YES

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))
 active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
 active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
 active(s(X)) -> s(active(X))
 active(plus(X1,X2)) -> plus(active(X1),X2)
 active(plus(X1,X2)) -> plus(X1,active(X2))
 U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
 U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
 s(mark(X)) -> mark(s(X))
 plus(mark(X1),X2) -> mark(plus(X1,X2))
 plus(X1,mark(X2)) -> mark(plus(X1,X2))
 proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
 proper(tt()) -> ok(tt())
 proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
 proper(s(X)) -> s(proper(X))
 proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
 proper(0()) -> ok(0())
 U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
 U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
 s(ok(X)) -> ok(s(X))
 plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [top](x0) = x0,
   
   [ok](x0) = x0,
   
   [proper](x0) = x0,
   
   [0] = 4,
   
   [s](x0) = x0 + 2,
   
   [plus](x0, x1) = x0 + 4x1,
   
   [mark](x0) = x0,
   
   [U12](x0, x1, x2) = x0 + 4x1 + x2 + 2,
   
   [active](x0) = x0,
   
   [U11](x0, x1, x2) = x0 + 4x1 + x2 + 2,
   
   [tt] = 0
  orientation:
   active(U11(tt(),M,N)) = 4M + N + 2 >= 4M + N + 2 = mark(U12(tt(),M,N))
   
   active(U12(tt(),M,N)) = 4M + N + 2 >= 4M + N + 2 = mark(s(plus(N,M)))
   
   active(plus(N,0())) = N + 16 >= N = mark(N)
   
   active(plus(N,s(M))) = 4M + N + 8 >= 4M + N + 2 = mark(U11(tt(),M,N))
   
   active(U11(X1,X2,X3)) = X1 + 4X2 + X3 + 2 >= X1 + 4X2 + X3 + 2 = U11(active(X1),X2,X3)
   
   active(U12(X1,X2,X3)) = X1 + 4X2 + X3 + 2 >= X1 + 4X2 + X3 + 2 = U12(active(X1),X2,X3)
   
   active(s(X)) = X + 2 >= X + 2 = s(active(X))
   
   active(plus(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = plus(active(X1),X2)
   
   active(plus(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = plus(X1,active(X2))
   
   U11(mark(X1),X2,X3) = X1 + 4X2 + X3 + 2 >= X1 + 4X2 + X3 + 2 = mark(U11(X1,X2,X3))
   
   U12(mark(X1),X2,X3) = X1 + 4X2 + X3 + 2 >= X1 + 4X2 + X3 + 2 = mark(U12(X1,X2,X3))
   
   s(mark(X)) = X + 2 >= X + 2 = mark(s(X))
   
   plus(mark(X1),X2) = X1 + 4X2 >= X1 + 4X2 = mark(plus(X1,X2))
   
   plus(X1,mark(X2)) = X1 + 4X2 >= X1 + 4X2 = mark(plus(X1,X2))
   
   proper(U11(X1,X2,X3)) = X1 + 4X2 + X3 + 2 >= X1 + 4X2 + X3 + 2 = U11(proper(X1),proper(X2),proper(X3))
   
   proper(tt()) = 0 >= 0 = ok(tt())
   
   proper(U12(X1,X2,X3)) = X1 + 4X2 + X3 + 2 >= X1 + 4X2 + X3 + 2 = U12(proper(X1),proper(X2),proper(X3))
   
   proper(s(X)) = X + 2 >= X + 2 = s(proper(X))
   
   proper(plus(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = plus(proper(X1),proper(X2))
   
   proper(0()) = 4 >= 4 = ok(0())
   
   U11(ok(X1),ok(X2),ok(X3)) = X1 + 4X2 + X3 + 2 >= X1 + 4X2 + X3 + 2 = ok(U11(X1,X2,X3))
   
   U12(ok(X1),ok(X2),ok(X3)) = X1 + 4X2 + X3 + 2 >= X1 + 4X2 + X3 + 2 = ok(U12(X1,X2,X3))
   
   s(ok(X)) = X + 2 >= X + 2 = ok(s(X))
   
   plus(ok(X1),ok(X2)) = X1 + 4X2 >= X1 + 4X2 = ok(plus(X1,X2))
   
   top(mark(X)) = X >= X = top(proper(X))
   
   top(ok(X)) = X >= X = top(active(X))
  problem:
   active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
   active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
   active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
   active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
   active(s(X)) -> s(active(X))
   active(plus(X1,X2)) -> plus(active(X1),X2)
   active(plus(X1,X2)) -> plus(X1,active(X2))
   U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
   U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
   s(mark(X)) -> mark(s(X))
   plus(mark(X1),X2) -> mark(plus(X1,X2))
   plus(X1,mark(X2)) -> mark(plus(X1,X2))
   proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
   proper(tt()) -> ok(tt())
   proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
   proper(s(X)) -> s(proper(X))
   proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
   proper(0()) -> ok(0())
   U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
   U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
   s(ok(X)) -> ok(s(X))
   plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  DP Processor:
   DPs:
    active#(U11(tt(),M,N)) -> U12#(tt(),M,N)
    active#(U12(tt(),M,N)) -> plus#(N,M)
    active#(U12(tt(),M,N)) -> s#(plus(N,M))
    active#(U11(X1,X2,X3)) -> active#(X1)
    active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3)
    active#(U12(X1,X2,X3)) -> active#(X1)
    active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3)
    active#(s(X)) -> active#(X)
    active#(s(X)) -> s#(active(X))
    active#(plus(X1,X2)) -> active#(X1)
    active#(plus(X1,X2)) -> plus#(active(X1),X2)
    active#(plus(X1,X2)) -> active#(X2)
    active#(plus(X1,X2)) -> plus#(X1,active(X2))
    U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
    U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
    s#(mark(X)) -> s#(X)
    plus#(mark(X1),X2) -> plus#(X1,X2)
    plus#(X1,mark(X2)) -> plus#(X1,X2)
    proper#(U11(X1,X2,X3)) -> proper#(X3)
    proper#(U11(X1,X2,X3)) -> proper#(X2)
    proper#(U11(X1,X2,X3)) -> proper#(X1)
    proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
    proper#(U12(X1,X2,X3)) -> proper#(X3)
    proper#(U12(X1,X2,X3)) -> proper#(X2)
    proper#(U12(X1,X2,X3)) -> proper#(X1)
    proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
    proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X))
    proper#(plus(X1,X2)) -> proper#(X2)
    proper#(plus(X1,X2)) -> proper#(X1)
    proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
    U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3)
    U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3)
    s#(ok(X)) -> s#(X)
    plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
    active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
    active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
    active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
    active(s(X)) -> s(active(X))
    active(plus(X1,X2)) -> plus(active(X1),X2)
    active(plus(X1,X2)) -> plus(X1,active(X2))
    U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
    U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
    s(mark(X)) -> mark(s(X))
    plus(mark(X1),X2) -> mark(plus(X1,X2))
    plus(X1,mark(X2)) -> mark(plus(X1,X2))
    proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
    proper(tt()) -> ok(tt())
    proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
    proper(s(X)) -> s(proper(X))
    proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
    proper(0()) -> ok(0())
    U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
    U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
    s(ok(X)) -> ok(s(X))
    plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X))
   TDG Processor:
    DPs:
     active#(U11(tt(),M,N)) -> U12#(tt(),M,N)
     active#(U12(tt(),M,N)) -> plus#(N,M)
     active#(U12(tt(),M,N)) -> s#(plus(N,M))
     active#(U11(X1,X2,X3)) -> active#(X1)
     active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3)
     active#(U12(X1,X2,X3)) -> active#(X1)
     active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3)
     active#(s(X)) -> active#(X)
     active#(s(X)) -> s#(active(X))
     active#(plus(X1,X2)) -> active#(X1)
     active#(plus(X1,X2)) -> plus#(active(X1),X2)
     active#(plus(X1,X2)) -> active#(X2)
     active#(plus(X1,X2)) -> plus#(X1,active(X2))
     U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
     U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
     s#(mark(X)) -> s#(X)
     plus#(mark(X1),X2) -> plus#(X1,X2)
     plus#(X1,mark(X2)) -> plus#(X1,X2)
     proper#(U11(X1,X2,X3)) -> proper#(X3)
     proper#(U11(X1,X2,X3)) -> proper#(X2)
     proper#(U11(X1,X2,X3)) -> proper#(X1)
     proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
     proper#(U12(X1,X2,X3)) -> proper#(X3)
     proper#(U12(X1,X2,X3)) -> proper#(X2)
     proper#(U12(X1,X2,X3)) -> proper#(X1)
     proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
     proper#(s(X)) -> proper#(X)
     proper#(s(X)) -> s#(proper(X))
     proper#(plus(X1,X2)) -> proper#(X2)
     proper#(plus(X1,X2)) -> proper#(X1)
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
     U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3)
     U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3)
     s#(ok(X)) -> s#(X)
     plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
     top#(mark(X)) -> proper#(X)
     top#(mark(X)) -> top#(proper(X))
     top#(ok(X)) -> active#(X)
     top#(ok(X)) -> top#(active(X))
    TRS:
     active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
     active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
     active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
     active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
     active(s(X)) -> s(active(X))
     active(plus(X1,X2)) -> plus(active(X1),X2)
     active(plus(X1,X2)) -> plus(X1,active(X2))
     U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
     U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
     s(mark(X)) -> mark(s(X))
     plus(mark(X1),X2) -> mark(plus(X1,X2))
     plus(X1,mark(X2)) -> mark(plus(X1,X2))
     proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
     proper(tt()) -> ok(tt())
     proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
     proper(s(X)) -> s(proper(X))
     proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
     U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
     s(ok(X)) -> ok(s(X))
     plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    graph:
     top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X))
     top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X)
     top#(ok(X)) -> top#(active(X)) ->
     top#(mark(X)) -> top#(proper(X))
     top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X)
     top#(ok(X)) -> active#(X) ->
     active#(plus(X1,X2)) -> plus#(X1,active(X2))
     top#(ok(X)) -> active#(X) -> active#(plus(X1,X2)) -> active#(X2)
     top#(ok(X)) -> active#(X) ->
     active#(plus(X1,X2)) -> plus#(active(X1),X2)
     top#(ok(X)) -> active#(X) -> active#(plus(X1,X2)) -> active#(X1)
     top#(ok(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
     top#(ok(X)) -> active#(X) -> active#(s(X)) -> active#(X)
     top#(ok(X)) -> active#(X) ->
     active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3)
     top#(ok(X)) -> active#(X) -> active#(U12(X1,X2,X3)) -> active#(X1)
     top#(ok(X)) -> active#(X) ->
     active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3)
     top#(ok(X)) -> active#(X) -> active#(U11(X1,X2,X3)) -> active#(X1)
     top#(ok(X)) -> active#(X) -> active#(U12(tt(),M,N)) -> s#(plus(N,M))
     top#(ok(X)) -> active#(X) -> active#(U12(tt(),M,N)) -> plus#(N,M)
     top#(ok(X)) -> active#(X) ->
     active#(U11(tt(),M,N)) -> U12#(tt(),M,N)
     top#(mark(X)) -> top#(proper(X)) ->
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X)
     top#(mark(X)) -> top#(proper(X)) ->
     top#(mark(X)) -> top#(proper(X))
     top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X)
     top#(mark(X)) -> proper#(X) ->
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
     top#(mark(X)) -> proper#(X) -> proper#(plus(X1,X2)) -> proper#(X1)
     top#(mark(X)) -> proper#(X) -> proper#(plus(X1,X2)) -> proper#(X2)
     top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
     top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
     top#(mark(X)) -> proper#(X) ->
     proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
     top#(mark(X)) -> proper#(X) ->
     proper#(U12(X1,X2,X3)) -> proper#(X1)
     top#(mark(X)) -> proper#(X) ->
     proper#(U12(X1,X2,X3)) -> proper#(X2)
     top#(mark(X)) -> proper#(X) ->
     proper#(U12(X1,X2,X3)) -> proper#(X3)
     top#(mark(X)) -> proper#(X) ->
     proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
     top#(mark(X)) -> proper#(X) ->
     proper#(U11(X1,X2,X3)) -> proper#(X1)
     top#(mark(X)) -> proper#(X) ->
     proper#(U11(X1,X2,X3)) -> proper#(X2)
     top#(mark(X)) -> proper#(X) ->
     proper#(U11(X1,X2,X3)) -> proper#(X3)
     proper#(s(X)) -> proper#(X) ->
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
     proper#(s(X)) -> proper#(X) -> proper#(plus(X1,X2)) -> proper#(X1)
     proper#(s(X)) -> proper#(X) -> proper#(plus(X1,X2)) -> proper#(X2)
     proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
     proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
     proper#(s(X)) -> proper#(X) ->
     proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
     proper#(s(X)) -> proper#(X) ->
     proper#(U12(X1,X2,X3)) -> proper#(X1)
     proper#(s(X)) -> proper#(X) ->
     proper#(U12(X1,X2,X3)) -> proper#(X2)
     proper#(s(X)) -> proper#(X) ->
     proper#(U12(X1,X2,X3)) -> proper#(X3)
     proper#(s(X)) -> proper#(X) ->
     proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
     proper#(s(X)) -> proper#(X) ->
     proper#(U11(X1,X2,X3)) -> proper#(X1)
     proper#(s(X)) -> proper#(X) ->
     proper#(U11(X1,X2,X3)) -> proper#(X2)
     proper#(s(X)) -> proper#(X) ->
     proper#(U11(X1,X2,X3)) -> proper#(X3)
     proper#(s(X)) -> s#(proper(X)) -> s#(ok(X)) -> s#(X)
     proper#(s(X)) -> s#(proper(X)) -> s#(mark(X)) -> s#(X)
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(plus(X1,X2)) -> proper#(X1)
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(plus(X1,X2)) -> proper#(X2)
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(s(X)) -> proper#(X)
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(U12(X1,X2,X3)) -> proper#(X1)
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(U12(X1,X2,X3)) -> proper#(X2)
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(U12(X1,X2,X3)) -> proper#(X3)
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(U11(X1,X2,X3)) -> proper#(X1)
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(U11(X1,X2,X3)) -> proper#(X2)
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(U11(X1,X2,X3)) -> proper#(X3)
     proper#(plus(X1,X2)) -> proper#(X1) ->
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
     proper#(plus(X1,X2)) -> proper#(X1) ->
     proper#(plus(X1,X2)) -> proper#(X1)
     proper#(plus(X1,X2)) -> proper#(X1) ->
     proper#(plus(X1,X2)) -> proper#(X2)
     proper#(plus(X1,X2)) -> proper#(X1) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(plus(X1,X2)) -> proper#(X1) ->
     proper#(s(X)) -> proper#(X)
     proper#(plus(X1,X2)) -> proper#(X1) ->
     proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
     proper#(plus(X1,X2)) -> proper#(X1) ->
     proper#(U12(X1,X2,X3)) -> proper#(X1)
     proper#(plus(X1,X2)) -> proper#(X1) ->
     proper#(U12(X1,X2,X3)) -> proper#(X2)
     proper#(plus(X1,X2)) -> proper#(X1) ->
     proper#(U12(X1,X2,X3)) -> proper#(X3)
     proper#(plus(X1,X2)) -> proper#(X1) ->
     proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
     proper#(plus(X1,X2)) -> proper#(X1) ->
     proper#(U11(X1,X2,X3)) -> proper#(X1)
     proper#(plus(X1,X2)) -> proper#(X1) ->
     proper#(U11(X1,X2,X3)) -> proper#(X2)
     proper#(plus(X1,X2)) -> proper#(X1) ->
     proper#(U11(X1,X2,X3)) -> proper#(X3)
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) ->
     plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) ->
     plus#(X1,mark(X2)) -> plus#(X1,X2)
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) ->
     plus#(mark(X1),X2) -> plus#(X1,X2)
     proper#(U12(X1,X2,X3)) -> proper#(X3) ->
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
     proper#(U12(X1,X2,X3)) -> proper#(X3) ->
     proper#(plus(X1,X2)) -> proper#(X1)
     proper#(U12(X1,X2,X3)) -> proper#(X3) ->
     proper#(plus(X1,X2)) -> proper#(X2)
     proper#(U12(X1,X2,X3)) -> proper#(X3) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(U12(X1,X2,X3)) -> proper#(X3) ->
     proper#(s(X)) -> proper#(X)
     proper#(U12(X1,X2,X3)) -> proper#(X3) ->
     proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
     proper#(U12(X1,X2,X3)) -> proper#(X3) ->
     proper#(U12(X1,X2,X3)) -> proper#(X1)
     proper#(U12(X1,X2,X3)) -> proper#(X3) ->
     proper#(U12(X1,X2,X3)) -> proper#(X2)
     proper#(U12(X1,X2,X3)) -> proper#(X3) ->
     proper#(U12(X1,X2,X3)) -> proper#(X3)
     proper#(U12(X1,X2,X3)) -> proper#(X3) ->
     proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
     proper#(U12(X1,X2,X3)) -> proper#(X3) ->
     proper#(U11(X1,X2,X3)) -> proper#(X1)
     proper#(U12(X1,X2,X3)) -> proper#(X3) ->
     proper#(U11(X1,X2,X3)) -> proper#(X2)
     proper#(U12(X1,X2,X3)) -> proper#(X3) ->
     proper#(U11(X1,X2,X3)) -> proper#(X3)
     proper#(U12(X1,X2,X3)) -> proper#(X2) ->
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
     proper#(U12(X1,X2,X3)) -> proper#(X2) ->
     proper#(plus(X1,X2)) -> proper#(X1)
     proper#(U12(X1,X2,X3)) -> proper#(X2) ->
     proper#(plus(X1,X2)) -> proper#(X2)
     proper#(U12(X1,X2,X3)) -> proper#(X2) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(U12(X1,X2,X3)) -> proper#(X2) ->
     proper#(s(X)) -> proper#(X)
     proper#(U12(X1,X2,X3)) -> proper#(X2) ->
     proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
     proper#(U12(X1,X2,X3)) -> proper#(X2) ->
     proper#(U12(X1,X2,X3)) -> proper#(X1)
     proper#(U12(X1,X2,X3)) -> proper#(X2) ->
     proper#(U12(X1,X2,X3)) -> proper#(X2)
     proper#(U12(X1,X2,X3)) -> proper#(X2) ->
     proper#(U12(X1,X2,X3)) -> proper#(X3)
     proper#(U12(X1,X2,X3)) -> proper#(X2) ->
     proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
     proper#(U12(X1,X2,X3)) -> proper#(X2) ->
     proper#(U11(X1,X2,X3)) -> proper#(X1)
     proper#(U12(X1,X2,X3)) -> proper#(X2) ->
     proper#(U11(X1,X2,X3)) -> proper#(X2)
     proper#(U12(X1,X2,X3)) -> proper#(X2) ->
     proper#(U11(X1,X2,X3)) -> proper#(X3)
     proper#(U12(X1,X2,X3)) -> proper#(X1) ->
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
     proper#(U12(X1,X2,X3)) -> proper#(X1) ->
     proper#(plus(X1,X2)) -> proper#(X1)
     proper#(U12(X1,X2,X3)) -> proper#(X1) ->
     proper#(plus(X1,X2)) -> proper#(X2)
