Problem:
 active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
 active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
 active(plus(N,0())) -> mark(N)
 active(plus(N,s(M))) -> mark(U11(tt(),M,N))
 mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
 mark(tt()) -> active(tt())
 mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
 mark(s(X)) -> active(s(mark(X)))
 mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
 mark(0()) -> active(0())
 U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
 U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
 U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
 U11(active(X1),X2,X3) -> U11(X1,X2,X3)
 U11(X1,active(X2),X3) -> U11(X1,X2,X3)
 U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
 U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
 U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
 U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
 U12(active(X1),X2,X3) -> U12(X1,X2,X3)
 U12(X1,active(X2),X3) -> U12(X1,X2,X3)
 U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
 s(mark(X)) -> s(X)
 s(active(X)) -> s(X)
 plus(mark(X1),X2) -> plus(X1,X2)
 plus(X1,mark(X2)) -> plus(X1,X2)
 plus(active(X1),X2) -> plus(X1,X2)
 plus(X1,active(X2)) -> plus(X1,X2)

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {8,7,6,5,4,3}
   transitions:
    active1(10) -> 4*
    01() -> 10*
    tt1() -> 10*
    active0(2) -> 3*
    active0(1) -> 3*
    U110(1,1,1) -> 5*
    U110(2,2,1) -> 5*
    U110(1,1,2) -> 5*
    U110(2,2,2) -> 5*
    U110(1,2,1) -> 5*
    U110(2,1,1) -> 5*
    U110(1,2,2) -> 5*
    U110(2,1,2) -> 5*
    tt0() -> 1*
    mark0(2) -> 4*
    mark0(1) -> 4*
    U120(1,1,1) -> 6*
    U120(2,2,1) -> 6*
    U120(1,1,2) -> 6*
    U120(2,2,2) -> 6*
    U120(1,2,1) -> 6*
    U120(2,1,1) -> 6*
    U120(1,2,2) -> 6*
    U120(2,1,2) -> 6*
    s0(2) -> 7*
    s0(1) -> 7*
    plus0(1,2) -> 8*
    plus0(2,1) -> 8*
    plus0(1,1) -> 8*
    plus0(2,2) -> 8*
    00() -> 2*
  problem:
   
  Qed