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.
   |0|()	weight: (/ 1 2); (/ 104551 2)
     a(x1,x2)	weight: x2_1 + x1_1; 104552 + x2_1 + x1_2
     b(x1,x2)	weight: (/ 209105 2) + x1_1; x2_1 + x1_2
     c(x1)	weight: x1_2; 0
   #a(x1,x2)	weight: x2_1 + x1_1 + x1_2; x2_1 + x1_1 + x1_2
   #b(x1,x2)	weight: (/ 104553 2) + x2_2 + x1_1; (/ 104553 2) + x2_1 + x2_2 + x1_1
    Usable rules: { 1..3 }
    Removed DPs: #1..5
Number of SCCs: 0, DPs: 0, edges: 0
YES