Input TRS:
    1: b(b(|0|(),y),x) -> y
    2: c(c(c(y))) -> c(c(a(a(c(b(|0|(),y)),|0|()),|0|())))
    3: a(y,|0|()) -> b(y,|0|())
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing b
1: b❆2_|0|(y,x) -> y
2: c(c(c(y))) -> c(c(a(a(c(b❆1_|0|(y)),|0|()),|0|())))
3: a(y,|0|()) -> b(y,|0|())
4: b(|0|(),_1) ->= b❆1_|0|(_1)
5: b(b❆1_|0|(_1),_2) ->= b❆2_|0|(_1,_2)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #c(c(c(y))) -> #c(c(a(a(c(b❆1_|0|(y)),|0|()),|0|())))
   #2: #c(c(c(y))) -> #c(a(a(c(b❆1_|0|(y)),|0|()),|0|()))
   #3: #c(c(c(y))) -> #a(a(c(b❆1_|0|(y)),|0|()),|0|())
   #4: #c(c(c(y))) -> #a(c(b❆1_|0|(y)),|0|())
   #5: #c(c(c(y))) -> #c(b❆1_|0|(y))
   #6: #b(b❆1_|0|(_1),_2) ->? #b❆2_|0|(_1,_2)
   #7: #a(y,|0|()) -> #b(y,|0|())
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #1 #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
     a(x1,x2)	weight: x1
#b❆2_|0|(x1,x2)	weight: 0
     b(x1,x2)	weight: x1 + x2
b❆1_|0|(x1)	weight: x1
     c(x1)	weight: (/ 1 4) + x1
b❆2_|0|(x1,x2)	weight: x1
   #c(x1)	weight: x1
   #a(x1,x2)	weight: 0
   #b(x1,x2)	weight: 0
    Usable rules: { 1..5 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... succeeded.
   |0|()	weight: 0; 0
     a(x1,x2)	weight: x1_1; (/ 1 8) + x1_1
#b❆2_|0|(x1,x2)	weight: 0; 0
     b(x1,x2)	weight: x2_1 + x2_2 + x1_1; x1_1
b❆1_|0|(x1)	weight: x1_1 + x1_2; 0
     c(x1)	weight: x1_2; (/ 1 4) + x1_1 + x1_2
b❆2_|0|(x1,x2)	weight: x1_1; x1_1 + x1_2
   #c(x1)	weight: x1_1; x1_1 + x1_2
   #a(x1,x2)	weight: 0; 0
   #b(x1,x2)	weight: 0; 0
    Usable rules: { 1..5 }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES