YES
We show the termination of the TRS R:

  not(not(x)) -> x
  not(or(x,y)) -> and(not(x),not(y))
  not(and(x,y)) -> or(not(x),not(y))
  and(x,or(y,z)) -> or(and(x,y),and(x,z))
  and(or(y,z),x) -> or(and(x,y),and(x,z))


-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: not#(or(x,y)) -> and#(not(x),not(y))
p2: not#(or(x,y)) -> not#(x)
p3: not#(or(x,y)) -> not#(y)
p4: not#(and(x,y)) -> not#(x)
p5: not#(and(x,y)) -> not#(y)
p6: and#(x,or(y,z)) -> and#(x,y)
p7: and#(x,or(y,z)) -> and#(x,z)
p8: and#(or(y,z),x) -> and#(x,y)
p9: and#(or(y,z),x) -> and#(x,z)

and R consists of:

r1: not(not(x)) -> x
r2: not(or(x,y)) -> and(not(x),not(y))
r3: not(and(x,y)) -> or(not(x),not(y))
r4: and(x,or(y,z)) -> or(and(x,y),and(x,z))
r5: and(or(y,z),x) -> or(and(x,y),and(x,z))

The estimated dependency graph contains the following SCCs:

  {p2, p3, p4, p5}
  {p6, p7, p8, p9}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: not#(and(x,y)) -> not#(y)
p2: not#(and(x,y)) -> not#(x)
p3: not#(or(x,y)) -> not#(y)
p4: not#(or(x,y)) -> not#(x)

and R consists of:

r1: not(not(x)) -> x
r2: not(or(x,y)) -> and(not(x),not(y))
r3: not(and(x,y)) -> or(not(x),not(y))
r4: and(x,or(y,z)) -> or(and(x,y),and(x,z))
r5: and(or(y,z),x) -> or(and(x,y),and(x,z))

The set of usable rules consists of

  r1

Take the monotone reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          not#_A(x1) = x1
          and_A(x1,x2) = x1 + x2 + 5
          or_A(x1,x2) = x1 + x2 + 2
          not_A(x1) = x1 + 1
  
    base order 2:
  
      precedence:
      
        and = or > not# = not
      
  
    partial status:
  
      pi(not#) = [1]
      pi(and) = [1, 2]
      pi(or) = [1, 2]
      pi(not) = [1]

The following rules are removed:

  p1



-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: not#(and(x,y)) -> not#(x)
p2: not#(or(x,y)) -> not#(y)
p3: not#(or(x,y)) -> not#(x)

and R consists of:

r1: not(not(x)) -> x
r2: not(or(x,y)) -> and(not(x),not(y))
r3: not(and(x,y)) -> or(not(x),not(y))
r4: and(x,or(y,z)) -> or(and(x,y),and(x,z))
r5: and(or(y,z),x) -> or(and(x,y),and(x,z))

The estimated dependency graph contains the following SCCs:

  {p1, p2, p3}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: not#(and(x,y)) -> not#(x)
p2: not#(or(x,y)) -> not#(x)
p3: not#(or(x,y)) -> not#(y)

and R consists of:

r1: not(not(x)) -> x
r2: not(or(x,y)) -> and(not(x),not(y))
r3: not(and(x,y)) -> or(not(x),not(y))
r4: and(x,or(y,z)) -> or(and(x,y),and(x,z))
r5: and(or(y,z),x) -> or(and(x,y),and(x,z))

The set of usable rules consists of

  r1

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          not#_A(x1) = x1
          and_A(x1,x2) = x1 + x2 + 5
          or_A(x1,x2) = x1 + x2 + 2
          not_A(x1) = x1 + 1
  
    base order 2:
  
      precedence:
      
        and = or > not# = not
      
  
    partial status:
  
      pi(not#) = []
      pi(and) = [1]
      pi(or) = [2]
      pi(not) = []

The following rules are removed:

  p1



-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: not#(or(x,y)) -> not#(x)
p2: not#(or(x,y)) -> not#(y)

and R consists of:

r1: not(not(x)) -> x
r2: not(or(x,y)) -> and(not(x),not(y))
r3: not(and(x,y)) -> or(not(x),not(y))
r4: and(x,or(y,z)) -> or(and(x,y),and(x,z))
r5: and(or(y,z),x) -> or(and(x,y),and(x,z))

The estimated dependency graph contains the following SCCs:

  {p1, p2}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: not#(or(x,y)) -> not#(x)
p2: not#(or(x,y)) -> not#(y)

and R consists of:

r1: not(not(x)) -> x
r2: not(or(x,y)) -> and(not(x),not(y))
r3: not(and(x,y)) -> or(not(x),not(y))
r4: and(x,or(y,z)) -> or(and(x,y),and(x,z))
r5: and(or(y,z),x) -> or(and(x,y),and(x,z))

The set of usable rules consists of

  r1

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          not#_A(x1) = x1
          or_A(x1,x2) = x1 + x2 + 4
          not_A(x1) = x1 + 1
  
    base order 2:
  
      precedence:
      
        or > not# > not
      
  
    partial status:
  
      pi(not#) = []
      pi(or) = [2]
      pi(not) = [1]

The following rules are removed:

  p1



-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: not#(or(x,y)) -> not#(y)

and R consists of:

r1: not(not(x)) -> x
r2: not(or(x,y)) -> and(not(x),not(y))
r3: not(and(x,y)) -> or(not(x),not(y))
r4: and(x,or(y,z)) -> or(and(x,y),and(x,z))
r5: and(or(y,z),x) -> or(and(x,y),and(x,z))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: not#(or(x,y)) -> not#(y)

and R consists of:

r1: not(not(x)) -> x
r2: not(or(x,y)) -> and(not(x),not(y))
r3: not(and(x,y)) -> or(not(x),not(y))
r4: and(x,or(y,z)) -> or(and(x,y),and(x,z))
r5: and(or(y,z),x) -> or(and(x,y),and(x,z))

