Certificate for #5113 ⟨a, b | aaabbba=bbaa

Completion settings:

[1] aaabbba=bbaa

Axiom: aaabbba=bbaa.

Referenced by [3].

[2] bbaa=c

Axiom: bbaa=c.

Defines rule #2.

Referenced by [3], [4], [5], [6], [7], [8].

[3] aaabbba=c

Simplify [1] aaabbba=bbaa.

Reduce RHS:

[2](bbaa)
c

Defines rule #14.

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

[4] aaabc=ca

Overlap of [3] aaabbba=c with [2] bbaa=c:

aaab bba bbaa

Critical pair: aaabc=ca.

Defines rule #4.

Referenced by [7], [8], [9], [10], [12], [20], [32].

[5] cabbba=bbc

Overlap of [2] bbaa=c with [3] aaabbba=c:

bb aa aaabbba

Critical pair: bbc=cabbba.

Flip LHS and RHS.

Defines rule #5.

Referenced by [10], [11], [13], [14], [15].

[6] caabbba=bbac

Overlap of [2] bbaa=c with [3] aaabbba=c:

bba a aaabbba

Critical pair: bbac=caabbba.

Flip LHS and RHS.

Defines rule #9.

Referenced by [10], [14], [15].

[7] bbca=cabc

Overlap of [2] bbaa=c with [4] aaabc=ca:

bb aa aaabc

Critical pair: bbca=cabc.

Defines rule #1.

Referenced by [9], [11], [14], [16], [18], [21], [26], [29], [33], [42].

[8] bbaca=caabc

Overlap of [2] bbaa=c with [4] aaabc=ca:

bba a aaabc

Critical pair: bbaca=caabc.

Defines rule #3.

Referenced by [12], [13], [15], [17], [19], [22], [27], [30], [34], [43].

[9] cabcaabc=bbcca

Overlap of [7] bbca=cabc with [4] aaabc=ca:

bbc a aaabc

Critical pair: bbcca=cabcaabc.

Flip LHS and RHS.

Defines rule #7.

Referenced by [18], [19], [23], [35].

[10] aaabbbc=bbac

Overlap of [4] aaabc=ca with [5] cabbba=bbc:

aaab c cabbba

Critical pair: aaabbbc=caabbba.

Reduce RHS:

[6](caabbba)
bbac

Defines rule #13.

Referenced by [16], [17].

[11] cabcbbba=bbbbc

Overlap of [7] bbca=cabc with [5] cabbba=bbc:

bb ca cabbba

Critical pair: bbbbc=cabcbbba.

Flip LHS and RHS.

Defines rule #10.

Referenced by [20], [21], [22], [23], [24], [25], [26], [27], [31].

[12] caabcaabc=bbacca

Overlap of [8] bbaca=caabc with [4] aaabc=ca:

bbac a aaabc

Critical pair: bbacca=caabcaabc.

Flip LHS and RHS.

Defines rule #11.

Referenced by [25], [36].

[13] caabcbbba=bbabbc

Overlap of [8] bbaca=caabc with [5] cabbba=bbc:

bba ca cabbba

Critical pair: bbabbc=caabcbbba.

Flip LHS and RHS.

Defines rule #15.

Referenced by [20], [23], [25], [26], [27], [28], [31], [39].

[14] bbbbac=cabbbc

Overlap of [7] bbca=cabc with [6] caabbba=bbac:

bb ca caabbba

Critical pair: bbbbac=cabcabbba.

Reduce RHS:

[5]cab(cabbba)
cabbbc

Defines rule #6.

[15] bbabbac=caabbbc

Overlap of [8] bbaca=caabc with [6] caabbba=bbac:

bba ca caabbba

Critical pair: bbabbac=caabcabbba.

Reduce RHS:

[5]caab(cabbba)
caabbbc

Defines rule #8.

Referenced by [24], [28], [38], [44].

[16] cabcaabbbc=bbcbbac

Overlap of [7] bbca=cabc with [10] aaabbbc=bbac:

bbc a aaabbbc

Critical pair: bbcbbac=cabcaabbbc.

Flip LHS and RHS.

Defines rule #20.

[17] caabcaabbbc=bbacbbac

Overlap of [8] bbaca=caabc with [10] aaabbbc=bbac:

bbac a aaabbbc

Critical pair: bbacbbac=caabcaabbbc.

Flip LHS and RHS.

Defines rule #24.

[18] cabcbcaabc=bbbbcca

Overlap of [7] bbca=cabc with [9] cabcaabc=bbcca:

bb ca cabcaabc

Critical pair: bbbbcca=cabcbcaabc.

Flip LHS and RHS.

Defines rule #12.

Referenced by [29], [30], [31], [37].

[19] caabcbcaabc=bbabbcca

Overlap of [8] bbaca=caabc with [9] cabcaabc=bbcca:

bba ca cabcaabc

Critical pair: bbabbcca=caabcbcaabc.

Flip LHS and RHS.

Defines rule #17.

