Certificate for #15905 ⟨a, b | aba=bb, aaaaa=a

Completion settings:

[1] aba=bb

Axiom: aba=bb.

Defines rule #4.

Referenced by [3], [4], [5], [6], [7], [9], [10], [12], [15], [16].

[2] aaaaa=a

Axiom: aaaaa=a.

Defines rule #15.

Referenced by [4], [5].

[3] bbba=abbb

Overlap of [1] aba=bb with [1] aba=bb:

ab a aba

Critical pair: abbb=bbba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [7], [8], [9], [11], [12], [16], [18].

[4] bbaaaa=bb

Overlap of [1] aba=bb with [2] aaaaa=a:

ab a aaaaa

Critical pair: aba=bbaaaa.

Reduce LHS:

[1](aba)
bb

Flip LHS and RHS.

Defines rule #14.

[5] aaaabb=bb

Overlap of [2] aaaaa=a with [1] aba=bb:

aaaa a aba

Critical pair: aaaabb=aba.

Reduce RHS:

[1](aba)
bb

Defines rule #12.

Referenced by [6], [7], [14], [16].

[6] bbaaabb=abbb

Overlap of [1] aba=bb with [5] aaaabb=bb:

ab a aaaabb

Critical pair: abbb=bbaaabb.

Flip LHS and RHS.

Defines rule #11.

[7] aaabbbbb=babbb

Overlap of [5] aaaabb=bb with [3] bbba=abbb:

aaaab b bbba

Critical pair: aaaababbb=bbbba.

Reduce LHS:

[1]aaa(aba)bbb
aaabbbbb

Reduce RHS:

[3]b(bbba)
babbb

Referenced by [8], [9], [17].

[8] aaabbabbb=baabbb

Overlap of [7] aaabbbbb=babbb with [3] bbba=abbb:

aaabb bbb bbba

Critical pair: aaabbabbb=babbba.

Reduce RHS:

[3]ba(bbba)
baabbb

Defines rule #13.

Referenced by [10], [11], [12], [19].

[9] babbabbb=aabbbbbbbb

Overlap of [7] aaabbbbb=babbb with [3] bbba=abbb:

aaabbbb b bbba

Critical pair: aaabbbbabbb=babbbbba.

Reduce LHS:

[3]aaab(bbba)bbb
[1]aa(aba)bbbbbb
aabbbbbbbb

Reduce RHS:

[3]babb(bbba)
babbabbb

Flip LHS and RHS.

Defines rule #6.

Referenced by [12].

[10] bbaabbabbb=abbaabbb

Overlap of [1] aba=bb with [8] aaabbabbb=baabbb:

ab a aaabbabbb

Critical pair: abbaabbb=bbaabbabbb.

Flip LHS and RHS.

Referenced by [13].

[11] aaabbaabbb=baaabbb

Overlap of [8] aaabbabbb=baabbb with [3] bbba=abbb:

aaabba bbb bbba

Critical pair: aaabbaabbb=baabbba.

Reduce RHS:

[3]baa(bbba)
baaabbb

Referenced by [14].

[12] baabbabbb=aabbabbbbbbbb

Overlap of [8] aaabbabbb=baabbb with [3] bbba=abbb:

aaabbabb b bbba

Critical pair: aaabbabbabbb=baabbbbba.

Reduce LHS:

[9]aaab(babbabbb)
[1]aa(aba)abbbbbbbb
aabbabbbbbbbb

Reduce RHS:

[3]baabb(bbba)
baabbabbb

Flip LHS and RHS.

Defines rule #10.

Referenced by [13].

[13] abbaabbb=aabbabbbbbbbbbbbbb

Overlap of [10] bbaabbabbb=abbaabbb with [12] baabbabbb=aabbabbbbbbbb:

b baabbabbb baabbabbb

Critical pair: baabbabbbbbbbb=abbaabbb.

Reduce LHS:

[12](baabbabbb)bbbbb
aabbabbbbbbbbbbbbb

Flip LHS and RHS.

Referenced by [14].

[14] baaabbb=bbabbbbbbbbbbbbb

Overlap of [11] aaabbaabbb=baaabbb with [13] abbaabbb=aabbabbbbbbbbbbbbb:

aa abbaabbb abbaabbb

Critical pair: aaaabbabbbbbbbbbbbbb=baaabbb.

Reduce LHS:

[5](aaaabb)abbbbbbbbbbbbb
bbabbbbbbbbbbbbb

Flip LHS and RHS.

Defines rule #9.

Referenced by [15], [16].

[15] bbaabbb=abbabbbbbbbbbbbbb

Overlap of [1] aba=bb with [14] baaabbb=bbabbbbbbbbbbbbb:

a ba baaabbb

Critical pair: abbabbbbbbbbbbbbb=bbaabbb.

Flip LHS and RHS.

Defines rule #7.

[16] bbbbbbbbbbbbbbbb=bbbb

Overlap of [14] baaabbb=bbabbbbbbbbbbbbb with [3] bbba=abbb:

baaa bbb bbba

Critical pair: baaaabbb=bbabbbbbbbbbbbbba.

Reduce LHS:

[5]b(aaaabb)b
bbbb

Reduce RHS:

[3]bbabbbbbbbbbb(bbba)
[3]bbabbbbbbb(bbba)bbb
[3]bbabbbb(bbba)bbbbbb
[3]bbab(bbba)bbbbbbbbb
[1]bb(aba)bbbbbbbbbbbb
bbbbbbbbbbbbbbbb

Flip LHS and RHS.

Defines rule #1.

Referenced by [17], [18].

[17] aaabbbb=babbbbbbbbbbbbbb

Overlap of [7] aaabbbbb=babbb with [16] bbbbbbbbbbbbbbbb=bbbb:

aaa bbbbb bbbbbbbbbbbbbbbb

Critical pair: aaabbbb=babbbbbbbbbbbbbb.

Defines rule #8.

[18] babbbbbbbbbbbbbbb=babbb

Overlap of [16] bbbbbbbbbbbbbbbb=bbbb with [3] bbba=abbb:

bbbbbbbbbbbbb bbb bbba

Critical pair: bbbbbbbbbbbbbabbb=bbbba.

Reduce LHS:

[3]bbbbbbbbbb(bbba)bbb
[3]bbbbbbb(bbba)bbbbbb
[3]bbbb(bbba)bbbbbbbbb
[3]b(bbba)bbbbbbbbbbbb
babbbbbbbbbbbbbbb

Reduce RHS:

[3]b(bbba)
babbb

Defines rule #2.

Referenced by [19].

[19] baabbbbbbbbbbbbbbb=baabbb

Overlap of [8] aaabbabbb=baabbb with [18] babbbbbbbbbbbbbbb=babbb:

aaab babbb babbbbbbbbbbbbbbb

Critical pair: aaabbabbb=baabbbbbbbbbbbbbbb.

Reduce LHS:

[8](aaabbabbb)
baabbb

Flip LHS and RHS.

Defines rule #5.