Input TRS:
    1: a(h(),h(),h(),x) -> s(x)
    2: a(l,x,s(y),h()) -> a(l,x,y,s(h()))
    3: a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
    4: a(l,s(x),h(),z) -> a(l,x,z,z)
    5: a(s(l),h(),h(),z) -> a(l,z,h(),z)
    6: +(x,h()) -> x
    7: +(h(),x) -> x
    8: +(s(x),s(y)) -> s(s(+(x,y)))
    9: +(+(x,y),z) -> +(x,+(y,z))
    10: s(h()) -> 1()
    11: *(h(),x) -> h()
    12: *(x,h()) -> h()
    13: *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
Number of strict rules: 13
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a(l,x,s(y),h()) -> #a(l,x,y,s(h()))
   #2: #a(l,x,s(y),h()) -> #s(h())
   #3: #*(s(x),s(y)) -> #s(+(+(*(x,y),x),y))
   #4: #*(s(x),s(y)) -> #+(+(*(x,y),x),y)
   #5: #*(s(x),s(y)) -> #+(*(x,y),x)
   #6: #*(s(x),s(y)) -> #*(x,y)
   #7: #+(+(x,y),z) -> #+(x,+(y,z))
   #8: #+(+(x,y),z) -> #+(y,z)
   #9: #a(s(l),h(),h(),z) -> #a(l,z,h(),z)
   #10: #a(l,x,s(y),s(z)) -> #a(l,x,y,a(l,x,s(y),z))
   #11: #a(l,x,s(y),s(z)) -> #a(l,x,s(y),z)
   #12: #a(h(),h(),h(),x) -> #s(x)
   #13: #+(s(x),s(y)) -> #s(s(+(x,y)))
   #14: #+(s(x),s(y)) -> #s(+(x,y))
   #15: #+(s(x),s(y)) -> #+(x,y)
   #16: #a(l,s(x),h(),z) -> #a(l,x,z,z)
Number of SCCs: 3, DPs: 9, edges: 28
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     h()	weight: 0
     a(x1,x2,x3,x4)	weight: 0
     1()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
   #*(x1,x2)	weight: x2
   #s(x1)	weight: 0
   #a(x1,x2,x3,x4)	weight: 0
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #6
Number of SCCs: 2, DPs: 8, edges: 27
	SCC { #7 #8 #15 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     h()	weight: 0
     a(x1,x2,x3,x4)	weight: 0
     1()	weight: 0
     s(x1)	weight: (/ 1 4) + x1
   #*(x1,x2)	weight: 0
   #s(x1)	weight: 0
   #a(x1,x2,x3,x4)	weight: 0
     +(x1,x2)	weight: (/ 1 4) + x1 + x2
   #+(x1,x2)	weight: x1
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #7 #8 #15
Number of SCCs: 1, DPs: 5, edges: 18
	SCC { #1 #9..11 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     h()	weight: 0
     a(x1,x2,x3,x4)	weight: (/ 1 4) + x1
     1()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
   #*(x1,x2)	weight: 0
   #s(x1)	weight: 0
   #a(x1,x2,x3,x4)	weight: x1
     +(x1,x2)	weight: (/ 1 4) + x1 + x2
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #9
Number of SCCs: 1, DPs: 4, edges: 13
	SCC { #1 #10 #11 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     h()	weight: 0
     a(x1,x2,x3,x4)	weight: (/ 1 4) + x1
     1()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
   #*(x1,x2)	weight: 0
   #s(x1)	weight: 0
   #a(x1,x2,x3,x4)	weight: x2
     +(x1,x2)	weight: (/ 1 4) + x1 + x2
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #16
Number of SCCs: 1, DPs: 3, edges: 7
	SCC { #1 #10 #11 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     h()	weight: 0
     a(x1,x2,x3,x4)	weight: (/ 1 4) + x1
     1()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
   #*(x1,x2)	weight: 0
   #s(x1)	weight: 0
   #a(x1,x2,x3,x4)	weight: x3
     +(x1,x2)	weight: (/ 1 4) + x1 + x2
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { 10 }
    Removed DPs: #1 #10
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #11 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     h()	weight: (/ 1 4)
     a(x1,x2,x3,x4)	weight: 0
     1()	weight: (/ 3 4)
     s(x1)	weight: (/ 1 4) + x1
   #*(x1,x2)	weight: 0
   #s(x1)	weight: 0
   #a(x1,x2,x3,x4)	weight: max{0, (/ 1 4) + x4}
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #11
Number of SCCs: 0, DPs: 0, edges: 0
YES