Input TRS:
    1: *(x,+(y,z)) -> +(*(x,y),*(x,z))
    2: *(+(y,z),x) -> +(*(x,y),*(x,z))
    3: *(*(x,y),z) -> *(x,*(y,z))
    4: +(+(x,y),z) -> +(x,+(y,z))
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #*(+(y,z),x) -> #+(*(x,y),*(x,z))
   #2: #*(+(y,z),x) -> #*(x,y)
   #3: #*(+(y,z),x) -> #*(x,z)
   #4: #*(*(x,y),z) -> #*(x,*(y,z))
   #5: #*(*(x,y),z) -> #*(y,z)
   #6: #*(x,+(y,z)) -> #+(*(x,y),*(x,z))
   #7: #*(x,+(y,z)) -> #*(x,y)
   #8: #*(x,+(y,z)) -> #*(x,z)
   #9: #+(+(x,y),z) -> #+(x,+(y,z))
   #10: #+(+(x,y),z) -> #+(y,z)
Number of SCCs: 2, DPs: 8, edges: 40
	SCC { #9 #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   #*(x1,x2)	weight: 0
     +(x1,x2)	weight: (/ 1 2) + x1 + x2
   #+(x1,x2)	weight: x1
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #9 #10
Number of SCCs: 1, DPs: 6, edges: 36
	SCC { #2..5 #7 #8 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
   #*(x1,x2)	weight: max{0, (- (/ 1 8)) + x2 + x1}
     +(x1,x2)	weight: max{0, (/ 3 8) + x1, x2}
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: max{0, (/ 1 4) + x2 + x1}
    Usable rules: { 1..4 }
    Removed DPs: #2 #5 #7
Number of SCCs: 1, DPs: 3, edges: 9
	SCC { #3 #4 #8 }
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...  failed.
MAYBE