Referenced by [41].

[20] aaabbbbbc=bbabbc

Overlap of [4] aaabc=ca with [11] cabcbbba=bbbbc:

aaab c cabcbbba

Critical pair: aaabbbbbc=caabcbbba.

Reduce RHS:

[13](caabcbbba)
bbabbc

Defines rule #26.

[21] cabcbcbbba=bbbbbbc

Overlap of [7] bbca=cabc with [11] cabcbbba=bbbbc:

bb ca cabcbbba

Critical pair: bbbbbbc=cabcbcbbba.

Flip LHS and RHS.

Defines rule #16.

Referenced by [32], [33], [34], [35], [36], [37], [38], [40], [41], [42], [43], [46].

[22] caabcbcbbba=bbabbbbc

Overlap of [8] bbaca=caabc with [11] cabcbbba=bbbbc:

bba ca cabcbbba

Critical pair: bbabbbbc=caabcbcbbba.

Flip LHS and RHS.

Defines rule #21.

Referenced by [32], [35], [36], [37], [41], [42], [43], [44], [45], [46], [47].

[23] cabcaabbbbbc=bbcbbabbc

Overlap of [9] cabcaabc=bbcca with [11] cabcbbba=bbbbc:

cabcaab c cabcbbba

Critical pair: cabcaabbbbbc=bbccaabcbbba.

Reduce RHS:

[13]bbc(caabcbbba)
bbcbbabbc

Defines rule #31.

[24] cabcbcaabbbc=bbbbcbbac

Overlap of [11] cabcbbba=bbbbc with [15] bbabbac=caabbbc:

cabcb bba bbabbac

Critical pair: cabcbcaabbbc=bbbbcbbac.

Defines rule #25.

[25] caabcaabbbbbc=bbacbbabbc

Overlap of [12] caabcaabc=bbacca with [11] cabcbbba=bbbbc:

caabcaab c cabcbbba

Critical pair: caabcaabbbbbc=bbaccaabcbbba.

Reduce RHS:

[13]bbac(caabcbbba)
bbacbbabbc

Defines rule #35.

[26] bbbbabbc=cabbbbbc

Overlap of [7] bbca=cabc with [13] caabcbbba=bbabbc:

bb ca caabcbbba

Critical pair: bbbbabbc=cabcabcbbba.

Reduce RHS:

[11]cab(cabcbbba)
cabbbbbc

Defines rule #19.

[27] bbabbabbc=caabbbbbc

Overlap of [8] bbaca=caabc with [13] caabcbbba=bbabbc:

bba ca caabcbbba

Critical pair: bbabbabbc=caabcabcbbba.

Reduce RHS:

[11]caab(cabcbbba)
caabbbbbc

Defines rule #23.

Referenced by [39], [40], [45].

[28] caabcbcaabbbc=bbabbcbbac

Overlap of [13] caabcbbba=bbabbc with [15] bbabbac=caabbbc:

caabcb bba bbabbac

Critical pair: caabcbcaabbbc=bbabbcbbac.

Defines rule #28.

[29] cabcbcbcaabc=bbbbbbcca

Overlap of [7] bbca=cabc with [18] cabcbcaabc=bbbbcca:

bb ca cabcbcaabc

Critical pair: bbbbbbcca=cabcbcbcaabc.

Flip LHS and RHS.

Defines rule #18.

Referenced by [46].

[30] caabcbcbcaabc=bbabbbbcca

Overlap of [8] bbaca=caabc with [18] cabcbcaabc=bbbbcca:

bba ca cabcbcaabc

Critical pair: bbabbbbcca=caabcbcbcaabc.

Flip LHS and RHS.

Defines rule #22.

[31] cabcbcaabbbbbc=bbbbcbbabbc

Overlap of [18] cabcbcaabc=bbbbcca with [11] cabcbbba=bbbbc:

cabcbcaab c cabcbbba

Critical pair: cabcbcaabbbbbc=bbbbccaabcbbba.

Reduce RHS:

[13]bbbbc(caabcbbba)
bbbbcbbabbc

Defines rule #36.

[32] aaabbbbbbbc=bbabbbbc

Overlap of [4] aaabc=ca with [21] cabcbcbbba=bbbbbbc:

aaab c cabcbcbbba

Critical pair: aaabbbbbbbc=caabcbcbbba.

Reduce RHS:

[22](caabcbcbbba)
bbabbbbc

Defines rule #37.

[33] bbbbbbbbc=cabcbcbcbbba

Overlap of [7] bbca=cabc with [21] cabcbcbbba=bbbbbbc:

bb ca cabcbcbbba

Critical pair: bbbbbbbbc=cabcbcbcbbba.

Defines rule #27.

[34] bbabbbbbbc=caabcbcbcbbba

Overlap of [8] bbaca=caabc with [21] cabcbcbbba=bbbbbbc:

bba ca cabcbcbbba

Critical pair: bbabbbbbbc=caabcbcbcbbba.

