Certificate for #1137 ⟨a, b | abbbba=bab

Completion settings:

[1] abbbba=bab

Axiom: abbbba=bab.

Referenced by [6].

[2] ab=c

Axiom: ab=c.

Defines rule #1.

Referenced by [6], [7], [8], [12].

[3] cb=d

Axiom: cb=d.

Defines rule #2.

Referenced by [7], [8], [9], [13].

[4] db=e

Axiom: db=e.

Defines rule #3.

Referenced by [7], [9], [10], [14].

[5] eb=f

Axiom: eb=f.

Defines rule #4.

Referenced by [7], [10], [11], [15].

[6] abbbba=bc

Simplify [1] abbbba=bab.

Reduce RHS:

[2]b(ab)
bc

Referenced by [7].

[7] fa=bc

Overlap of [6] abbbba=bc with [2] ab=c:

abbbba ab

Critical pair: cbbba=bc.

Reduce LHS:

[3](cb)bba
[4](db)ba
[5](eb)a
fa

Defines rule #5.

Referenced by [8].

[8] fc=bd

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

f a ab

Critical pair: fc=bcb.

Reduce RHS:

[3]b(cb)
bd

Defines rule #6.

Referenced by [9].

[9] fd=be

Overlap of [8] fc=bd with [3] cb=d:

f c cb

Critical pair: fd=bdb.

Reduce RHS:

[4]b(db)
be

Defines rule #7.

Referenced by [10].

[10] fe=bf

Overlap of [9] fd=be with [4] db=e:

f d db

Critical pair: fe=beb.

Reduce RHS:

[5]b(eb)
bf

Defines rule #8.

Referenced by [11].

[11] bfb=ff

Overlap of [10] fe=bf with [5] eb=f:

f e eb

Critical pair: ff=bfb.

Flip LHS and RHS.

Defines rule #9.

Referenced by [12], [13], [14], [15].

[12] cfb=aff

Overlap of [2] ab=c with [11] bfb=ff:

a b bfb

Critical pair: aff=cfb.

Flip LHS and RHS.

Defines rule #10.

[13] dfb=cff

Overlap of [3] cb=d with [11] bfb=ff:

c b bfb

Critical pair: cff=dfb.

Flip LHS and RHS.

Defines rule #11.

[14] efb=dff

Overlap of [4] db=e with [11] bfb=ff:

d b bfb

Critical pair: dff=efb.

Flip LHS and RHS.

Defines rule #12.

[15] ffb=eff

Overlap of [5] eb=f with [11] bfb=ff:

e b bfb

Critical pair: eff=ffb.

Flip LHS and RHS.

Defines rule #13.