| Back: | ⟨a, b | aabbaaab=aba⟩ |
|---|
Completion settings:
Axiom: aabbaaab=aba.
Referenced by [5].
Axiom: ab=c.
Defines rule #36.
Referenced by [5], [6], [8], [14], [21], [86].
Axiom: caca=d.
Referenced by [7].
Axiom: acbaa=e.
Defines rule #88.
Referenced by [6], [14], [15], [16], [18], [22], [25], [41], [87].
Simplify [1] aabbaaab=aba.
Reduce RHS:
| [2] | (ab)a |
| ⇒ ca |
Referenced by [6].
Overlap of [5] aabbaaab=ca with [2] ab=c:
Critical pair: acbaaab=ca.
Reduce LHS:
| [4] | (acbaa)ab |
| [2] | ⇒ e(ab) |
| ⇒ ec |
Flip LHS and RHS.
Defines rule #37.
Referenced by [7], [8], [9], [13], [15], [16], [17], [19], [25], [27], [28], [32], [36], [41], [87].
Overlap of [3] caca=d with [6] ca=ec:
Critical pair: ecca=d.
Reduce LHS:
| [6] | ec(ca) |
| ⇒ ecec |
Defines rule #7.
Referenced by [9], [10], [11], [24], [29], [31], [32], [34], [35], [38], [43], [44], [46], [50], [56], [61], [62], [64], [66], [72], [74], [77], [79], [81], [84], [89].
Overlap of [6] ca=ec with [2] ab=c:
Critical pair: cc=ecb.
Flip LHS and RHS.
Defines rule #1.
Referenced by [11], [12], [15], [25], [30], [39], [41], [48], [53], [54], [55], [58], [59], [60], [68], [87].
Overlap of [7] ecec=d with [6] ca=ec:
Critical pair: eceec=da.
Flip LHS and RHS.
Defines rule #42.
Referenced by [36].
Overlap of [7] ecec=d with [7] ecec=d:
Critical pair: ecd=dec.
Flip LHS and RHS.
Defines rule #4.
Referenced by [12].
Overlap of [7] ecec=d with [8] ecb=cc:
Critical pair: eccc=db.
Defines rule #6.
Referenced by [13], [22], [23], [26], [31], [40], [41], [42], [45], [47], [51], [52], [61], [65], [67], [73], [78], [80], [85], [88], [90], [91].
Overlap of [10] dec=ecd with [8] ecb=cc:
Critical pair: dcc=ecdb.
Defines rule #3.
Overlap of [11] eccc=db with [6] ca=ec:
Critical pair: eccec=dba.
Flip LHS and RHS.
Defines rule #43.
Overlap of [4] acbaa=e with [2] ab=c:
Critical pair: acbac=eb.
Defines rule #75.
Referenced by [17], [18], [19], [20], [23], [37], [39], [48], [58], [68].
Overlap of [4] acbaa=e with [4] acbaa=e:
Critical pair: acbae=ecbaa.
Reduce RHS:
| [8] | (ecb)aa |
| [6] | ⇒ c(ca)a |
| [6] | ⇒ ce(ca) |
| ⇒ ceec |
Defines rule #76.
Referenced by [19], [36], [37], [38], [39], [40], [48], [58], [68].
Overlap of [6] ca=ec with [4] acbaa=e:
Critical pair: ce=eccbaa.
Flip LHS and RHS.
Defines rule #81.
Referenced by [24], [25], [27], [32], [51].
Overlap of [6] ca=ec with [14] acbac=eb:
Critical pair: ceb=eccbac.
Flip LHS and RHS.
Defines rule #51.
Referenced by [34], [35], [52].
Overlap of [14] acbac=eb with [4] acbaa=e:
Critical pair: acbe=ebbaa.
Flip LHS and RHS.
Defines rule #78.
Overlap of [14] acbac=eb with [6] ca=ec:
Critical pair: acbaec=eba.
Reduce LHS:
| [15] | (acbae)c |
| ⇒ ceecc |
Flip LHS and RHS.
Defines rule #38.
Referenced by [21], [22], [23], [40], [73].
Overlap of [14] acbac=eb with [14] acbac=eb:
Critical pair: acbeb=ebbac.
Flip LHS and RHS.
Defines rule #39.
Overlap of [19] eba=ceecc with [2] ab=c:
Critical pair: ebc=ceeccb.