     proper#(U12(X1,X2,X3)) -> proper#(X1) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(U12(X1,X2,X3)) -> proper#(X1) ->
     proper#(s(X)) -> proper#(X)
     proper#(U12(X1,X2,X3)) -> proper#(X1) ->
     proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
     proper#(U12(X1,X2,X3)) -> proper#(X1) ->
     proper#(U12(X1,X2,X3)) -> proper#(X1)
     proper#(U12(X1,X2,X3)) -> proper#(X1) ->
     proper#(U12(X1,X2,X3)) -> proper#(X2)
     proper#(U12(X1,X2,X3)) -> proper#(X1) ->
     proper#(U12(X1,X2,X3)) -> proper#(X3)
     proper#(U12(X1,X2,X3)) -> proper#(X1) ->
     proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
     proper#(U12(X1,X2,X3)) -> proper#(X1) ->
     proper#(U11(X1,X2,X3)) -> proper#(X1)
     proper#(U12(X1,X2,X3)) -> proper#(X1) ->
     proper#(U11(X1,X2,X3)) -> proper#(X2)
     proper#(U12(X1,X2,X3)) -> proper#(X1) ->
     proper#(U11(X1,X2,X3)) -> proper#(X3)
     proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) ->
     U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3)
     proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) ->
     U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
     proper#(U11(X1,X2,X3)) -> proper#(X3) ->
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
     proper#(U11(X1,X2,X3)) -> proper#(X3) ->
     proper#(plus(X1,X2)) -> proper#(X1)
     proper#(U11(X1,X2,X3)) -> proper#(X3) ->
     proper#(plus(X1,X2)) -> proper#(X2)
     proper#(U11(X1,X2,X3)) -> proper#(X3) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(U11(X1,X2,X3)) -> proper#(X3) ->
     proper#(s(X)) -> proper#(X)
     proper#(U11(X1,X2,X3)) -> proper#(X3) ->
     proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
     proper#(U11(X1,X2,X3)) -> proper#(X3) ->
     proper#(U12(X1,X2,X3)) -> proper#(X1)
     proper#(U11(X1,X2,X3)) -> proper#(X3) ->
     proper#(U12(X1,X2,X3)) -> proper#(X2)
     proper#(U11(X1,X2,X3)) -> proper#(X3) ->
     proper#(U12(X1,X2,X3)) -> proper#(X3)
     proper#(U11(X1,X2,X3)) -> proper#(X3) ->
     proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
     proper#(U11(X1,X2,X3)) -> proper#(X3) ->
     proper#(U11(X1,X2,X3)) -> proper#(X1)
     proper#(U11(X1,X2,X3)) -> proper#(X3) ->
     proper#(U11(X1,X2,X3)) -> proper#(X2)
     proper#(U11(X1,X2,X3)) -> proper#(X3) ->
     proper#(U11(X1,X2,X3)) -> proper#(X3)
     proper#(U11(X1,X2,X3)) -> proper#(X2) ->
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
     proper#(U11(X1,X2,X3)) -> proper#(X2) ->
     proper#(plus(X1,X2)) -> proper#(X1)
     proper#(U11(X1,X2,X3)) -> proper#(X2) ->
     proper#(plus(X1,X2)) -> proper#(X2)
     proper#(U11(X1,X2,X3)) -> proper#(X2) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(U11(X1,X2,X3)) -> proper#(X2) ->
     proper#(s(X)) -> proper#(X)
     proper#(U11(X1,X2,X3)) -> proper#(X2) ->
     proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
     proper#(U11(X1,X2,X3)) -> proper#(X2) ->
     proper#(U12(X1,X2,X3)) -> proper#(X1)
     proper#(U11(X1,X2,X3)) -> proper#(X2) ->
     proper#(U12(X1,X2,X3)) -> proper#(X2)
     proper#(U11(X1,X2,X3)) -> proper#(X2) ->
     proper#(U12(X1,X2,X3)) -> proper#(X3)
     proper#(U11(X1,X2,X3)) -> proper#(X2) ->
     proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
     proper#(U11(X1,X2,X3)) -> proper#(X2) ->
     proper#(U11(X1,X2,X3)) -> proper#(X1)
     proper#(U11(X1,X2,X3)) -> proper#(X2) ->
     proper#(U11(X1,X2,X3)) -> proper#(X2)
     proper#(U11(X1,X2,X3)) -> proper#(X2) ->
     proper#(U11(X1,X2,X3)) -> proper#(X3)
     proper#(U11(X1,X2,X3)) -> proper#(X1) ->
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
     proper#(U11(X1,X2,X3)) -> proper#(X1) ->
     proper#(plus(X1,X2)) -> proper#(X1)
     proper#(U11(X1,X2,X3)) -> proper#(X1) ->
     proper#(plus(X1,X2)) -> proper#(X2)
     proper#(U11(X1,X2,X3)) -> proper#(X1) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(U11(X1,X2,X3)) -> proper#(X1) ->
