Input TRS:
    1: times(x,plus(y,1())) -> plus(times(x,plus(y,times(1(),0()))),x)
    2: times(x,1()) -> x
    3: plus(x,0()) -> x
    4: times(x,0()) -> 0()
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #times(x,plus(y,1())) -> #plus(times(x,plus(y,times(1(),0()))),x)
   #2: #times(x,plus(y,1())) -> #times(x,plus(y,times(1(),0())))
   #3: #times(x,plus(y,1())) -> #plus(y,times(1(),0()))
   #4: #times(x,plus(y,1())) -> #times(1(),0())
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... succeeded.
     1()	status: []	precedence above: 0 times
#plus(x1,x2)	status: [x2]	precedence above:
#times(x1,x2)	status: [x2]	precedence above: 1 0 times plus
     0()	status: []	precedence above:
 times(x1,x2)	status: [x2]	precedence above: 0
  plus(x1,x2)	status: [x1,x2]	precedence above: 1 0 times
    Usable rules: { 3 4 }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0, edges: 0
YES