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-dp
    automaton:
     final states: {6}
     transitions:
      00() -> 4*
      h{#,1}(1,33) -> 3*
      h{#,1}(62,30) -> 6*
      h{#,1}(27,30) -> 3,5,6
      h{#,1}(26,51) -> 3,5
      h{#,1}(2,30) -> 3,5
      h{#,1}(19,2) -> 6,3
      h{#,1}(19,4) -> 6,3
      h{#,1}(8,33) -> 3,5,6
      h{#,1}(3,33) -> 3*
      h{#,1}(25,1) -> 3*
      h{#,1}(25,3) -> 3*
      h{#,1}(54,30) -> 3,5,6
      h{#,1}(39,30) -> 3,5,6
      h{#,1}(19,30) -> 3,5,6
      h{#,1}(4,30) -> 3,5
      h{#,1}(26,2) -> 3,5,6
      h{#,1}(26,4) -> 3,5,6
      h{#,1}(39,52) -> 3,5,6
      h{#,1}(35,33) -> 3,5,6
      h{#,1}(25,33) -> 6,3
      h{#,1}(19,52) -> 3,5,6
      h{#,1}(5,33) -> 3,5,6
      h{#,1}(27,1) -> 6*
      h{#,1}(27,3) -> 6*
      h{#,1}(26,30) -> 3,5,6
      h{#,1}(25,51) -> 6*
      h{#,1}(1,30) -> 3,5
      h{#,1}(26,52) -> 3,5,6
      h{#,1}(27,33) -> 3,5,6
      h{#,1}(2,33) -> 3*
      h{#,1}(54,5) -> 3,5,6
      h{#,1}(19,1) -> 6,3
      h{#,1}(19,3) -> 6,3
      h{#,1}(8,30) -> 3,5,6
      h{#,1}(3,30) -> 3,5
      h{#,1}(25,2) -> 3*
      h{#,1}(25,4) -> 3*
      h{#,1}(59,33) -> 6*
      h{#,1}(54,33) -> 3,5,6
      h{#,1}(19,33) -> 6,3
      h{#,1}(4,33) -> 3*
      h{#,1}(80,30) -> 6*
      h{#,1}(26,1) -> 3,5,6
      h{#,1}(26,3) -> 3,5,6
      h{#,1}(25,30) -> 3,5,6
      h{#,1}(19,51) -> 3,5,6
      h{#,1}(5,30) -> 3,5,6
      h{#,1}(27,2) -> 6*
      h{#,1}(27,4) -> 6*
      h{#,1}(26,33) -> 3,5,6
      c1(5,52) -> 30*
      c1(1,33) -> 30*
      c1(18,1) -> 19*
      c1(18,3) -> 19*
      c1(3,1) -> 30*
      c1(3,3) -> 30*
      c1(32,30) -> 33*
      c1(53,19) -> 54*
      c1(2,30) -> 30*
      c1(1,51) -> 63*
      c1(53,25) -> 54*
      c1(18,19) -> 19*
      c1(24,2) -> 25*
      c1(24,4) -> 19*
      c1(4,2) -> 30*
      c1(18,25) -> 19*
      c1(1,63) -> 30*
      c1(4,4) -> 30*
      c1(24,8) -> 27*
      c1(18,27) -> 26*
      c1(32,52) -> 30*
      c1(53,39) -> 54*
      c1(2,52) -> 30*
      c1(3,33) -> 63*
      c1(18,39) -> 19*
      c1(24,26) -> 26*
      c1(5,5) -> 30*
      c1(4,30) -> 30*
      c1(3,51) -> 30*
      c1(53,67) -> 54*
      c1(1,2) -> 30*
      c1(3,63) -> 30*
      c1(18,67) -> 19*
      c1(1,4) -> 30*
      c1(24,54) -> 26*
      c1(4,52) -> 30*
      c1(5,33) -> 30*
      c1(24,62) -> 26*
      c1(32,5) -> 30*
      c1(2,1) -> 30*
      c1(24,66) -> 26*
      c1(2,3) -> 30*
      c1(1,30) -> 30*
      c1(5,51) -> 30*
      c1(24,80) -> 19*
      c1(18,2) -> 19*
      c1(18,4) -> 19*
      c1(3,2) -> 30*
      c1(5,63) -> 30*
      c1(3,4) -> 30*
      c1(18,8) -> 26*
      c1(32,33) -> 30*
      c1(1,52) -> 30*
      c1(2,33) -> 63*
      c1(53,26) -> 54*
      c1(24,1) -> 19*
