Certificate for #5375 ⟨a, b | ababbba=baba

Completion settings:

[1] ababbba=baba

Axiom: ababbba=baba.

Referenced by [5].

[2] bbbaba=c

Axiom: bbbaba=c.

Referenced by [6].

[3] bb=d

Axiom: bb=d.

Defines rule #24.

Referenced by [5], [6], [7], [9], [11], [16], [19].

[4] badba=e

Axiom: badba=e.

Defines rule #26.

Referenced by [5], [11], [12], [13], [14], [16], [24].

[5] baba=ae

Overlap of [1] ababbba=baba with [3] bb=d:

aba bbba bb

Critical pair: abadba=baba.

Reduce LHS:

[4]a(badba)
ae

Flip LHS and RHS.

Defines rule #25.

Referenced by [6], [9], [10], [13], [14], [19], [25].

[6] dae=c

Overlap of [2] bbbaba=c with [3] bb=d:

bbbaba bb

Critical pair: dbaba=c.

Reduce LHS:

[5]d(baba)
dae

Defines rule #7.

Referenced by [8], [13], [16], [17], [18], [19], [23], [25], [26], [27], [28], [29].

[7] bd=db

Overlap of [3] bb=d with [3] bb=d:

b b bb

Critical pair: bd=db.

Defines rule #22.

Referenced by [8], [22].

[8] dbae=bc

Overlap of [7] bd=db with [6] dae=c:

b d dae

Critical pair: bc=dbae.

Flip LHS and RHS.

Referenced by [17].

[9] bae=daba

Overlap of [3] bb=d with [5] baba=ae:

b b baba

Critical pair: bae=daba.

Referenced by [14], [15].

[10] baae=aeba

Overlap of [5] baba=ae with [5] baba=ae:

ba ba baba

Critical pair: baae=aeba.

Defines rule #21.

Referenced by [19], [20].

[11] be=dadba

Overlap of [3] bb=d with [4] badba=e:

b b badba

Critical pair: be=dadba.

Defines rule #17.

[12] bade=edba

Overlap of [4] badba=e with [4] badba=e:

bad ba badba

Critical pair: bade=edba.

Defines rule #23.

Referenced by [20], [22].

[13] bac=eba

Overlap of [4] badba=e with [5] baba=ae:

bad ba baba

Critical pair: badae=eba.

Reduce LHS:

[6]ba(dae)
bac

Defines rule #20.

Referenced by [20], [22].

[14] daba=aedba

Overlap of [5] baba=ae with [4] badba=e:

ba ba badba

Critical pair: bae=aedba.

Reduce LHS:

[9](bae)
daba

Defines rule #15.

Referenced by [15].

[15] bae=aedba

Simplify [9] bae=daba.

Reduce RHS:

[14](daba)
aedba

Defines rule #19.

Referenced by [16], [17], [19], [22].

[16] aede=c

Overlap of [3] bb=d with [15] bae=aedba:

b b bae

Critical pair: baedba=dae.

Reduce LHS:

[15](bae)dba
[4]aed(badba)
aede

Reduce RHS:

[6](dae)
c

Defines rule #3.

Referenced by [18], [20], [21], [22], [30].

[17] bc=cdba

Overlap of [8] dbae=bc with [15] bae=aedba:

d bae bae

Critical pair: daedba=bc.

Reduce LHS:

[6](dae)dba
cdba

Flip LHS and RHS.

Defines rule #18.

[18] dc=cde

Overlap of [6] dae=c with [16] aede=c:

d ae aede

Critical pair: dc=cde.

Defines rule #6.

[19] daae=aec

Overlap of [3] bb=d with [10] baae=aeba:

b b baae

Critical pair: baeba=daae.

Reduce LHS:

[15](bae)ba
[5]aed(baba)
[6]ae(dae)
aec

Flip LHS and RHS.

Defines rule #11.

Referenced by [21], [23], [27], [29].

[20] aeedba=eba

Overlap of [10] baae=aeba with [16] aede=c:

ba ae aede

Critical pair: bac=aebade.

Reduce LHS:

[13](bac)
eba

Reduce RHS:

[12]ae(bade)
aeedba

Flip LHS and RHS.

Defines rule #13.

Referenced by [23], [24], [25].

[21] dac=aecde

Overlap of [19] daae=aec with [16] aede=c:

da ae aede

Critical pair: dac=aecde.

Defines rule #9.

Referenced by [22].

[22] deba=cedba

Overlap of [7] bd=db with [21] dac=aecde:

b d dac

Critical pair: baecde=dbac.

Reduce LHS:

[15](bae)cde
[13]aed(bac)de
[16](aede)bade
[12]c(bade)
cedba

Reduce RHS:

[13]d(bac)
deba

Flip LHS and RHS.

Defines rule #16.

[23] aecedba=cba

Overlap of [19] daae=aec with [20] aeedba=eba:

da ae aeedba

Critical pair: daeba=aecedba.

Reduce LHS:

[6](dae)ba
cba

Flip LHS and RHS.

Defines rule #14.

[24] aeede=ee

Overlap of [20] aeedba=eba with [4] badba=e:

aeed ba badba

Critical pair: aeede=ebadba.

Reduce RHS:

[4]e(badba)
ee

Defines rule #4.

Referenced by [28], [29].

[25] aeec=eae

Overlap of [20] aeedba=eba with [5] baba=ae:

aeed ba baba

Critical pair: aeedae=ebaba.

Reduce LHS:

[6]aee(dae)
aeec

Reduce RHS:

[5]e(baba)
eae

Defines rule #1.

Referenced by [26], [27].

[26] deae=cec

Overlap of [6] dae=c with [25] aeec=eae:

d ae aeec

Critical pair: deae=cec.

Defines rule #12.

Referenced by [30].

[27] aecec=cae

Overlap of [19] daae=aec with [25] aeec=eae:

da ae aeec

Critical pair: daeae=aecec.

Reduce LHS:

[6](dae)ae
cae

Flip LHS and RHS.

Defines rule #2.

[28] dee=cede

Overlap of [6] dae=c with [24] aeede=ee:

d ae aeede

Critical pair: dee=cede.

Defines rule #8.

[29] aecede=ce

Overlap of [19] daae=aec with [24] aeede=ee:

da ae aeede

Critical pair: daee=aecede.

Reduce LHS:

[6](dae)e
ce

Flip LHS and RHS.

Defines rule #5.

[30] dec=cecde

Overlap of [26] deae=cec with [16] aede=c:

de ae aede

Critical pair: dec=cecde.

Defines rule #10.