YES(?,O(n^1))

Problem:
 +(*(x,y),*(x,z)) -> *(x,+(y,z))
 +(+(x,y),z) -> +(x,+(y,z))
 +(*(x,y),+(*(x,z),u())) -> +(*(x,+(y,z)),u())

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3}
   transitions:
    *0(1,2) -> 1*
    *0(2,1) -> 1*
    *0(1,1) -> 1*
    *0(2,2) -> 1*
    u0() -> 2*
    *1(2,3) -> 3*
    *1(1,3) -> 3*
    +1(1,2) -> 3*
    +1(2,1) -> 3*
    +1(1,1) -> 3*
    +1(2,2) -> 3*
  problem:
   
  Qed