Flip LHS and RHS.
Defines rule #14.
Referenced by [26], [27], [33], [36], [43], [49], [69].
Overlap of [19] eba=ceecc with [4] acbaa=e:
Critical pair: ebe=ceecccbaa.
Reduce RHS:
| [11] | ce(eccc)baa |
| ⇒ cedbbaa |
Flip LHS and RHS.
Defines rule #80.
Referenced by [56], [57], [70].
Overlap of [19] eba=ceecc with [14] acbac=eb:
Critical pair: ebeb=ceecccbac.
Reduce RHS:
| [11] | ce(eccc)bac |
| ⇒ cedbbac |
Flip LHS and RHS.
Defines rule #48.
Referenced by [62], [63], [71].
Overlap of [7] ecec=d with [16] eccbaa=ce:
Critical pair: ecce=dcbaa.
Flip LHS and RHS.
Defines rule #79.
Referenced by [41].
Overlap of [16] eccbaa=ce with [4] acbaa=e:
Critical pair: eccbae=cecbaa.
Reduce RHS:
| [8] | c(ecb)aa |
| [6] | ⇒ cc(ca)a |
| [6] | ⇒ cce(ca) |
| ⇒ cceec |
Defines rule #52.
Overlap of [11] eccc=db with [21] ceeccb=ebc:
Critical pair: eccebc=dbeeccb.
Flip LHS and RHS.
Defines rule #20.
Overlap of [21] ceeccb=ebc with [16] eccbaa=ce:
Critical pair: cece=ebcaa.
Reduce RHS:
| [6] | eb(ca)a |
| [6] | ⇒ ebe(ca) |
| ⇒ ebeec |
Flip LHS and RHS.
Defines rule #9.
Referenced by [28], [29], [30], [31], [32], [33], [35], [43], [53], [57], [63], [75], [82].
Overlap of [27] ebeec=cece with [6] ca=ec:
Critical pair: ebeeec=cecea.
Flip LHS and RHS.
Defines rule #60.
Referenced by [66], [67], [68].
Overlap of [27] ebeec=cece with [7] ecec=d:
Critical pair: ebed=ceceec.
Flip LHS and RHS.
Defines rule #22.
Referenced by [46], [47], [48], [49].
Overlap of [27] ebeec=cece with [8] ecb=cc:
Critical pair: ebecc=ceceb.
Defines rule #8.
Referenced by [42], [43], [54].
Overlap of [27] ebeec=cece with [11] eccc=db:
Critical pair: ebedb=cececc.
Reduce RHS:
| [7] | c(ecec)c |
| ⇒ cdc |
Defines rule #2.
Overlap of [27] ebeec=cece with [16] eccbaa=ce:
Critical pair: ebece=cececbaa.
Reduce RHS:
| [7] | c(ecec)baa |
| [13] | ⇒ c(dba)a |
| [6] | ⇒ cecce(ca) |
| ⇒ cecceec |
Flip LHS and RHS.
Defines rule #28.
Referenced by [69], [70], [71], [76], [83].
Overlap of [27] ebeec=cece with [21] ceeccb=ebc:
Critical pair: ebeeebc=ceceeeccb.
Flip LHS and RHS.
Defines rule #33.
Overlap of [7] ecec=d with [17] eccbac=ceb:
Critical pair: ecceb=dcbac.
Flip LHS and RHS.
Defines rule #44.
Referenced by [51], [52], [53], [54], [55], [59], [65], [78].
Overlap of [27] ebeec=cece with [17] eccbac=ceb:
Critical pair: ebeceb=cececbac.
Reduce RHS:
| [7] | c(ecec)bac |
| [13] | ⇒ c(dba)c |
| ⇒ ceccecc |
Flip LHS and RHS.
Defines rule #27.
Overlap of [9] da=eceec with [15] acbae=ceec:
Critical pair: dceec=eceeccbae.
Reduce RHS:
| [21] | e(ceeccb)ae |
| [6] | ⇒ eeb(ca)e |
| ⇒ eebece |
Defines rule #17.
Overlap of [14] acbac=eb with [15] acbae=ceec:
Critical pair: acbceec=ebbae.
Flip LHS and RHS.
Defines rule #40.
Referenced by [72].
