YES(?,O(n^1))

Problem:
 f(x,f(s(s(y)),f(z,w))) -> f(s(x),f(y,f(s(z),w)))
 L(f(s(s(y)),f(z,w))) -> L(f(s(0()),f(y,f(s(z),w))))
 f(x,f(s(s(y)),nil())) -> f(s(x),f(y,f(s(0()),nil())))

Proof:
 Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {5,4}
   transitions:
    f0(3,1) -> 4*
    f0(3,3) -> 4*
    f0(1,2) -> 4*
    f0(2,1) -> 4*
    f0(2,3) -> 4*
    f0(3,2) -> 4*
    f0(1,1) -> 4*
    f0(1,3) -> 4*
    f0(2,2) -> 4*
    s0(2) -> 1*
    s0(1) -> 1*
    s0(3) -> 1*
    L0(2) -> 5*
    L0(1) -> 5*
    L0(3) -> 5*
    00() -> 2*
    nil0() -> 3*
  problem:
   
  Qed