Input TRS:
    1: +(x,+(y,z)) -> +(+(x,y),z)
    2: *(x,+(y,z)) -> +(*(x,y),*(x,z))
    3: +(+(x,*(y,z)),*(y,u)) -> +(x,*(y,+(z,u)))
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #*(x,+(y,z)) -> #+(*(x,y),*(x,z))
   #2: #*(x,+(y,z)) -> #*(x,y)
   #3: #*(x,+(y,z)) -> #*(x,z)
   #4: #+(+(x,*(y,z)),*(y,u)) -> #+(x,*(y,+(z,u)))
   #5: #+(+(x,*(y,z)),*(y,u)) -> #*(y,+(z,u))
   #6: #+(+(x,*(y,z)),*(y,u)) -> #+(z,u)
   #7: #+(x,+(y,z)) -> #+(+(x,y),z)
   #8: #+(x,+(y,z)) -> #+(x,y)
Number of SCCs: 1, DPs: 8, edges: 34
	SCC { #1..8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   #*(x1,x2)	weight: x2
     +(x1,x2)	weight: (/ 1 2) + x1 + x2
   #+(x1,x2)	weight: (/ 1 4) + x1 + x2
     *(x1,x2)	weight: x2
    Usable rules: { 1..3 }
    Removed DPs: #1..3 #5 #6 #8
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #4 #7 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed.
Removing edges: failed.
Finding a loop...  found.
  #+(x_{2},+(*(x_{i139},y_{i139}),*(x_{i139},z_{i139})))	-#7->
  #+(+(x_{2},*(x_{i139},y_{i139})),*(x_{i139},z_{i139}))	--->*
  #+(+(x_{2},*(x_{i139},y_{i139})),*(x_{i139},z_{i139}))	-#4->
  #+(x_{2},*(x_{i139},+(y_{i139},z_{i139})))	--->*
  #+(x_{2},+(*(x_{i139},y_{i139}),*(x_{i139},z_{i139})))
  Looping with: [ x_{i139} := x_{i139}; x_{2} := x_{2}; y_{i139} := y_{i139}; z_{i139} := z_{i139}; ]
NO