Certificate for #27655 ⟨a, b | aa=1, ababbb=bab

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #3.

Referenced by [3], [4], [7], [10], [11], [13], [15], [16].

[2] ababbb=bab

Axiom: ababbb=bab.

Referenced by [3], [7].

[3] abab=babbb

Overlap of [1] aa=1 with [2] ababbb=bab:

a a ababbb

Critical pair: abab=babbb.

Defines rule #4.

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

[4] babbbbb=bab

Overlap of [1] aa=1 with [3] abab=babbb:

a a abab

Critical pair: ababbb=bab.

Reduce LHS:

[3](abab)bb
babbbbb

Defines rule #1.

Referenced by [6], [7], [8], [9], [12], [14], [15].

[5] babbbab=abbabbb

Overlap of [3] abab=babbb with [3] abab=babbb:

ab ab abab

Critical pair: abbabbb=babbbab.

Flip LHS and RHS.

Defines rule #6.

Referenced by [6], [7], [9], [10], [12], [13].

[6] babbabbabbb=abbbabbb

Overlap of [5] babbbab=abbabbb with [5] babbbab=abbabbb:

babb bab babbbab

Critical pair: babbabbabbb=abbabbbbbab.

Reduce RHS:

[4]ab(babbbbb)ab
[3]abb(abab)
abbbabbb

Referenced by [7], [8].

[7] abbabbbbab=bbbbabbb

Overlap of [2] ababbb=bab with [6] babbabbabbb=abbbabbb:

ababb b babbabbabbb

Critical pair: ababbabbbabbb=bababbabbabbb.

Reduce LHS:

[5]abab(babbbab)bb
[4]ababab(babbbbb)
[3](abab)abbab
[5](babbbab)bab
abbabbbbab

Reduce RHS:

[6]ba(babbabbabbb)
[1]b(aa)bbbabbb
bbbbabbb

Referenced by [13].

[8] babbabbab=abbbab

Overlap of [6] babbabbabbb=abbbabbb with [4] babbbbb=bab:

babbab babbb babbbbb

Critical pair: babbabbab=abbbabbbbb.

Reduce RHS:

[4]abb(babbbbb)
abbbab

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

[9] bbabbbbab=abbbbabbb

Overlap of [8] babbabbab=abbbab with [3] abab=babbb:

babbabb ab abab

Critical pair: babbabbbabbb=abbbabab.

Reduce LHS:

[5]bab(babbbab)bb
[4]babab(babbbbb)
[3]b(abab)bab
bbabbbbab

Reduce RHS:

[3]abbb(abab)
abbbbabbb

Defines rule #7.

Referenced by [15].

[10] abbbabbab=bbbabbb

Overlap of [8] babbabbab=abbbab with [8] babbabbab=abbbab:

bab babbab babbabbab

Critical pair: bababbbab=abbbabbab.

Reduce LHS:

[5]ba(babbbab)
[1]b(aa)bbabbb
bbbabbb

Flip LHS and RHS.

Referenced by [11], [12].

[11] bbbabbab=abbbabbb

Overlap of [1] aa=1 with [10] abbbabbab=bbbabbb:

a a abbbabbab

Critical pair: abbbabbb=bbbabbab.

Flip LHS and RHS.

Defines rule #8.

[12] abbabbab=bbabbabbb

Overlap of [10] abbbabbab=bbbabbb with [3] abab=babbb:

abbbabb ab abab

Critical pair: abbbabbbabbb=bbbabbbab.

Reduce LHS:

[5]abb(babbbab)bb
[4]abbab(babbbbb)
abbabbab

Reduce RHS:

[5]bb(babbbab)
bbabbabbb

Defines rule #9.

Referenced by [13].

[13] bbbbbbabbb=bbabbb

Overlap of [12] abbabbab=bbabbabbb with [8] babbabbab=abbbab:

ab babbab babbabbab

Critical pair: ababbbab=bbabbabbbbab.

Reduce LHS:

[5]a(babbbab)
[1](aa)bbabbb
bbabbb

Reduce RHS:

[7]bb(abbabbbbab)
bbbbbbabbb

Flip LHS and RHS.

Referenced by [14].

[14] bbbbbbab=bbab

Overlap of [13] bbbbbbabbb=bbabbb with [4] babbbbb=bab:

bbbbb babbb babbbbb

Critical pair: bbbbbbab=bbabbbbb.

Reduce RHS:

[4]b(babbbbb)
bbab

Defines rule #2.

[15] abbbbbabbb=bbbbbab

Overlap of [3] abab=babbb with [9] bbabbbbab=abbbbabbb:

aba b bbabbbbab

Critical pair: abaabbbbabbb=babbbbabbbbab.

Reduce LHS:

[1]ab(aa)bbbbabbb
abbbbbabbb

Reduce RHS:

[9]babb(bbabbbbab)
[9]ba(bbabbbbab)bb
[1]b(aa)bbbbabbbbb
[4]bbbb(babbbbb)
bbbbbab

Referenced by [16].

[16] abbbbbab=bbbbbabbb

Overlap of [1] aa=1 with [15] abbbbbabbb=bbbbbab:

a a abbbbbabbb

Critical pair: abbbbbab=bbbbbabbb.

Defines rule #5.