Certificate for #10004 ⟨a, b | aa=1, ababba=bb

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #1.

Referenced by [3], [4], [6], [11], [12], [15].

[2] ababba=bb

Axiom: ababba=bb.

Referenced by [3], [4], [5], [7], [13].

[3] babba=abb

Overlap of [1] aa=1 with [2] ababba=bb:

a a ababba

Critical pair: abb=babba.

Flip LHS and RHS.

Referenced by [5], [6], [7], [8], [9], [10], [14], [16], [17].

[4] ababb=bba

Overlap of [2] ababba=bb with [1] aa=1:

ababb a aa

Critical pair: ababb=bba.

Referenced by [5], [8], [10].

[5] abbba=bbbba

Overlap of [2] ababba=bb with [3] babba=abb:

abab ba babba

Critical pair: abababb=bbbba.

Reduce LHS:

[4]ab(ababb)
abbba

Referenced by [7], [9], [11].

[6] abba=babb

Overlap of [3] babba=abb with [1] aa=1:

babb a aa

Critical pair: babb=abba.

Flip LHS and RHS.

Referenced by [9], [10], [11].

[7] babbbb=bbbabb

Overlap of [3] babba=abb with [2] ababba=bb:

babb a ababba

Critical pair: babbbb=abbbabba.

Reduce RHS:

[5](abbba)bba
[3]bbb(babba)
bbbabb

Referenced by [10], [11].

[8] abbbba=bbba

Overlap of [3] babba=abb with [3] babba=abb:

bab ba babba

Critical pair: bababb=abbbba.

Reduce LHS:

[4]b(ababb)
bbba

Flip LHS and RHS.

Referenced by [9].

[9] bbbbbabb=bbba

Overlap of [3] babba=abb with [6] abba=babb:

babb a abba

Critical pair: babbbabb=abbbba.

Reduce LHS:

[5]b(abbba)bb
bbbbbabb

Reduce RHS:

[8](abbbba)
bbba

Referenced by [13].

[10] bbabb=bba

Overlap of [6] abba=babb with [3] babba=abb:

ab ba babba

Critical pair: ababb=babbbba.

Reduce LHS:

[4](ababb)
bba

Reduce RHS:

[7](babbbb)a
[3]bb(babba)
bbabb

Flip LHS and RHS.

Referenced by [11], [14].

[11] bbbba=bbb

Overlap of [6] abba=babb with [6] abba=babb:

abb a abba

Critical pair: abbbabb=babbbba.

Reduce LHS:

[5](abbba)bb
[10]bb(bbabb)
bbbba

Reduce RHS:

[7](babbbb)a
[10]b(bbabb)a
[1]bbb(aa)
bbb

Referenced by [12], [13], [14].

[12] bbba=bbbb

Overlap of [11] bbbba=bbb with [1] aa=1:

bbbb a aa

Critical pair: bbbb=bbba.

Flip LHS and RHS.

Referenced by [13], [14], [15], [16].

[13] bbbbb=bbb

Overlap of [12] bbba=bbbb with [2] ababba=bb:

bbb a ababba

Critical pair: bbbbb=bbbbbabba.

Reduce RHS:

[9](bbbbbabb)a
[12](bbba)a
[11](bbbba)
bbb

Referenced by [14].

[14] bba=bbb

Overlap of [12] bbba=bbbb with [3] babba=abb:

bb ba babba

Critical pair: bbabb=bbbbbba.

Reduce LHS:

[10](bbabb)
bba

Reduce RHS:

[13](bbbbb)ba
[11](bbbba)
bbb

Defines rule #2.

Referenced by [15], [16], [17].

[15] bbbb=bb

Overlap of [14] bba=bbb with [1] aa=1:

bb a aa

Critical pair: bb=bbba.

Reduce RHS:

[12](bbba)
bbbb

Flip LHS and RHS.

Defines rule #4.

Referenced by [16].

[16] babb=bb

Overlap of [14] bba=bbb with [3] babba=abb:

b ba babba

Critical pair: babb=bbbbba.

Reduce RHS:

[15](bbbb)ba
[12](bbba)
[15](bbbb)
bb

Referenced by [17].

[17] abb=bbb

Overlap of [3] babba=abb with [16] babb=bb:

babba babb

Critical pair: bba=abb.

Reduce LHS:

[14](bba)
bbb

Flip LHS and RHS.

Defines rule #3.