pair: cbbbcacbbbcabccbbbb=abbbbbbaccbccbccbc.

Defines rule #61.

[58] cbbbcacbbbcacbbbca=abbbbbbacbbccbcbc

Overlap of [48] cbbbcacbbbcaa=abbbbbbacbbbc with [12] abbbbbc=cbbbca:

cbbbcacbbbca a abbbbbc

Critical pair: cbbbcacbbbcacbbbca=abbbbbbacbbbcbbbbbc.

Reduce RHS:

[7]abbbbbbacbb(bcbb)bbbc
[7]abbbbbbacbbc(bcbb)bc
abbbbbbacbbccbcbc

Defines rule #59.

Referenced by [67].

[59] cbbbcacbbbcacbbbbbb=abbbbbbacbbcbcccbc

Overlap of [48] cbbbcacbbbcaa=abbbbbbacbbbc with [15] abbccbc=cbbbbbb:

cbbbcacbbbca a abbccbc

Critical pair: cbbbcacbbbcacbbbbbb=abbbbbbacbbbcbbccbc.

Reduce RHS:

[7]abbbbbbacbb(bcbb)ccbc
abbbbbbacbbcbcccbc

Defines rule #60.

[60] cbbbcacbbbcacbbbccbbbc=abbbbbbacbbccbcccbccbb

Overlap of [48] cbbbcacbbbcaa=abbbbbbacbbbc with [31] abbbbccbccbb=cbbbccbbbc:

cbbbcacbbbca a abbbbccbccbb

Critical pair: cbbbcacbbbcacbbbccbbbc=abbbbbbacbbbcbbbbccbccbb.

Reduce RHS:

[7]abbbbbbacbb(bcbb)bbccbccbb
[7]abbbbbbacbbc(bcbb)ccbccbb
abbbbbbacbbccbcccbccbb

Defines rule #66.

[61] cbbbcacbbbcabccbbbc=abbbbbbaccbcccbccbb

Overlap of [47] cbbbcaabbbbbb=abbbbbbaccbc with [37] abbbbbbccbccbb=cbbbcabccbbbc:

cbbbca abbbbbb abbbbbbccbccbb

Critical pair: cbbbcacbbbcabccbbbc=abbbbbbaccbcccbccbb.

Defines rule #62.

[62] abbbbccbcccbccbcbc=cbbbccbbbccbbbccbb

Overlap of [16] cbbbba=abbbbc with [54] bacbcccbccbcbc=ccbbbccbbbccbb:

cbbb ba bacbcccbccbcbc

Critical pair: cbbbccbbbccbbbccbb=abbbbccbcccbccbcbc.

Flip LHS and RHS.

Defines rule #58.

[63] ccbbbccbbbccbbbb=bacbcccbccbccbc

Overlap of [54] bacbcccbccbcbc=ccbbbccbbbccbb with [7] bcbb=cbc:

bacbcccbccbc bc bcbb

Critical pair: bacbcccbccbccbc=ccbbbccbbbccbbbb.

Flip LHS and RHS.

Defines rule #48.

[64] ccbbbccbbbccbbbc=bacbcccbcccbccbb

Overlap of [54] bacbcccbccbcbc=ccbbbccbbbccbb with [9] bcbcbc=cbccbb:

bacbcccbcc bcbc bcbcbc

Critical pair: bacbcccbcccbccbb=ccbbbccbbbccbbbc.

Flip LHS and RHS.

Defines rule #50.

[65] cbbbcacbbbcacbbbbbcbc=abbbbbbacbbcbcccbccbb

Overlap of [50] abbbbbbacbbcbccbc=cbbbcacbbbcacbbbb with [9] bcbcbc=cbccbb:

abbbbbbacbbcbcc bc bcbcbc

Critical pair: abbbbbbacbbcbcccbccbb=cbbbcacbbbcacbbbbbcbc.

Flip LHS and RHS.

Defines rule #64.

[66] abbbbbbacbbccbccbcbc=cbbbcacbbbcacbbbccbb

Overlap of [51] abbbbbbacbbccbccbb=cbbbcacbbbcacbbbc with [7] bcbb=cbc:

abbbbbbacbbccbccb b bcbb

Critical pair: abbbbbbacbbccbccbcbc=cbbbcacbbbcacbbbccbb.

Defines rule #63.

[67] cbbbcacbbbcacbbbccbbbb=abbbbbbacbbccbccbccbc

Overlap of [58] cbbbcacbbbcacbbbca=abbbbbbacbbccbcbc with [11] abbcbc=cbbbb:

cbbbcacbbbcacbbbc a abbcbc

Critical pair: cbbbcacbbbcacbbbccbbbb=abbbbbbacbbccbcbcbbcbc.

Reduce RHS:

[7]abbbbbbacbbccbc(bcbb)cbc
abbbbbbacbbccbccbccbc

Defines rule #65.