YES(?,O(n^1))

Problem:
 f(a(),a()) -> f(a(),b())
 f(a(),b()) -> f(s(a()),c())
 f(s(X),c()) -> f(X,c())
 f(c(),c()) -> f(a(),a())

Proof:
 Bounds Processor:
  bound: 4
  enrichment: match
  automaton:
   final states: {5}
   transitions:
    c3() -> 18*
    s3(19) -> 20*
    a3() -> 19*
    f4(19,24) -> 5*
    c4() -> 24*
    f0(3,1) -> 5*
    f0(3,3) -> 5*
    f0(4,2) -> 5*
    f0(4,4) -> 5*
    f0(1,2) -> 5*
    f0(1,4) -> 5*
    f0(2,1) -> 5*
    f0(2,3) -> 5*
    f0(3,2) -> 5*
    f0(3,4) -> 5*
    f0(4,1) -> 5*
    f0(4,3) -> 5*
    f0(1,1) -> 5*
    f0(1,3) -> 5*
    f0(2,2) -> 5*
    f0(2,4) -> 5*
    a0() -> 1*
    b0() -> 2*
    s0(2) -> 3*
    s0(4) -> 3*
    s0(1) -> 3*
    s0(3) -> 3*
    c0() -> 4*
    f1(4,10) -> 5*
    f1(11,10) -> 5*
    f1(1,10) -> 5*
    f1(7,7) -> 5*
    f1(3,10) -> 5*
    f1(7,6) -> 5*
    f1(2,10) -> 5*
    a1() -> 7*
    c1() -> 10*
    s1(7) -> 11*
    b1() -> 6*
    f2(17,16) -> 5*
    f2(7,16) -> 5*
    f2(15,14) -> 5*
    c2() -> 16*
    s2(15) -> 17*
    a2() -> 15*
    b2() -> 14*
    f3(20,18) -> 5*
    f3(15,18) -> 5*
  problem:
   
  Qed