YES

Problem:
 h(x,c(y,z)) -> h(c(s(y),x),z)
 h(c(s(x),c(s(0()),y)),z) -> h(y,c(s(0()),c(x,z)))

Proof:
 DP Processor:
  DPs:
   h#(x,c(y,z)) -> h#(c(s(y),x),z)
   h#(c(s(x),c(s(0()),y)),z) -> h#(y,c(s(0()),c(x,z)))
  TRS:
   h(x,c(y,z)) -> h(c(s(y),x),z)
   h(c(s(x),c(s(0()),y)),z) -> h(y,c(s(0()),c(x,z)))
  Usable Rule Processor:
   DPs:
    h#(x,c(y,z)) -> h#(c(s(y),x),z)
    h#(c(s(x),c(s(0()),y)),z) -> h#(y,c(s(0()),c(x,z)))
   TRS:
    
   Bounds Processor:
    bound: 2
    enrichment: match
    automaton:
     final states: {6}
     transitions:
      00() -> 5*
      h{#,1}(10,5) -> 6*
      h{#,1}(10,14) -> 6*
      h{#,1}(5,14) -> 6*
      c1(13,11) -> 14*
      c1(9,10) -> 10*
      c1(9,20) -> 10*
      c1(5,5) -> 11*
      c1(13,14) -> 14*
      c1(9,5) -> 10*
      c1(5,14) -> 11*
      s1(5) -> 9*
      s1(12) -> 13*
      01() -> 12*
      h{#,2}(18,11) -> 6*
      h{#,2}(20,5) -> 6*
      h{#,2}(18,14) -> 6*
      h{#,2}(20,14) -> 6*
      h{#,0}(5,5) -> 6*
      c2(17,18) -> 18*
      c2(17,20) -> 18*
      c2(19,18) -> 20*
      c2(17,5) -> 18*
      c2(17,10) -> 18*
      c0(5,5) -> 5*
      s2(5) -> 19*
      s2(13) -> 17*
      s0(5) -> 5*
    problem:
     DPs:
      
     TRS:
      
    Qed