Input TRS:
    1: and(tt(),X) -> activate(X)
    2: plus(N,0()) -> N
    3: plus(N,s(M)) -> s(plus(N,M))
    4: x(N,0()) -> 0()
    5: x(N,s(M)) -> plus(x(N,M),N)
    6: activate(X) -> X
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #x(N,s(M)) -> #plus(x(N,M),N)
   #2: #x(N,s(M)) -> #x(N,M)
   #3: #plus(N,s(M)) -> #plus(N,M)
   #4: #and(tt(),X) -> #activate(X)
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
activate(x1)	weight: 0
   and(x1,x2)	weight: 0
#plus(x1,x2)	weight: x2
#activate(x1)	weight: 0
     x(x1,x2)	weight: 0
     0()	weight: 0
   #x(x1,x2)	weight: 0
  plus(x1,x2)	weight: 0
    tt()	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
activate(x1)	weight: 0
   and(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
#activate(x1)	weight: 0
     x(x1,x2)	weight: 0
     0()	weight: 0
   #x(x1,x2)	weight: x2
  plus(x1,x2)	weight: 0
    tt()	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0, edges: 0
YES