Overlap of [15] acbae=ceec with [7] ecec=d:
Critical pair: acbad=ceeccec.
Defines rule #77.
Referenced by [73].
Overlap of [15] acbae=ceec with [31] ebedb=cdc:
Critical pair: acbacdc=ceecbedb.
Reduce LHS:
| [14] | (acbac)dc |
| ⇒ ebdc |
Reduce RHS:
| [8] | ce(ecb)edb |
| ⇒ ceccedb |
Flip LHS and RHS.
Defines rule #21.
Overlap of [19] eba=ceecc with [15] acbae=ceec:
Critical pair: ebceec=ceecccbae.
Reduce RHS:
| [11] | ce(eccc)bae |
| ⇒ cedbbae |
Flip LHS and RHS.
Defines rule #49.
Referenced by [74], [75], [76].
Overlap of [24] dcbaa=ecce with [4] acbaa=e:
Critical pair: dcbae=eccecbaa.
Reduce RHS:
| [8] | ecc(ecb)aa |
| [11] | ⇒ (eccc)caa |
| [6] | ⇒ db(ca)a |
| [6] | ⇒ dbe(ca) |
| ⇒ dbeec |
Defines rule #45.
Referenced by [50], [51], [52], [53], [54], [55], [59], [65], [78].
Overlap of [30] ebecc=ceceb with [11] eccc=db:
Critical pair: ebdb=cecebc.
Flip LHS and RHS.
Defines rule #13.
Overlap of [30] ebecc=ceceb with [21] ceeccb=ebc:
Critical pair: ebecebc=cecebeeccb.
Reduce RHS:
| [27] | cec(ebeec)cb |
| [7] | ⇒ cecc(ecec)b |
| ⇒ ceccdb |
Defines rule #15.
Overlap of [7] ecec=d with [42] cecebc=ebdb:
Critical pair: eebdb=debc.
Flip LHS and RHS.
Defines rule #5.
Overlap of [11] eccc=db with [42] cecebc=ebdb:
Critical pair: eccebdb=dbecebc.
Flip LHS and RHS.
Defines rule #19.
Overlap of [7] ecec=d with [29] ceceec=ebed:
Critical pair: eebed=deec.
Flip LHS and RHS.
Defines rule #12.
Overlap of [11] eccc=db with [29] ceceec=ebed:
Critical pair: eccebed=dbeceec.
Flip LHS and RHS.
Defines rule #25.
Overlap of [14] acbac=eb with [29] ceceec=ebed:
Critical pair: acbaebed=ebeceec.
Reduce LHS:
| [15] | (acbae)bed |
| [8] | ⇒ ce(ecb)ed |
| ⇒ cecced |
Flip LHS and RHS.
Defines rule #23.
Overlap of [29] ceceec=ebed with [21] ceeccb=ebc:
Critical pair: ceebc=ebedcb.
Flip LHS and RHS.
Defines rule #10.
Overlap of [41] dcbae=dbeec with [7] ecec=d:
Critical pair: dcbad=dbeeccec.
Defines rule #46.
Overlap of [41] dcbae=dbeec with [16] eccbaa=ce:
Critical pair: dcbace=dbeecccbaa.
Reduce LHS:
| [34] | (dcbac)e |
| ⇒ eccebe |
Reduce RHS:
| [11] | dbe(eccc)baa |
| ⇒ dbedbbaa |
Flip LHS and RHS.
Defines rule #83.
Overlap of [41] dcbae=dbeec with [17] eccbac=ceb:
Critical pair: dcbaceb=dbeecccbac.
Reduce LHS:
| [34] | (dcbac)eb |
| ⇒ eccebeb |
Reduce RHS:
| [11] | dbe(eccc)bac |
| ⇒ dbedbbac |
Flip LHS and RHS.
Defines rule #57.
Overlap of [41] dcbae=dbeec with [27] ebeec=cece:
Critical pair: dcbacece=dbeecbeec.
Reduce LHS:
| [34] | (dcbac)ece |
| ⇒ eccebece |
Reduce RHS:
| [8] | dbe(ecb)eec |
| ⇒ dbecceec |
Flip LHS and RHS.
Defines rule #31.
Overlap of [41] dcbae=dbeec with [30] ebecc=ceceb:
Critical pair: dcbaceceb=dbeecbecc.
