Confluence Problems (Cops)

438 problems found.
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765.trs

(VAR x y z)
(RULES
   xor(x,0) -> x
   xor(0,x) -> x
   xor(x,x) -> 0
   and(x,0) -> 0
   and(0,x) -> 0
   and(x,1) -> x
   and(1,x) -> x
   and(x,x) -> x
   xor(xor(x,y),z) -> xor(x,xor(y,z))
   xor(x,xor(y,z)) -> xor(y,xor(x,z))
   xor(x,y) -> xor(y,x)
   xor(x,xor(x,y)) -> y
   and(and(x,y),z) -> and(x,and(y,z))
   and(x,and(y,z)) -> and(y,and(x,z))
   and(x,y) -> and(y,x)
   and(x,and(x,y)) -> and(x,y)
   and(x,xor(y,z)) -> xor(and(x,y),xor(x,z))
   and(xor(x,y),z) -> xor(and(x,z),and(y,z))
)
(COMMENT
[113] Example 4.15; correction of Cops #536
submitted by: Takahito Aoto
)
format:
properties:
CoCo:

763.trs

(VAR x)
(RULES
  f(f(x)) -> f(g(f(x),f(x)))
)
(COMMENT
[130] Example 4.24
submitted by: Julian Nagele
)
format:
properties:
CoCo:

762.trs

(VAR x)
(RULES
  a -> b
  f(a,b) -> f(a,a)
  f(b,a) -> f(a,a)
  f(a,a) -> c
  g(x) -> f(x,x)
)
(COMMENT
doi:10.23638/LMCS-13(2:4)2017
[131] Example 5.11
submitted by: Julian Nagele
)
format:
properties:
CoCo:

761.trs

(VAR )
(RULES
  a -> b
  a -> d
  b -> a
  c -> a
  c -> b
)
(COMMENT
doi:10.23638/LMCS-13(2:4)2017
[131] Example 5.2
submitted by: Julian Nagele
)
format:
properties:
CoCo:

760.trs

(VAR x)
(RULES
  f(x) -> f(f(x))
  g(x) -> f(x)
  f(x) -> g(x)
)
(COMMENT
[130] Example 3.29
submitted by: Julian Nagele
)
format:
properties:
CoCo:

741.trs

(VAR x)
(RULES
  if(true,a,x) -> a
  if(true,b,x) -> b
  if(true,g(a),x) -> g(a)
  if(true,g(b),x) -> g(b)
  if(false,x,a) -> a
  if(false,x,b) -> b
  if(false,x,g(a)) -> g(a)
  if(false,x,g(b)) -> g(b)
  g(a) -> g(g(a))
  g(b) -> a
  f(a,b) -> b
  f(g(g(a)),x) -> b
)
(COMMENT
handcrafted "UNC & ~NFP"
submitted by: Franziska Rapp
)
format:
properties:
CoCo:

739.trs

(VAR x)
(RULES
  a -> a
  g(g(a)) -> b
  g(g(x)) -> g(g(g(b)))
)
(COMMENT
generated by FORT "UN & ~UNC"
submitted by: Franziska Rapp
)
format:
properties:
CoCo:

738.trs

(VAR x)
(RULES
  a -> a
  f(b,a) -> f(a,b)
  f(x,a) -> b
)
(COMMENT
generated by FORT "UN & ~NFP"
submitted by: Franziska Rapp
)
format:
properties:
CoCo:

733.trs

(VAR x0)
(RULES
  a -> a
  a -> b
  a -> f(a,a)
  f(b,b) -> f(a,b)
  f(x0,a) -> f(b,b)
)
(COMMENT
generated by FORT -f "a:0 b:0 f:2" -r 5 "UN & ~UNC & GUNC"
submitted by: Franziska Rapp
)
format:
properties:
CoCo:

732.trs

(VAR x0)
(RULES
  a -> a
  a -> b
  a -> f(a,a)
  f(b,b) -> f(a,a)
  f(x0,a) -> f(a,b)
)
(COMMENT
generated by FORT -f "a:0 b:0 f:2" -r 5 "UN & ~UNC & ~SN"
submitted by: Franziska Rapp
)
format:
properties:
CoCo:

731.trs

(VAR x)
(RULES
  a -> a
  a -> b
  f(b,b) -> f(a,b)
  f(x,a) -> f(a,b)
)
(COMMENT
generated by FORT -f "a:0 b:0 f:2" -r 4 "UN & ~UNC & ~SN"
submitted by: Franziska Rapp
)
format:
properties:
CoCo:

721.trs

(RULES
  b -> h(b,a)
  b -> h(f(b),f(h(b,a)))
)
(COMMENT
Cops #647 - #721: generated ground TRSs; evenly distributed in the
UNR/UNC/NFP/CR hierarchy
submitted by: Bertram Felgenhauer
)
format:
properties:
CoCo:

720.trs

(RULES
  b -> f(f(b))
  f(a) -> c
  f(a) -> b
  b -> f(h(a,b))
)
(COMMENT
Cops #647 - #721: generated ground TRSs; evenly distributed in the
UNR/UNC/NFP/CR hierarchy
submitted by: Bertram Felgenhauer
)
format:
properties:
CoCo:

719.trs

(RULES
  b -> f(b)
  c -> b
  f(f(f(c))) -> a
  f(h(b,b)) -> h(h(c,a),b)
)
(COMMENT
Cops #647 - #721: generated ground TRSs; evenly distributed in the
UNR/UNC/NFP/CR hierarchy
submitted by: Bertram Felgenhauer
)
format:
properties:
CoCo:

718.trs

(RULES
  h(c,c) -> h(b,f(b))
  f(h(a,h(c,a))) -> c
  h(c,b) -> f(a)
)
(COMMENT
Cops #647 - #721: generated ground TRSs; evenly distributed in the
UNR/UNC/NFP/CR hierarchy
submitted by: Bertram Felgenhauer
)
format:
properties:
CoCo:

717.trs

(RULES
  a -> c
  f(f(c)) -> h(a,h(h(c,c),b))
  f(f(a)) -> b
  b -> f(f(b))
)
(COMMENT
Cops #647 - #721: generated ground TRSs; evenly distributed in the
UNR/UNC/NFP/CR hierarchy
submitted by: Bertram Felgenhauer
)
format:
properties:
CoCo:

716.trs

(RULES
  a -> h(a,f(b))
  f(f(h(a,a))) -> f(f(f(a)))
  f(h(a,h(a,a))) -> f(a)
  f(h(h(b,a),h(f(c),c))) -> c
)
(COMMENT
Cops #647 - #721: generated ground TRSs; evenly distributed in the
UNR/UNC/NFP/CR hierarchy
submitted by: Bertram Felgenhauer
)
format:
properties:
CoCo:

715.trs

(RULES
  c -> c
  b -> f(c)
  h(b,h(a,f(h(a,f(f(f(b))))))) -> h(a,f(a))
  b -> h(b,a)
  h(f(b),c) -> f(c)
)
(COMMENT
Cops #647 - #721: generated ground TRSs; evenly distributed in the
UNR/UNC/NFP/CR hierarchy
submitted by: Bertram Felgenhauer
)
format:
properties:
CoCo:

714.trs

(RULES
  a -> h(f(a),c)
  a -> f(c)
)
(COMMENT
Cops #647 - #721: generated ground TRSs; evenly distributed in the
UNR/UNC/NFP/CR hierarchy
submitted by: Bertram Felgenhauer
)
format:
properties:
CoCo:

713.trs

(RULES
  a -> c
  h(h(b,b),a) -> a
  f(a) -> b
)
(COMMENT
Cops #647 - #721: generated ground TRSs; evenly distributed in the
UNR/UNC/NFP/CR hierarchy
submitted by: Bertram Felgenhauer
)
format:
properties:
CoCo:

712.trs

(RULES
  c -> a
  f(c) -> f(h(b,c))
  a -> c
  c -> h(f(c),h(b,h(h(b,c),a)))
  c -> b
)
(COMMENT
Cops #647 - #721: generated ground TRSs; evenly distributed in the
UNR/UNC/NFP/CR hierarchy
submitted by: Bertram Felgenhauer
)
format:
properties:
CoCo:

711.trs

(RULES
  f(h(f(b),a)) -> b
  f(c) -> b
  b -> f(b)
)
(COMMENT
Cops #647 - #721: generated ground TRSs; evenly distributed in the
UNR/UNC/NFP/CR hierarchy
submitted by: Bertram Felgenhauer
)
format:
properties:
CoCo:

710.trs

(RULES
  c -> f(b)
  c -> b
)
(COMMENT
Cops #647 - #721: generated ground TRSs; evenly distributed in the
UNR/UNC/NFP/CR hierarchy
submitted by: Bertram Felgenhauer
)
format:
properties:
CoCo:

709.trs

(RULES
  b -> c
  a -> a
)
(COMMENT
Cops #647 - #721: generated ground TRSs; evenly distributed in the
UNR/UNC/NFP/CR hierarchy
submitted by: Bertram Felgenhauer
)
format:
properties:
CoCo:

708.trs

(RULES
  h(f(f(c)),h(c,h(c,h(h(f(b),f(f(f(f(b))))),b)))) -> h(h(a,a),f(c))
  h(b,h(c,h(b,h(a,b)))) -> a
  f(c) -> f(f(a))
  a -> f(f(b))
)
(COMMENT
Cops #647 - #721: generated ground TRSs; evenly distributed in the
UNR/UNC/NFP/CR hierarchy
submitted by: Bertram Felgenhauer
)
format:
properties:
CoCo:
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