      c1(24,3) -> 19*
      c1(4,1) -> 30*
      c1(4,3) -> 30*
      c1(18,26) -> 26*
      c1(32,51) -> 30*
      c1(3,30) -> 30*
      c1(2,51) -> 30*
      c1(24,19) -> 19*
      c1(32,63) -> 30*
      c1(24,25) -> 19*
      c1(24,27) -> 26*
      c1(2,63) -> 30*
      c1(18,54) -> 26*
      c1(3,52) -> 30*
      c1(53,62) -> 54*
      c1(4,33) -> 30*
      c1(24,39) -> 19*
      c1(53,66) -> 54*
      c1(18,62) -> 26*
      c1(1,1) -> 30*
      c1(18,66) -> 26*
      c1(1,3) -> 30*
      c1(5,30) -> 30*
      c1(4,51) -> 63*
      c1(18,80) -> 19*
      c1(2,2) -> 30*
      c1(4,63) -> 30*
      c1(24,67) -> 19*
      c1(2,4) -> 30*
      s1(5) -> 53*
      s1(2) -> 18*
      s1(4) -> 24*
      s1(31) -> 32*
      s1(1) -> 24*
      s1(3) -> 18*
      01() -> 31*
      h{#,2}(67,30) -> 3,5,6
      h{#,2}(62,30) -> 3,5,6
      h{#,2}(66,51) -> 3,5,6
      h{#,2}(66,63) -> 3,5,6
      h{#,2}(39,2) -> 6,3,5
      h{#,2}(39,4) -> 6,3,5
      h{#,2}(67,52) -> 3,5,6
      h{#,2}(62,52) -> 3,5,6
      h{#,2}(80,5) -> 3,5,6
      h{#,2}(65,5) -> 3,5,6
      h{#,2}(64,30) -> 3,5,6
      h{#,2}(35,5) -> 3,5,6
      h{#,2}(59,30) -> 3,5,6
      h{#,2}(39,30) -> 3,5,6
      h{#,2}(66,2) -> 6*
      h{#,2}(66,4) -> 6*
      h{#,2}(80,33) -> 3,5,6
      h{#,2}(64,52) -> 3,5,6
      h{#,2}(65,33) -> 3,5,6
      h{#,2}(59,52) -> 3,5,6
      h{#,2}(39,52) -> 3,5,6
      h{#,2}(35,33) -> 3,5,6
      h{#,2}(67,1) -> 6*
      h{#,2}(62,1) -> 3,5,6
      h{#,2}(67,3) -> 6*
      h{#,2}(62,3) -> 3,5,6
      h{#,2}(80,51) -> 3,5,6
      h{#,2}(66,30) -> 3,5,6
      h{#,2}(65,51) -> 3,5,6
      h{#,2}(35,51) -> 3,5,6
      h{#,2}(80,63) -> 3,5,6
      h{#,2}(65,63) -> 6,3,5
      h{#,2}(35,63) -> 3,5,6
      h{#,2}(66,52) -> 3,5,6
      h{#,2}(67,33) -> 6,3,5
      h{#,2}(62,33) -> 3,5,6
      h{#,2}(64,5) -> 3,5,6
      h{#,2}(59,5) -> 3,5,6
      h{#,2}(39,1) -> 6,3,5
      h{#,2}(39,3) -> 6,3,5
      h{#,2}(67,51) -> 3,5,6
      h{#,2}(62,51) -> 3,5,6
      h{#,2}(67,63) -> 3,5,6
      h{#,2}(62,63) -> 3,5,6
      h{#,2}(64,33) -> 3,5,6
      h{#,2}(59,33) -> 3,5,6
      h{#,2}(39,33) -> 3,5,6
      h{#,2}(66,1) -> 6*
      h{#,2}(66,3) -> 6*
      h{#,2}(80,30) -> 3,5,6
      h{#,2}(65,30) -> 3,5,6
      h{#,2}(64,51) -> 3,5,6
      h{#,2}(59,51) -> 3,5,6
      h{#,2}(35,30) -> 6,3,5
      h{#,2}(39,51) -> 3,5,6
      h{#,2}(67,2) -> 6*
      h{#,2}(62,2) -> 3,5,6
      h{#,2}(64,63) -> 3,5,6
      h{#,2}(67,4) -> 6*
      h{#,2}(59,63) -> 3,5,6
      h{#,2}(62,4) -> 3,5,6
      h{#,2}(39,63) -> 3,5,6
      h{#,2}(80,52) -> 3,5,6
      h{#,2}(65,52) -> 3,5,6
      h{#,2}(66,33) -> 3,5,6
      h{#,2}(35,52) -> 3,5,6
      h{#,0}(3,1) -> 3*
      h{#,0}(3,3) -> 3*
      h{#,0}(8,5) -> 6*