Reduce LHS:
| [34] | (dcbac)eceb |
| ⇒ eccebeceb |
Reduce RHS:
| [8] | dbe(ecb)ecc |
| ⇒ dbeccecc |
Flip LHS and RHS.
Defines rule #30.
Overlap of [41] dcbae=dbeec with [31] ebedb=cdc:
Critical pair: dcbacdc=dbeecbedb.
Reduce LHS:
| [34] | (dcbac)dc |
| ⇒ eccebdc |
Reduce RHS:
| [8] | dbe(ecb)edb |
| ⇒ dbeccedb |
Flip LHS and RHS.
Defines rule #24.
Overlap of [7] ecec=d with [22] cedbbaa=ebe:
Critical pair: eceebe=dedbbaa.
Flip LHS and RHS.
Defines rule #82.
Overlap of [27] ebeec=cece with [22] cedbbaa=ebe:
Critical pair: ebeeebe=ceceedbbaa.
Flip LHS and RHS.
Defines rule #85.
Overlap of [15] acbae=ceec with [49] ebedcb=ceebc:
Critical pair: acbaceebc=ceecbedcb.
Reduce LHS:
| [14] | (acbac)eebc |
| ⇒ ebeebc |
Reduce RHS:
| [8] | ce(ecb)edcb |
| ⇒ ceccedcb |
Flip LHS and RHS.
Defines rule #29.
Referenced by [77].
Overlap of [41] dcbae=dbeec with [49] ebedcb=ceebc:
Critical pair: dcbaceebc=dbeecbedcb.
Reduce LHS:
| [34] | (dcbac)eebc |
| ⇒ eccebeebc |
Reduce RHS:
| [8] | dbe(ecb)edcb |
| ⇒ dbeccedcb |
Flip LHS and RHS.
Defines rule #32.
Overlap of [36] dceec=eebece with [8] ecb=cc:
Critical pair: dcecc=eebeceb.
Defines rule #16.
Overlap of [36] dceec=eebece with [11] eccc=db:
Critical pair: dcedb=eebececc.
Reduce RHS:
| [7] | eeb(ecec)c |
| ⇒ eebdc |
Defines rule #11.
Overlap of [7] ecec=d with [23] cedbbac=ebeb:
Critical pair: eceebeb=dedbbac.
Flip LHS and RHS.
Defines rule #54.
Overlap of [27] ebeec=cece with [23] cedbbac=ebeb:
Critical pair: ebeeebeb=ceceedbbac.
Flip LHS and RHS.
Defines rule #66.
Referenced by [88].
Overlap of [25] eccbae=cceec with [7] ecec=d:
Critical pair: eccbad=cceeccec.
Defines rule #53.
Referenced by [78].
Overlap of [41] dcbae=dbeec with [25] eccbae=cceec:
Critical pair: dcbacceec=dbeecccbae.
Reduce LHS:
| [34] | (dcbac)ceec |
| ⇒ eccebceec |
Reduce RHS:
| [11] | dbe(eccc)bae |
| ⇒ dbedbbae |
Flip LHS and RHS.
Defines rule #58.
Overlap of [7] ecec=d with [28] cecea=ebeeec:
Critical pair: eebeeec=dea.
Flip LHS and RHS.
Defines rule #47.
Overlap of [11] eccc=db with [28] cecea=ebeeec:
Critical pair: eccebeeec=dbecea.
Flip LHS and RHS.
Defines rule #62.
Overlap of [14] acbac=eb with [28] cecea=ebeeec:
Critical pair: acbaebeeec=ebecea.
Reduce LHS:
| [15] | (acbae)beeec |
| [8] | ⇒ ce(ecb)eeec |
| ⇒ cecceeec |
Flip LHS and RHS.
Defines rule #61.
Overlap of [32] cecceec=ebece with [21] ceeccb=ebc:
Critical pair: cecceeebc=ebeceeeccb.
Flip LHS and RHS.
Defines rule #34.
Overlap of [32] cecceec=ebece with [22] cedbbaa=ebe:
Critical pair: cecceeebe=ebeceedbbaa.
Flip LHS and RHS.
Defines rule #86.
Overlap of [32] cecceec=ebece with [23] cedbbac=ebeb:
Critical pair: cecceeebeb=ebeceedbbac.
Flip LHS and RHS.
Defines rule #69.
