Certificate for #3761 ⟨a, b | ababaabaab=a⟩

Completion settings:

• Reduction order:
  • Right-to-left recursive path with deg(e) = deg(d) = 0, e < d; deg(b) = deg(c) = deg(a) = 1, b < c < a
• Auxiliary generators:
  1. aa=c
  2. ba=d
  3. dad=e

Axiom: ababaabaab=a.

Referenced by [5].

Axiom: aa=c.

Defines rule #25.

Referenced by [6], [7], [9], [12], [13], [17], [21], [22], [26], [27], [28], [29], [34], [35], [36].

Axiom: ba=d.

Defines rule #21.

Referenced by [5], [7], [10], [12], [13], [15], [16].

Axiom: dad=e.

Defines rule #10.

Referenced by [5], [8], [11], [14], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29].

Overlap of [1] ababaabaab=a with [3] ba=d:

Critical pair: adbaabaab=a.

Reduce LHS:

Defines rule #32.

Referenced by [9], [10], [11], [12].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #22.

Referenced by [18], [25], [28], [29], [33], [36].

Overlap of [3] ba=d with [2] aa=c:

Critical pair: bc=da.

Defines rule #16.

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

Critical pair: dae=ead.

Flip LHS and RHS.

Defines rule #9.

Referenced by [12], [13], [15], [16], [18], [21], [22], [28].

Overlap of [2] aa=c with [5] adeab=a:

Critical pair: aa=cdeab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #30.

Overlap of [3] ba=d with [5] adeab=a:

Critical pair: ba=ddeab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #15.

Referenced by [14], [15].

Overlap of [4] dad=e with [5] adeab=a:

Critical pair: da=eeab.

Flip LHS and RHS.

Defines rule #13.

Referenced by [13], [19], [23].

Overlap of [5] adeab=a with [3] ba=d:

Critical pair: adead=aa.

Reduce LHS:

Reduce RHS:

Defines rule #26.

Referenced by [17], [18], [19], [20], [25], [33].

Overlap of [11] eeab=da with [3] ba=d:

Critical pair: eead=daa.

Reduce LHS:

Reduce RHS:

Defines rule #6.

Referenced by [20], [24].

Overlap of [4] dad=e with [10] ddeab=d:

Critical pair: dad=edeab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #14.

Referenced by [16].

Overlap of [10] ddeab=d with [3] ba=d:

Critical pair: ddead=da.

Reduce LHS:

Defines rule #8.

Referenced by [22], [23], [24], [26], [34].

Overlap of [14] edeab=e with [3] ba=d:

Critical pair: edead=ea.

Reduce LHS:

Defines rule #7.

Referenced by [21], [27], [35].

Overlap of [2] aa=c with [12] addae=c:

Critical pair: ac=cddae.

Flip LHS and RHS.

Defines rule #24.

Referenced by [28], [29], [36].

Overlap of [12] addae=c with [8] ead=dae:

Critical pair: addadae=cad.

Reduce LHS:

Reduce RHS:

Referenced by [32].

Overlap of [12] addae=c with [11] eeab=da:

Critical pair: addada=ceab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #29.

Overlap of [12] addae=c with [13] edae=dc:

Critical pair: addadc=cdae.

Reduce LHS:

Flip LHS and RHS.

Defines rule #23.

Overlap of [16] eddae=ea with [8] ead=dae:

Critical pair: eddadae=eaad.

Reduce LHS:

Reduce RHS:

Referenced by [30].

Overlap of [15] dddae=da with [8] ead=dae:

Critical pair: dddadae=daad.

Reduce LHS:

Reduce RHS:

Referenced by [31].

Overlap of [15] dddae=da with [11] eeab=da:

Critical pair: dddada=daeab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #31.

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

Overlap of [15] dddae=da with [13] edae=dc:

Critical pair: dddadc=dadae.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [25], [26], [27], [28], [29], [30], [31], [32].

Overlap of [12] addae=c with [24] eae=ddec:

Critical pair: addaddec=cae.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #19.

Overlap of [15] dddae=da with [24] eae=ddec:

Critical pair: dddaddec=daae.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [16] eddae=ea with [24] eae=ddec:

Critical pair: eddaddec=eaae.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [17] cddae=ac with [8] ead=dae:

Critical pair: cddadae=acad.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #18.

Overlap of [17] cddae=ac with [24] eae=ddec:

Critical pair: cddaddec=acae.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #17.

Simplify [21] edeae=ecd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Simplify [22] ddeae=dcd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [18] adeae=acd with [24] eae=ddec:

Critical pair: adddec=acd.

Flip LHS and RHS.

Defines rule #20.

Overlap of [12] addae=c with [23] daeab=ddea:

Critical pair: adddea=cab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #28.

Overlap of [15] dddae=da with [23] daeab=ddea:

Critical pair: ddddea=daab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #12.

Overlap of [16] eddae=ea with [23] daeab=ddea:

Critical pair: edddea=eaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #11.

Overlap of [17] cddae=ac with [23] daeab=ddea:

Critical pair: cdddea=acab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #27.