Input TRS:
    1: a(0(),b(0(),x)) -> b(0(),a(0(),x))
    2: a(0(),x) -> b(0(),b(0(),x))
    3: a(0(),a(1(),a(x,y))) -> a(1(),a(0(),a(x,y)))
    4: b(0(),a(1(),a(x,y))) -> b(1(),a(0(),a(x,y)))
    5: a(0(),a(x,y)) -> a(1(),a(1(),a(x,y)))
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... failed.
Freezing b
1: a(0(),b❆1_0(x)) -> b❆1_0(a(0(),x))
2: a(0(),x) -> b❆1_0(b❆1_0(x))
3: a(0(),a(1(),a(x,y))) -> a(1(),a(0(),a(x,y)))
4: b❆1_0(a(1(),a(x,y))) -> b❆1_1(a(0(),a(x,y)))
5: a(0(),a(x,y)) -> a(1(),a(1(),a(x,y)))
6: b(1(),_1) ->= b❆1_1(_1)
7: b(0(),_1) ->= b❆1_0(_1)
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... removes: 7 6
     a(x1,x2)	weight: 2 * x1 + x2
     1()	weight: 0
     b(x1,x2)	weight: (/ 1 2) + x1 + x2
b❆1_0(x1)	weight: x1
     0()	weight: 0
b❆1_1(x1)	weight: x1
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #a(0(),x) -> #b❆1_0(b❆1_0(x))
   #2: #a(0(),x) -> #b❆1_0(x)
   #3: #a(0(),a(x,y)) -> #a(1(),a(1(),a(x,y)))
   #4: #a(0(),a(x,y)) -> #a(1(),a(x,y))
   #5: #a(0(),a(1(),a(x,y))) -> #a(1(),a(0(),a(x,y)))
   #6: #a(0(),a(1(),a(x,y))) -> #a(0(),a(x,y))
   #7: #a(0(),b❆1_0(x)) -> #b❆1_0(a(0(),x))
   #8: #a(0(),b❆1_0(x)) -> #a(0(),x)
   #9: #b❆1_0(a(1(),a(x,y))) -> #a(0(),a(x,y))
Number of SCCs: 1, DPs: 5, edges: 14
	SCC { #2 #6..9 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
     a(x1,x2)	weight: max{0, (- (/ 1 8)) + x2 + x1}
     1()	weight: (/ 3 8)
     b(x1,x2)	weight: 0
b❆1_0(x1)	weight: max{0, (/ 1 4) + x1}
     0()	weight: (/ 5 8)
#b❆1_0(x1)	weight: max{0, (/ 1 8) + x1}
b❆1_1(x1)	weight: max{0, x1}
   #a(x1,x2)	weight: max{0, (/ 3 8) + x2}
    Usable rules: { 1..5 }
    Removed DPs: #2 #6 #8
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #7 #9 }
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