      h{#,0}(4,2) -> 3*
      h{#,0}(4,4) -> 3*
      h{#,0}(2,52) -> 6*
      h{#,0}(1,2) -> 3*
      h{#,0}(1,4) -> 3*
      h{#,0}(4,52) -> 6*
      h{#,0}(2,1) -> 3*
      h{#,0}(2,3) -> 3*
      h{#,0}(3,2) -> 3*
      h{#,0}(3,4) -> 3*
      h{#,0}(1,52) -> 6*
      h{#,0}(4,1) -> 3*
      h{#,0}(4,3) -> 3*
      h{#,0}(3,52) -> 6*
      h{#,0}(1,1) -> 3*
      h{#,0}(1,3) -> 3*
      h{#,0}(2,2) -> 3*
      h{#,0}(2,4) -> 3*
      c2(38,5) -> 62*
      c2(38,19) -> 62*
      c2(79,8) -> 80*
      c2(34,2) -> 35*
      c2(34,4) -> 35*
      c2(38,25) -> 62*
      c2(38,27) -> 62*
      c2(34,8) -> 59*
      c2(38,35) -> 39*
      c2(79,26) -> 80*
      c2(38,39) -> 39*
      c2(34,26) -> 59*
      c2(38,59) -> 62*
      c2(38,65) -> 67*
      c2(79,54) -> 80*
      c2(38,67) -> 35*
      c2(79,62) -> 80*
      c2(34,54) -> 35*
      c2(79,64) -> 80*
      c2(79,66) -> 35*
      c2(34,62) -> 59*
      c2(34,64) -> 35*
      c2(34,66) -> 59*
      c2(79,80) -> 35*
      c2(34,80) -> 35*
      c2(38,8) -> 39*
      c2(79,5) -> 80*
      c2(34,1) -> 35*
      c2(34,3) -> 35*
      c2(34,5) -> 59*
      c2(38,26) -> 62*
      c2(79,19) -> 80*
      c2(79,25) -> 80*
      c2(79,27) -> 80*
      c2(34,19) -> 35*
      c2(34,25) -> 35*
      c2(79,35) -> 80*
      c2(34,27) -> 59*
      c2(79,39) -> 80*
      c2(38,54) -> 62*
      c2(34,35) -> 65*
      c2(34,39) -> 59*
      c2(38,62) -> 62*
      c2(38,64) -> 66*
      c2(38,66) -> 39*
      c2(79,59) -> 80*
      c2(79,65) -> 80*
      c2(79,67) -> 35*
      c2(34,59) -> 64*
      c2(38,80) -> 35*
      c2(34,65) -> 35*
      c2(34,67) -> 35*
      c0(3,1) -> 2*
      c0(3,3) -> 2*
      c0(1,51) -> 52*
      c0(4,2) -> 2*
      c0(4,4) -> 2*
      c0(2,52) -> 51*
      c0(5,5) -> 51*
      c0(1,2) -> 2*
      c0(1,4) -> 2*
      c0(4,52) -> 51*
      c0(2,1) -> 2*
      c0(2,3) -> 2*
      c0(7,5) -> 8*
      c0(3,2) -> 2*
      c0(3,4) -> 2*
      c0(1,52) -> 51*
      c0(4,1) -> 2*
      c0(4,3) -> 2*
      c0(3,52) -> 51*
      c0(1,1) -> 2*
      c0(1,3) -> 2*
      c0(2,2) -> 2*
      c0(2,4) -> 2*
      s2(5) -> 79*
      s2(32) -> 34*
      s2(2) -> 38*
      s2(4) -> 38*
      s2(1) -> 38*
      s2(3) -> 38*
      s0(5) -> 7*
      s0(2) -> 1*
      s0(4) -> 1*
      s0(1) -> 1*
      s0(3) -> 1*
      1 -> 5*
      2 -> 5*
      3 -> 5*
      4 -> 5*
    problem:
     DPs:
      h#(c(s(x),c(s(0()),y)),z) -> h#(y,c(s(0()),c(x,z)))
     TRS:
      
    Restore Modifier:
     DPs:
      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)))
     Subterm Criterion Processor:
      simple projection:
       pi(h#) = 0
      problem:
       DPs:
        
       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)))
      Qed