Input TRS:
    1: b(x,y) -> c(a(c(y),a(0(),x)))
    2: a(y,x) -> y
    3: a(y,c(b(a(0(),x),0()))) -> b(a(c(b(0(),y)),x),0())
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a(y,c(b(a(0(),x),0()))) -> #b(a(c(b(0(),y)),x),0())
   #2: #a(y,c(b(a(0(),x),0()))) -> #a(c(b(0(),y)),x)
   #3: #a(y,c(b(a(0(),x),0()))) -> #b(0(),y)
   #4: #b(x,y) -> #a(c(y),a(0(),x))
   #5: #b(x,y) -> #a(0(),x)
Number of SCCs: 1, DPs: 5, edges: 13
	SCC { #1..5 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... succeeded.
     a(x1,x2)	weight: x2_1 + x1_1; (/ 5 16) + x2_1 + x1_2
     b(x1,x2)	weight: (/ 3 8) + x1_1; x2_1 + x1_2
     c(x1)	weight: x1_2; 0
     0()	weight: (/ 1 16); (/ 1 16)
   #a(x1,x2)	weight: x2_1 + x1_1 + x1_2; x2_1 + x1_1 + x1_2
   #b(x1,x2)	weight: (/ 3 16) + x2_1 + x2_2 + x1_1; (/ 1 4) + x2_1 + x2_2 + x1_1
    Usable rules: { 1..3 }
    Removed DPs: #1..5
Number of SCCs: 0, DPs: 0, edges: 0
YES