Certificate for #5045 ⟨a, b | aaababa=baaa

Completion settings:

[1] aaababa=baaa

Axiom: aaababa=baaa.

Referenced by [5].

[2] bab=c

Axiom: bab=c.

Defines rule #46.

Referenced by [5], [6], [11].

[3] aaca=d

Axiom: aaca=d.

Defines rule #7.

Referenced by [5], [7], [8], [12], [13], [16], [18], [19], [22], [27], [28], [32], [33], [41], [42], [45], [46].

[4] aacd=e

Axiom: aacd=e.

Defines rule #3.

Referenced by [7], [8], [9], [10], [14], [15], [20], [21], [29], [30], [34], [35], [37], [40], [43], [44], [47], [48].

[5] baaa=ad

Overlap of [1] aaababa=baaa with [2] bab=c:

aaa baba bab

Critical pair: aaaca=baaa.

Reduce LHS:

[3]a(aaca)
ad

Flip LHS and RHS.

Defines rule #36.

Referenced by [11], [12], [13], [14], [15], [24], [38], [39].

[6] cab=bac

Overlap of [2] bab=c with [2] bab=c:

ba b bab

Critical pair: bac=cab.

Flip LHS and RHS.

Defines rule #45.

Referenced by [22], [23].

[7] daca=e

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

aac a aaca

Critical pair: aacd=daca.

Reduce LHS:

[4](aacd)
e

Flip LHS and RHS.

Defines rule #6.

Referenced by [9], [10], [13], [17], [23].

[8] aace=dacd

Overlap of [3] aaca=d with [4] aacd=e:

aac a aacd

Critical pair: aace=dacd.

Defines rule #10.

Referenced by [9], [37].

[9] eaca=dacd

Overlap of [4] aacd=e with [7] daca=e:

aac d daca

Critical pair: aace=eaca.

Reduce LHS:

[8](aace)
dacd

Flip LHS and RHS.

Defines rule #8.

Referenced by [19], [28], [33], [40], [42], [46].

[10] dace=eacd

Overlap of [7] daca=e with [4] aacd=e:

dac a aacd

Critical pair: dace=eacd.

Defines rule #9.

[11] baad=caaa

Overlap of [2] bab=c with [5] baaa=ad:

ba b baaa

Critical pair: baad=caaa.

Referenced by [13], [26].

[12] bad=adca

Overlap of [5] baaa=ad with [3] aaca=d:

ba aa aaca

Critical pair: bad=adca.

Defines rule #27.

[13] caaa=ae

Overlap of [5] baaa=ad with [3] aaca=d:

baa a aaca

Critical pair: baad=adaca.

Reduce LHS:

[11](baad)
caaa

Reduce RHS:

[7]a(daca)
ae

Defines rule #21.

Referenced by [16], [17], [18], [19], [20], [21], [25], [26], [38], [39].

[14] bae=adcd

Overlap of [5] baaa=ad with [4] aacd=e:

ba aa aacd

Critical pair: bae=adcd.

Defines rule #30.

[15] baae=adacd

Overlap of [5] baaa=ad with [4] aacd=e:

baa a aacd

Critical pair: baae=adacd.

Defines rule #39.

Referenced by [38], [39].

[16] aaae=daa

Overlap of [3] aaca=d with [13] caaa=ae:

aa ca caaa

Critical pair: aaae=daa.

Defines rule #2.

Referenced by [24], [25].

[17] daae=eaa

Overlap of [7] daca=e with [13] caaa=ae:

da ca caaa

Critical pair: daae=eaa.

Defines rule #1.

Referenced by [31], [36].

[18] cad=aeca

Overlap of [13] caaa=ae with [3] aaca=d:

ca aa aaca

Critical pair: cad=aeca.

Defines rule #12.

[19] caad=adacd

Overlap of [13] caaa=ae with [3] aaca=d:

caa a aaca

Critical pair: caad=aeaca.

Reduce RHS:

[9]a(eaca)
adacd

Defines rule #18.

[20] cae=aecd

Overlap of [13] caaa=ae with [4] aacd=e:

ca aa aacd

Critical pair: cae=aecd.

Defines rule #15.

[21] caae=aeacd

Overlap of [13] caaa=ae with [4] aacd=e:

caa a aacd

Critical pair: caae=aeacd.

Defines rule #24.

[22] aabac=db

Overlap of [3] aaca=d with [6] cab=bac:

aa ca cab

Critical pair: aabac=db.

Defines rule #43.

Referenced by [39].

[23] dabac=eb

Overlap of [7] daca=e with [6] cab=bac:

da ca cab

Critical pair: dabac=eb.

Defines rule #42.

Referenced by [37], [38].

[24] bdaa=ade

Overlap of [5] baaa=ad with [16] aaae=daa:

b aaa aaae

Critical pair: bdaa=ade.

Defines rule #35.

Referenced by [32], [33], [34], [35], [36].

