YES

Problem:
 times(x,plus(y,1())) -> plus(times(x,plus(y,times(1(),0()))),x)
 times(x,1()) -> x
 plus(x,0()) -> x
 times(x,0()) -> 0()

Proof:
 DP Processor:
  DPs:
   times#(x,plus(y,1())) -> times#(1(),0())
   times#(x,plus(y,1())) -> plus#(y,times(1(),0()))
   times#(x,plus(y,1())) -> times#(x,plus(y,times(1(),0())))
   times#(x,plus(y,1())) -> plus#(times(x,plus(y,times(1(),0()))),x)
  TRS:
   times(x,plus(y,1())) -> plus(times(x,plus(y,times(1(),0()))),x)
   times(x,1()) -> x
   plus(x,0()) -> x
   times(x,0()) -> 0()
  EDG Processor:
   DPs:
    times#(x,plus(y,1())) -> times#(1(),0())
    times#(x,plus(y,1())) -> plus#(y,times(1(),0()))
    times#(x,plus(y,1())) -> times#(x,plus(y,times(1(),0())))
    times#(x,plus(y,1())) -> plus#(times(x,plus(y,times(1(),0()))),x)
   TRS:
    times(x,plus(y,1())) -> plus(times(x,plus(y,times(1(),0()))),x)
    times(x,1()) -> x
    plus(x,0()) -> x
    times(x,0()) -> 0()
   graph:
    times#(x,plus(y,1())) -> times#(x,plus(y,times(1(),0()))) ->
    times#(x,plus(y,1())) -> times#(1(),0())
    times#(x,plus(y,1())) -> times#(x,plus(y,times(1(),0()))) ->
    times#(x,plus(y,1())) -> plus#(y,times(1(),0()))
    times#(x,plus(y,1())) -> times#(x,plus(y,times(1(),0()))) ->
    times#(x,plus(y,1())) -> times#(x,plus(y,times(1(),0())))
    times#(x,plus(y,1())) -> times#(x,plus(y,times(1(),0()))) ->
    times#(x,plus(y,1())) -> plus#(times(x,plus(y,times(1(),0()))),x)
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 4/16
    DPs:
     times#(x,plus(y,1())) -> times#(x,plus(y,times(1(),0())))
    TRS:
     times(x,plus(y,1())) -> plus(times(x,plus(y,times(1(),0()))),x)
     times(x,1()) -> x
     plus(x,0()) -> x
     times(x,0()) -> 0()
    Usable Rule Processor:
     DPs:
      times#(x,plus(y,1())) -> times#(x,plus(y,times(1(),0())))
     TRS:
      times(x,0()) -> 0()
      plus(x,0()) -> x
     Bounds Processor:
      bound: 0
      enrichment: match-dp
      automaton:
       final states: {1}
       transitions:
        f60() -> 5*
        times{#,0}(5,6) -> 1*
        plus0(5,4) -> 6*
        times0(3,2) -> 4*
        10() -> 3*
        00() -> 4,2
        5 -> 6*
      problem:
       DPs:
        
       TRS:
        times(x,0()) -> 0()
        plus(x,0()) -> x
      Qed