Defines rule #32.

[35] cabcaabbbbbbbc=bbcbbabbbbc

Overlap of [9] cabcaabc=bbcca with [21] cabcbcbbba=bbbbbbc:

cabcaab c cabcbcbbba

Critical pair: cabcaabbbbbbbc=bbccaabcbcbbba.

Reduce RHS:

[22]bbc(caabcbcbbba)
bbcbbabbbbc

Defines rule #40.

[36] caabcaabbbbbbbc=bbacbbabbbbc

Overlap of [12] caabcaabc=bbacca with [21] cabcbcbbba=bbbbbbc:

caabcaab c cabcbcbbba

Critical pair: caabcaabbbbbbbc=bbaccaabcbcbbba.

Reduce RHS:

[22]bbac(caabcbcbbba)
bbacbbabbbbc

Defines rule #42.

[37] cabcbcaabbbbbbbc=bbbbcbbabbbbc

Overlap of [18] cabcbcaabc=bbbbcca with [21] cabcbcbbba=bbbbbbc:

cabcbcaab c cabcbcbbba

Critical pair: cabcbcaabbbbbbbc=bbbbccaabcbcbbba.

Reduce RHS:

[22]bbbbc(caabcbcbbba)
bbbbcbbabbbbc

Defines rule #43.

[38] cabcbcbcaabbbc=bbbbbbcbbac

Overlap of [21] cabcbcbbba=bbbbbbc with [15] bbabbac=caabbbc:

cabcbcb bba bbabbac

Critical pair: cabcbcbcaabbbc=bbbbbbcbbac.

Defines rule #29.

[39] caabcbcaabbbbbc=bbabbcbbabbc

Overlap of [13] caabcbbba=bbabbc with [27] bbabbabbc=caabbbbbc:

caabcb bba bbabbabbc

Critical pair: caabcbcaabbbbbc=bbabbcbbabbc.

Defines rule #38.

[40] cabcbcbcaabbbbbc=bbbbbbcbbabbc

Overlap of [21] cabcbcbbba=bbbbbbc with [27] bbabbabbc=caabbbbbc:

cabcbcb bba bbabbabbc

Critical pair: cabcbcbcaabbbbbc=bbbbbbcbbabbc.

Defines rule #39.

[41] caabcbcaabbbbbbbc=bbabbcbbabbbbc

Overlap of [19] caabcbcaabc=bbabbcca with [21] cabcbcbbba=bbbbbbc:

caabcbcaab c cabcbcbbba

Critical pair: caabcbcaabbbbbbbc=bbabbccaabcbcbbba.

Reduce RHS:

[22]bbabbc(caabcbcbbba)
bbabbcbbabbbbc

Defines rule #44.

[42] bbbbabbbbc=cabbbbbbbc

Overlap of [7] bbca=cabc with [22] caabcbcbbba=bbabbbbc:

bb ca caabcbcbbba

Critical pair: bbbbabbbbc=cabcabcbcbbba.

Reduce RHS:

[21]cab(cabcbcbbba)
cabbbbbbbc

Defines rule #30.

[43] bbabbabbbbc=caabbbbbbbc

Overlap of [8] bbaca=caabc with [22] caabcbcbbba=bbabbbbc:

bba ca caabcbcbbba

Critical pair: bbabbabbbbc=caabcabcbcbbba.

Reduce RHS:

[21]caab(cabcbcbbba)
caabbbbbbbc

Defines rule #34.

Referenced by [47].

[44] caabcbcbcaabbbc=bbabbbbcbbac

Overlap of [22] caabcbcbbba=bbabbbbc with [15] bbabbac=caabbbc:

caabcbcb bba bbabbac

Critical pair: caabcbcbcaabbbc=bbabbbbcbbac.

Defines rule #33.

[45] caabcbcbcaabbbbbc=bbabbbbcbbabbc

Overlap of [22] caabcbcbbba=bbabbbbc with [27] bbabbabbc=caabbbbbc:

caabcbcb bba bbabbabbc

Critical pair: caabcbcbcaabbbbbc=bbabbbbcbbabbc.

Defines rule #41.

[46] cabcbcbcaabbbbbbbc=bbbbbbcbbabbbbc

Overlap of [29] cabcbcbcaabc=bbbbbbcca with [21] cabcbcbbba=bbbbbbc:

cabcbcbcaab c cabcbcbbba

Critical pair: cabcbcbcaabbbbbbbc=bbbbbbccaabcbcbbba.

Reduce RHS:

[22]bbbbbbc(caabcbcbbba)
bbbbbbcbbabbbbc

Defines rule #45.

[47] caabcbcbcaabbbbbbbc=bbabbbbcbbabbbbc

Overlap of [22] caabcbcbbba=bbabbbbc with [43] bbabbabbbbc=caabbbbbbbc:

caabcbcb bba bbabbabbbbc

Critical pair: caabcbcbcaabbbbbbbc=bbabbbbcbbabbbbc.

Defines rule #46.