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

Completion settings:

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

Axiom: ababaabaab=a.

Referenced by [5].

Axiom: aa=c.

Defines rule #18.

Referenced by [6], [7], [9], [12], [13], [21], [24], [25], [27], [28], [35], [36], [37].

Axiom: ba=d.

Defines rule #32.

Referenced by [5], [7], [10], [12], [14], [20].

Axiom: dad=e.

Defines rule #5.

Referenced by [5], [8], [11], [15], [16], [19], [21], [23], [24], [27], [30], [33].

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

Critical pair: adbaabaab=a.

Reduce LHS:

Defines rule #30.

Referenced by [9], [10], [11], [12], [17], [22].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #15.

Referenced by [16], [25], [26], [27], [28], [30], [33], [34], [35].

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

Critical pair: bc=da.

Defines rule #31.

Referenced by [14].

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

Critical pair: dae=ead.

Defines rule #9.

Referenced by [22], [23], [25], [28].

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

Critical pair: aa=cdeab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #28.

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

Critical pair: ba=ddeab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #23.

Referenced by [19].

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

Critical pair: da=eeab.

Flip LHS and RHS.

Defines rule #22.

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

Critical pair: adead=aa.

Reduce RHS:

Defines rule #19.

Referenced by [13], [14], [15], [16], [17], [18], [23], [26], [34].

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

Critical pair: ac=cdead.

Flip LHS and RHS.

Defines rule #17.

Referenced by [27], [28], [35].

Overlap of [3] ba=d with [12] adead=c:

Critical pair: bc=ddead.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [21], [22], [23], [33], [36].

Overlap of [4] dad=e with [12] adead=c:

Critical pair: dc=eead.

Flip LHS and RHS.

Defines rule #6.

Overlap of [12] adead=c with [4] dad=e:

Critical pair: adeae=cad.

Reduce RHS:

Referenced by [31].

Overlap of [12] adead=c with [5] adeab=a:

Critical pair: adea=ceab.

Flip LHS and RHS.

Defines rule #27.

Overlap of [12] adead=c with [12] adead=c:

Critical pair: adec=cead.

Flip LHS and RHS.

Defines rule #16.

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

Critical pair: dad=edeab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #24.

Referenced by [20].

Overlap of [19] edeab=e with [3] ba=d:

Critical pair: edead=ea.

Defines rule #8.

Referenced by [24], [25], [26], [37].

Overlap of [14] ddead=da with [4] dad=e:

Critical pair: ddeae=daad.

Reduce RHS:

Referenced by [29].

Overlap of [14] ddead=da with [5] adeab=a:

Critical pair: ddea=daeab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #29.

Referenced by [34], [35], [36], [37].

Overlap of [14] ddead=da with [12] adead=c:

Critical pair: ddec=daead.

Reduce RHS:

Flip LHS and RHS.

Defines rule #10.

Referenced by [24], [25], [26], [27], [28], [29], [31].

Overlap of [20] edead=ea with [4] dad=e:

Critical pair: edeae=eaad.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [20] edead=ea with [8] dae=ead:

Critical pair: edeaead=eaae.

Reduce LHS:

Reduce RHS:

Referenced by [32].

Overlap of [20] edead=ea with [12] adead=c:

Critical pair: edec=eaead.

Reduce RHS:

Flip LHS and RHS.

Referenced by [28], [30], [32].

Overlap of [13] cdead=ac with [4] dad=e:

Critical pair: cdeae=acad.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #11.

Overlap of [13] cdead=ac with [8] dae=ead:

Critical pair: cdeaead=acae.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #12.

Simplify [21] ddeae=dcd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [30].

Overlap of [29] dcd=ddddec with [4] dad=e:

Critical pair: dce=ddddecad.

Reduce RHS:

Defines rule #3.

Overlap of [16] adeae=acd with [23] eae=ddec:

Critical pair: adddec=acd.

Flip LHS and RHS.

Defines rule #13.

Referenced by [33].

Overlap of [25] edddeacd=ece with [26] ddeacd=edec:

Critical pair: ededec=ece.

Flip LHS and RHS.

Defines rule #4.

Overlap of [31] acd=adddec with [4] dad=e:

Critical pair: ace=adddecad.

Reduce RHS:

Defines rule #14.

Overlap of [12] adead=c with [22] eadab=ddea:

Critical pair: adddea=cab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #26.

Overlap of [13] cdead=ac with [22] eadab=ddea:

Critical pair: cdddea=acab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #25.

Overlap of [14] ddead=da with [22] eadab=ddea:

Critical pair: ddddea=daab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #20.

Overlap of [20] edead=ea with [22] eadab=ddea:

Critical pair: edddea=eaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #21.