Input TRS:
    1: g(x) -> h(x,x)
    2: s(x) -> h(x,0())
    3: s(x) -> h(0(),x)
    4: f(g(x)) -> g(g(f(x)))
    5: g(s(x)) -> s(s(g(x)))
    6: h(f(x),g(x)) -> f(s(x))
    7: s(0()) -> f(0())
    8: s(s(0())) -> f(s(0()))
    9: f(s(0())) -> 0()
    10: s(s(s(s(s(s(s(0()))))))) -> f(s(s(0())))
    11: f(s(s(0()))) -> s(s(s(s(s(0())))))
    12: f(s(s(x))) -> h(f(x),g(h(x,x)))
Number of strict rules: 12
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #s(x) -> #h(x,0())
   #2: #h(f(x),g(x)) -> #f(s(x))
   #3: #h(f(x),g(x)) -> #s(x)
   #4: #f(s(s(0()))) -> #s(s(s(s(s(0())))))
   #5: #f(s(s(0()))) -> #s(s(s(s(0()))))
   #6: #f(s(s(0()))) -> #s(s(s(0())))
   #7: #f(s(s(x))) -> #h(f(x),g(h(x,x)))
   #8: #f(s(s(x))) -> #f(x)
   #9: #f(s(s(x))) -> #g(h(x,x))
   #10: #f(s(s(x))) -> #h(x,x)
   #11: #s(0()) -> #f(0())
   #12: #s(s(s(s(s(s(s(0()))))))) -> #f(s(s(0())))
   #13: #g(s(x)) -> #s(s(g(x)))
   #14: #g(s(x)) -> #s(g(x))
   #15: #g(s(x)) -> #g(x)
   #16: #s(x) -> #h(0(),x)
   #17: #g(x) -> #h(x,x)
   #18: #s(s(0())) -> #f(s(0()))
   #19: #f(g(x)) -> #g(g(f(x)))
   #20: #f(g(x)) -> #g(f(x))
   #21: #f(g(x)) -> #f(x)
Number of SCCs: 1, DPs: 14, edges: 50
	SCC { #2 #3 #7..10 #12..15 #17 #19..21 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... succeeded.
     h(x1,x2)	weight: x1_1; x1_2
     s(x1)	weight: x1_1; x1_2
     f(x1)	weight: x1_1 + x1_2; x1_1 + x1_2
     0()	weight: 0; 0
   #h(x1,x2)	weight: x1_1; 0
   #s(x1)	weight: 0; 0
   #f(x1)	weight: x1_1 + x1_2; 0
   #g(x1)	weight: x1_1; 0
     g(x1)	weight: (/ 1 4) + x1_1; (/ 1 4) + x1_2
    Usable rules: { 1..12 }
    Removed DPs: #19..21
Number of SCCs: 1, DPs: 11, edges: 29
	SCC { #2 #3 #7..10 #12..15 #17 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... succeeded.
     h(x1,x2)	weight: x1_1; x1_2
     s(x1)	weight: x1_1; x1_2
     f(x1)	weight: x1_1 + x1_2; x1_1 + x1_2
     0()	weight: 0; 0
   #h(x1,x2)	weight: x2_1 + x2_2; 0
   #s(x1)	weight: (/ 1 2); 0
   #f(x1)	weight: (/ 1 2) + x1_1 + x1_2; 0
   #g(x1)	weight: (/ 1 2) + x1_1 + x1_2; 0
     g(x1)	weight: (/ 1 4) + x1_1; (/ 1 4) + x1_2
    Usable rules: { 1..12 }
    Removed DPs: #10 #17
Number of SCCs: 1, DPs: 9, edges: 20
	SCC { #2 #3 #7..9 #12..15 }
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)... succeeded.
     h(x1,x2)	weight: max{0, x2_1 + x2_2}; x2_2 + x1_2
     s(x1)	weight: max{0, x1_1}; x1_2
     f(x1)	weight: max{0, x1_1}; x1_2
     0()	weight: (/ 1 4); (- (/ 1 4))
   #h(x1,x2)	weight: max{0, x2_1}; 0
   #s(x1)	weight: max{0, x1_1}; 0
   #f(x1)	weight: max{0, x1_1 + x1_2}; 0
   #g(x1)	weight: max{0, x1_1}; 0
     g(x1)	weight: max{0, x1_1}; 0
    Usable rules: { 1..12 }
    Removed DPs: #12
Number of SCCs: 2, DPs: 4, edges: 6
	SCC { #15 }
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)... succeeded.
     h(x1,x2)	weight: 0; 0
     s(x1)	weight: max{0, (/ 1 4) + x1_1}; (- (/ 1 4))
     f(x1)	weight: 0; 0
     0()	weight: 0; 0
   #h(x1,x2)	weight: 0; 0
   #s(x1)	weight: 0; 0
   #f(x1)	weight: 0; 0
   #g(x1)	weight: max{0, (/ 1 4) + x1_1}; 0
     g(x1)	weight: 0; 0
    Usable rules: { }
    Removed DPs: #15
Number of SCCs: 1, DPs: 3, edges: 5
	SCC { #2 #7 #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