YES(?,O(n^1))

Problem:
 f(0()) -> s(0())
 f(s(0())) -> s(s(0()))
 f(s(0())) -> *(s(s(0())),f(0()))
 f(+(x,s(0()))) -> +(s(s(0())),f(x))
 f(+(x,y)) -> *(f(x),f(y))

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {5,4,3,2,1}
   transitions:
    s3(20) -> 16*
    *1(1,9) -> 12,1
    *1(12,12) -> 12,1
    03() -> 20*
    f1(5) -> 12*
    f1(12) -> 12*
    f1(7) -> 9*
    f1(2) -> 12*
    f1(4) -> 12*
    f1(1) -> 12*
    f1(3) -> 12*
    *3(25,24) -> 25,23,24,18
    +1(1,12) -> 12,1
    f3(12) -> 25*
    f3(19) -> 24*
    s1(7) -> 12,1
    s1(1) -> 12,1
    01() -> 7*
    *2(12,16) -> 25,18,19,12
    *2(18,23) -> 12*
    *2(19,18) -> 25,18,19,12
    f0(5) -> 1*
    f0(2) -> 1*
    f0(4) -> 1*
    f0(1) -> 1*
    f0(3) -> 1*
    f2(12) -> 18*
    f2(19) -> 23*
    f2(14) -> 16*
    f2(1) -> 19*
    00() -> 2*
    s2(14) -> 9*
    s2(9) -> 25,18,19,12
    s0(5) -> 3*
    s0(2) -> 3*
    s0(4) -> 3*
    s0(1) -> 3*
    s0(3) -> 3*
    02() -> 14*
    *0(3,1) -> 4*
    *0(3,3) -> 4*
    *0(3,5) -> 4*
    *0(4,2) -> 4*
    *0(4,4) -> 4*
    *0(5,1) -> 4*
    *0(5,3) -> 4*
    *0(5,5) -> 4*
    *0(1,2) -> 4*
    *0(1,4) -> 4*
    *0(2,1) -> 4*
    *0(2,3) -> 4*
    *0(2,5) -> 4*
    *0(3,2) -> 4*
    *0(3,4) -> 4*
    *0(4,1) -> 4*
    *0(4,3) -> 4*
    *0(4,5) -> 4*
    *0(5,2) -> 4*
    *0(5,4) -> 4*
    *0(1,1) -> 4*
    *0(1,3) -> 4*
    *0(1,5) -> 4*
    *0(2,2) -> 4*
    *0(2,4) -> 4*
    +2(12,19) -> 25,18,12,19
    +0(3,1) -> 5*
    +0(3,3) -> 5*
    +0(3,5) -> 5*
    +0(4,2) -> 5*
    +0(4,4) -> 5*
    +0(5,1) -> 5*
    +0(5,3) -> 5*
    +0(5,5) -> 5*
    +0(1,2) -> 5*
    +0(1,4) -> 5*
    +0(2,1) -> 5*
    +0(2,3) -> 5*
    +0(2,5) -> 5*
    +0(3,2) -> 5*
    +0(3,4) -> 5*
    +0(4,1) -> 5*
    +0(4,3) -> 5*
    +0(4,5) -> 5*
    +0(5,2) -> 5*
    +0(5,4) -> 5*
    +0(1,1) -> 5*
    +0(1,3) -> 5*
    +0(1,5) -> 5*
    +0(2,2) -> 5*
    +0(2,4) -> 5*
  problem:
   
  Qed