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: {6}
   transitions:
    c3() -> 15*
    s3(16) -> 17*
    a3() -> 16*
    f4(16,20) -> 6*
    c4() -> 20*
    f0(6,6) -> 6*
    a0() -> 6*
    b0() -> 6*
    s0(6) -> 6*
    c0() -> 6*
    f1(10,9) -> 6*
    f1(10,10) -> 6*
    f1(6,9) -> 6*
    a1() -> 10*
    c1() -> 9*
    s1(10) -> 10*
    b1() -> 9*
    f2(10,13) -> 6*
    f2(14,13) -> 6*
    c2() -> 13*
    s2(14) -> 14*
    a2() -> 14*
    b2() -> 13*
    f3(17,15) -> 6*
    f3(14,15) -> 6*
  problem:
   
  Qed