Overlap of [37] ebbae=acbceec with [7] ecec=d:
Critical pair: ebbad=acbceeccec.
Defines rule #41.
Overlap of [19] eba=ceecc with [38] acbad=ceeccec:
Critical pair: ebceeccec=ceecccbad.
Reduce RHS:
| [11] | ce(eccc)bad |
| ⇒ cedbbad |
Flip LHS and RHS.
Defines rule #50.
Referenced by [81], [82], [83].
Overlap of [7] ecec=d with [40] cedbbae=ebceec:
Critical pair: eceebceec=dedbbae.
Flip LHS and RHS.
Defines rule #55.
Overlap of [27] ebeec=cece with [40] cedbbae=ebceec:
Critical pair: ebeeebceec=ceceedbbae.
Flip LHS and RHS.
Defines rule #67.
Referenced by [90].
Overlap of [32] cecceec=ebece with [40] cedbbae=ebceec:
Critical pair: cecceeebceec=ebeceedbbae.
Flip LHS and RHS.
Defines rule #70.
Overlap of [7] ecec=d with [58] ceccedcb=ebeebc:
Critical pair: eebeebc=dcedcb.
Flip LHS and RHS.
Defines rule #18.
Overlap of [41] dcbae=dbeec with [64] eccbad=cceeccec:
Critical pair: dcbacceeccec=dbeecccbad.
Reduce LHS:
| [34] | (dcbac)ceeccec |
| ⇒ eccebceeccec |
Reduce RHS:
| [11] | dbe(eccc)bad |
| ⇒ dbedbbad |
Flip LHS and RHS.
Defines rule #59.
Overlap of [7] ecec=d with [33] ceceeeccb=ebeeebc:
Critical pair: eebeeebc=deeeccb.
Flip LHS and RHS.
Defines rule #26.
Overlap of [11] eccc=db with [33] ceceeeccb=ebeeebc:
Critical pair: eccebeeebc=dbeceeeccb.
Flip LHS and RHS.
Defines rule #35.
Overlap of [7] ecec=d with [73] cedbbad=ebceeccec:
Critical pair: eceebceeccec=dedbbad.
Flip LHS and RHS.
Defines rule #56.
Overlap of [27] ebeec=cece with [73] cedbbad=ebceeccec:
Critical pair: ebeeebceeccec=ceceedbbad.
Flip LHS and RHS.
Defines rule #68.
Referenced by [91].
Overlap of [32] cecceec=ebece with [73] cedbbad=ebceeccec:
Critical pair: cecceeebceeccec=ebeceedbbad.
Flip LHS and RHS.
Defines rule #71.
Overlap of [7] ecec=d with [57] ceceedbbaa=ebeeebe:
Critical pair: eebeeebe=deedbbaa.
Flip LHS and RHS.
Defines rule #84.
Overlap of [11] eccc=db with [57] ceceedbbaa=ebeeebe:
Critical pair: eccebeeebe=dbeceedbbaa.
Flip LHS and RHS.
Defines rule #87.
Overlap of [84] deedbbaa=eebeeebe with [2] ab=c:
Critical pair: deedbbac=eebeeebeb.
Defines rule #63.
Overlap of [84] deedbbaa=eebeeebe with [4] acbaa=e:
Critical pair: deedbbae=eebeeebecbaa.
Reduce RHS:
| [8] | eebeeeb(ecb)aa |
| [6] | ⇒ eebeeebc(ca)a |
| [6] | ⇒ eebeeebce(ca) |
| ⇒ eebeeebceec |
Defines rule #64.
Referenced by [89].
Overlap of [11] eccc=db with [63] ceceedbbac=ebeeebeb:
Critical pair: eccebeeebeb=dbeceedbbac.
Flip LHS and RHS.
Defines rule #72.
Overlap of [87] deedbbae=eebeeebceec with [7] ecec=d:
Critical pair: deedbbad=eebeeebceeccec.
Defines rule #65.
Overlap of [11] eccc=db with [75] ceceedbbae=ebeeebceec:
Critical pair: eccebeeebceec=dbeceedbbae.
Flip LHS and RHS.
Defines rule #73.
Overlap of [11] eccc=db with [82] ceceedbbad=ebeeebceeccec:
Critical pair: eccebeeebceeccec=dbeceedbbad.
Flip LHS and RHS.
Defines rule #74.