[25] cdaa=aee

Overlap of [13] caaa=ae with [16] aaae=daa:

c aaa aaae

Critical pair: cdaa=aee.

Defines rule #20.

Referenced by [27], [28], [29], [30], [31].

[26] baad=ae

Simplify [11] baad=caaa.

Reduce RHS:

[13](caaa)
ae

Defines rule #33.

[27] cdd=aeeca

Overlap of [25] cdaa=aee with [3] aaca=d:

cd aa aaca

Critical pair: cdd=aeeca.

Defines rule #11.

[28] cdad=aedacd

Overlap of [25] cdaa=aee with [3] aaca=d:

cda a aaca

Critical pair: cdad=aeeaca.

Reduce RHS:

[9]ae(eaca)
aedacd

Defines rule #17.

[29] cde=aeecd

Overlap of [25] cdaa=aee with [4] aacd=e:

cd aa aacd

Critical pair: cde=aeecd.

Defines rule #14.

[30] cdae=aeeacd

Overlap of [25] cdaa=aee with [4] aacd=e:

cda a aacd

Critical pair: cdae=aeeacd.

Defines rule #23.

[31] ceaa=aeee

Overlap of [25] cdaa=aee with [17] daae=eaa:

c daa daae

Critical pair: ceaa=aeee.

Defines rule #22.

Referenced by [41], [42], [43], [44].

[32] bdd=adeca

Overlap of [24] bdaa=ade with [3] aaca=d:

bd aa aaca

Critical pair: bdd=adeca.

Defines rule #26.

[33] bdad=addacd

Overlap of [24] bdaa=ade with [3] aaca=d:

bda a aaca

Critical pair: bdad=adeaca.

Reduce RHS:

[9]ad(eaca)
addacd

Defines rule #32.

[34] bde=adecd

Overlap of [24] bdaa=ade with [4] aacd=e:

bd aa aacd

Critical pair: bde=adecd.

Defines rule #29.

[35] bdae=adeacd

Overlap of [24] bdaa=ade with [4] aacd=e:

bda a aacd

Critical pair: bdae=adeacd.

Defines rule #38.

[36] beaa=adee

Overlap of [24] bdaa=ade with [17] daae=eaa:

b daa daae

Critical pair: beaa=adee.

Defines rule #37.

Referenced by [45], [46], [47], [48].

[37] dacdb=eabac

Overlap of [4] aacd=e with [23] dabac=eb:

aac d dabac

Critical pair: aaceb=eabac.

Reduce LHS:

[8](aace)b
dacdb

Defines rule #44.

[38] daadacd=ead

Overlap of [23] dabac=eb with [13] caaa=ae:

daba c caaa

Critical pair: dabaae=ebaaa.

Reduce LHS:

[15]da(baae)
daadacd

Reduce RHS:

[5]e(baaa)
ead

Defines rule #4.

[39] aaadacd=dad

Overlap of [22] aabac=db with [13] caaa=ae:

aaba c caaa

Critical pair: aabaae=dbaaa.

Reduce LHS:

[15]aa(baae)
aaadacd

Reduce RHS:

[5]d(baaa)
dad

Defines rule #5.

[40] dacdacd=eace

Overlap of [9] eaca=dacd with [4] aacd=e:

eac a aacd

Critical pair: eace=dacdacd.

Flip LHS and RHS.

Defines rule #41.

[41] ced=aeeeca

Overlap of [31] ceaa=aeee with [3] aaca=d:

ce aa aaca

Critical pair: ced=aeeeca.

Defines rule #13.

[42] cead=aeedacd

Overlap of [31] ceaa=aeee with [3] aaca=d:

cea a aaca

Critical pair: cead=aeeeaca.

Reduce RHS:

[9]aee(eaca)
aeedacd

Defines rule #19.

[43] cee=aeeecd

Overlap of [31] ceaa=aeee with [4] aacd=e:

ce aa aacd

Critical pair: cee=aeeecd.

Defines rule #16.

[44] ceae=aeeeacd

Overlap of [31] ceaa=aeee with [4] aacd=e:

cea a aacd

Critical pair: ceae=aeeeacd.

Defines rule #25.

[45] bed=adeeca

Overlap of [36] beaa=adee with [3] aaca=d:

be aa aaca

Critical pair: bed=adeeca.

Defines rule #28.

[46] bead=adedacd

Overlap of [36] beaa=adee with [3] aaca=d:

bea a aaca

Critical pair: bead=adeeaca.

Reduce RHS:

[9]ade(eaca)
adedacd

Defines rule #34.

[47] bee=adeecd

Overlap of [36] beaa=adee with [4] aacd=e:

be aa aacd

Critical pair: bee=adeecd.

Defines rule #31.

[48] beae=adeeacd

Overlap of [36] beaa=adee with [4] aacd=e:

bea a aacd

Critical pair: beae=adeeacd.

Defines rule #40.