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.
     a(x1,x2)	weight: x1
     b(x1,x2)	weight: x1 + x2
b❆1_0(x1)	weight: x1
b❆2_0(x1,x2)	weight: x1
     c(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
#b❆2_0(x1,x2)	weight: 0
   #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.
     a(x1,x2)	weight: x2_1 + x2_2 + x1_2; (/ 1 16) + x2_1 + x1_2
     b(x1,x2)	weight: x2_1 + x1_2; x2_1 + x2_2 + x1_2
b❆1_0(x1)	weight: (/ 1 16) + x1_1; (/ 1 16) + x1_1 + x1_2
b❆2_0(x1,x2)	weight: x1_1; x1_1 + x1_2
     c(x1)	weight: (/ 3 8) + x1_1; (/ 1 16)
     0()	weight: (/ 1 16); (/ 1 16)
#b❆2_0(x1,x2)	weight: 0; 0
   #c(x1)	weight: x1_1; 0
   #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