The set of usable rules consists of

  r1

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          not#_A(x1) = x1
          or_A(x1,x2) = x1 + x2 + 2
          not_A(x1) = x1 + 1
  
    base order 2:
  
      precedence:
      
        or > not# > not
      
  
    partial status:
  
      pi(not#) = []
      pi(or) = []
      pi(not) = []

The following rules are removed:

  p1

Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: and#(x,or(y,z)) -> and#(x,y)
p2: and#(or(y,z),x) -> and#(x,z)
p3: and#(or(y,z),x) -> and#(x,y)
p4: and#(x,or(y,z)) -> and#(x,z)

and R consists of:

r1: not(not(x)) -> x
r2: not(or(x,y)) -> and(not(x),not(y))
r3: not(and(x,y)) -> or(not(x),not(y))
r4: and(x,or(y,z)) -> or(and(x,y),and(x,z))
r5: and(or(y,z),x) -> or(and(x,y),and(x,z))

The set of usable rules consists of

  r1

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          and#_A(x1,x2) = x1 + x2 + 5
          or_A(x1,x2) = x1 + x2 + 4
          not_A(x1) = x1 + 1
  
    base order 2:
  
      precedence:
      
        and# > or > not
      
  
    partial status:
  
      pi(and#) = []
      pi(or) = [2]
      pi(not) = [1]

The following rules are removed:

  p1



-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: and#(or(y,z),x) -> and#(x,z)
p2: and#(or(y,z),x) -> and#(x,y)
p3: and#(x,or(y,z)) -> and#(x,z)

and R consists of:

r1: not(not(x)) -> x
r2: not(or(x,y)) -> and(not(x),not(y))
r3: not(and(x,y)) -> or(not(x),not(y))
r4: and(x,or(y,z)) -> or(and(x,y),and(x,z))
r5: and(or(y,z),x) -> or(and(x,y),and(x,z))

The estimated dependency graph contains the following SCCs:

  {p1, p2, p3}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: and#(or(y,z),x) -> and#(x,z)
p2: and#(x,or(y,z)) -> and#(x,z)
p3: and#(or(y,z),x) -> and#(x,y)

and R consists of:

r1: not(not(x)) -> x
r2: not(or(x,y)) -> and(not(x),not(y))
r3: not(and(x,y)) -> or(not(x),not(y))
r4: and(x,or(y,z)) -> or(and(x,y),and(x,z))
r5: and(or(y,z),x) -> or(and(x,y),and(x,z))

The set of usable rules consists of

  r1

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          and#_A(x1,x2) = x1 + x2 + 5
          or_A(x1,x2) = x1 + x2 + 4
          not_A(x1) = x1 + 1
  
    base order 2:
  
      precedence:
      
        and# > or > not
      
  
    partial status:
  
      pi(and#) = []
      pi(or) = [2]
      pi(not) = [1]

The following rules are removed:

  p1



-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: and#(x,or(y,z)) -> and#(x,z)
p2: and#(or(y,z),x) -> and#(x,y)

and R consists of:

r1: not(not(x)) -> x
r2: not(or(x,y)) -> and(not(x),not(y))
r3: not(and(x,y)) -> or(not(x),not(y))
r4: and(x,or(y,z)) -> or(and(x,y),and(x,z))
r5: and(or(y,z),x) -> or(and(x,y),and(x,z))

The estimated dependency graph contains the following SCCs:

  {p1, p2}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: and#(x,or(y,z)) -> and#(x,z)
p2: and#(or(y,z),x) -> and#(x,y)

and R consists of:

r1: not(not(x)) -> x
r2: not(or(x,y)) -> and(not(x),not(y))
r3: not(and(x,y)) -> or(not(x),not(y))
r4: and(x,or(y,z)) -> or(and(x,y),and(x,z))
r5: and(or(y,z),x) -> or(and(x,y),and(x,z))

The set of usable rules consists of

  r1

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          and#_A(x1,x2) = x1 + x2 + 5
          or_A(x1,x2) = x1 + x2 + 4
          not_A(x1) = x1 + 1
  
    base order 2:
  
      precedence:
      
        and# > or > not
      
  
    partial status:
  
      pi(and#) = [1]
      pi(or) = []
      pi(not) = [1]

The following rules are removed:

  p2



-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: and#(x,or(y,z)) -> and#(x,z)

and R consists of:

r1: not(not(x)) -> x
r2: not(or(x,y)) -> and(not(x),not(y))
r3: not(and(x,y)) -> or(not(x),not(y))
r4: and(x,or(y,z)) -> or(and(x,y),and(x,z))
r5: and(or(y,z),x) -> or(and(x,y),and(x,z))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: and#(x,or(y,z)) -> and#(x,z)

and R consists of:

r1: not(not(x)) -> x
r2: not(or(x,y)) -> and(not(x),not(y))
r3: not(and(x,y)) -> or(not(x),not(y))
r4: and(x,or(y,z)) -> or(and(x,y),and(x,z))
r5: and(or(y,z),x) -> or(and(x,y),and(x,z))

The set of usable rules consists of

  r1

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          and#_A(x1,x2) = x2
          or_A(x1,x2) = x1 + x2 + 4
          not_A(x1) = x1 + 1
  
    base order 2:
  
      precedence:
      
        or > and# = not
      
  
    partial status:
  
      pi(and#) = []
      pi(or) = [2]
      pi(not) = [1]

The following rules are removed:

  p1

Then no dependency pair remains.