Certificate for #2361 ⟨a, b | abbbbba=bab

Completion settings:

[1] abbbbba=bab

Axiom: abbbbba=bab.

Referenced by [7].

[2] ab=c

Axiom: ab=c.

Defines rule #1.

Referenced by [7], [8], [9], [14].

[3] cb=d

Axiom: cb=d.

Defines rule #2.

Referenced by [8], [9], [10], [15].

[4] db=e

Axiom: db=e.

Defines rule #3.

Referenced by [8], [10], [11], [16].

[5] eb=f

Axiom: eb=f.

Defines rule #4.

Referenced by [8], [11], [12], [17].

[6] fb=g

Axiom: fb=g.

Defines rule #5.

Referenced by [8], [12], [13], [18].

[7] abbbbba=bc

Simplify [1] abbbbba=bab.

Reduce RHS:

[2]b(ab)
bc

Referenced by [8].

[8] ga=bc

Overlap of [7] abbbbba=bc with [2] ab=c:

abbbbba ab

Critical pair: cbbbba=bc.

Reduce LHS:

[3](cb)bbba
[4](db)bba
[5](eb)ba
[6](fb)a
ga

Defines rule #6.

Referenced by [9].

[9] gc=bd

Overlap of [8] ga=bc with [2] ab=c:

g a ab

Critical pair: gc=bcb.

Reduce RHS:

[3]b(cb)
bd

Defines rule #7.

Referenced by [10].

[10] gd=be

Overlap of [9] gc=bd with [3] cb=d:

g c cb

Critical pair: gd=bdb.

Reduce RHS:

[4]b(db)
be

Defines rule #8.

Referenced by [11].

[11] ge=bf

Overlap of [10] gd=be with [4] db=e:

g d db

Critical pair: ge=beb.

Reduce RHS:

[5]b(eb)
bf

Defines rule #9.

Referenced by [12].

[12] gf=bg

Overlap of [11] ge=bf with [5] eb=f:

g e eb

Critical pair: gf=bfb.

Reduce RHS:

[6]b(fb)
bg

Defines rule #10.

Referenced by [13].

[13] bgb=gg

Overlap of [12] gf=bg with [6] fb=g:

g f fb

Critical pair: gg=bgb.

Flip LHS and RHS.

Defines rule #11.

Referenced by [14], [15], [16], [17], [18].

[14] cgb=agg

Overlap of [2] ab=c with [13] bgb=gg:

a b bgb

Critical pair: agg=cgb.

Flip LHS and RHS.

Defines rule #12.

[15] dgb=cgg

Overlap of [3] cb=d with [13] bgb=gg:

c b bgb

Critical pair: cgg=dgb.

Flip LHS and RHS.

Defines rule #13.

[16] egb=dgg

Overlap of [4] db=e with [13] bgb=gg:

d b bgb

Critical pair: dgg=egb.

Flip LHS and RHS.

Defines rule #14.

[17] fgb=egg

Overlap of [5] eb=f with [13] bgb=gg:

e b bgb

Critical pair: egg=fgb.

Flip LHS and RHS.

Defines rule #15.

[18] ggb=fgg

Overlap of [6] fb=g with [13] bgb=gg:

f b bgb

Critical pair: fgg=ggb.

Flip LHS and RHS.

Defines rule #16.