     proper#(s(X)) -> proper#(X)
     proper#(U11(X1,X2,X3)) -> proper#(X1) ->
     proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
     proper#(U11(X1,X2,X3)) -> proper#(X1) ->
     proper#(U12(X1,X2,X3)) -> proper#(X1)
     proper#(U11(X1,X2,X3)) -> proper#(X1) ->
     proper#(U12(X1,X2,X3)) -> proper#(X2)
     proper#(U11(X1,X2,X3)) -> proper#(X1) ->
     proper#(U12(X1,X2,X3)) -> proper#(X3)
     proper#(U11(X1,X2,X3)) -> proper#(X1) ->
     proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
     proper#(U11(X1,X2,X3)) -> proper#(X1) ->
     proper#(U11(X1,X2,X3)) -> proper#(X1)
     proper#(U11(X1,X2,X3)) -> proper#(X1) ->
     proper#(U11(X1,X2,X3)) -> proper#(X2)
     proper#(U11(X1,X2,X3)) -> proper#(X1) ->
     proper#(U11(X1,X2,X3)) -> proper#(X3)
     proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) ->
     U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3)
     proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) ->
     U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
     U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3) ->
     U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3)
     U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3) ->
     U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
     U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) ->
     U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3)
     U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) ->
     U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
     s#(ok(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
     s#(ok(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
     s#(mark(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
     s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
     plus#(ok(X1),ok(X2)) -> plus#(X1,X2) ->
     plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
     plus#(ok(X1),ok(X2)) -> plus#(X1,X2) ->
     plus#(X1,mark(X2)) -> plus#(X1,X2)
     plus#(ok(X1),ok(X2)) -> plus#(X1,X2) ->
     plus#(mark(X1),X2) -> plus#(X1,X2)
     plus#(mark(X1),X2) -> plus#(X1,X2) ->
     plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
     plus#(mark(X1),X2) -> plus#(X1,X2) ->
     plus#(X1,mark(X2)) -> plus#(X1,X2)
     plus#(mark(X1),X2) -> plus#(X1,X2) ->
     plus#(mark(X1),X2) -> plus#(X1,X2)
     plus#(X1,mark(X2)) -> plus#(X1,X2) ->
     plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
     plus#(X1,mark(X2)) -> plus#(X1,X2) ->
     plus#(X1,mark(X2)) -> plus#(X1,X2)
     plus#(X1,mark(X2)) -> plus#(X1,X2) ->
     plus#(mark(X1),X2) -> plus#(X1,X2)
     U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3) ->
     U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3)
     U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3) ->
     U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
     U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) ->
     U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3)
     U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) ->
     U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
     active#(s(X)) -> s#(active(X)) -> s#(ok(X)) -> s#(X)
     active#(s(X)) -> s#(active(X)) -> s#(mark(X)) -> s#(X)
     active#(s(X)) -> active#(X) ->
     active#(plus(X1,X2)) -> plus#(X1,active(X2))
     active#(s(X)) -> active#(X) -> active#(plus(X1,X2)) -> active#(X2)
     active#(s(X)) -> active#(X) ->
     active#(plus(X1,X2)) -> plus#(active(X1),X2)
     active#(s(X)) -> active#(X) -> active#(plus(X1,X2)) -> active#(X1)
     active#(s(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
     active#(s(X)) -> active#(X) -> active#(s(X)) -> active#(X)
     active#(s(X)) -> active#(X) ->
     active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3)
     active#(s(X)) -> active#(X) ->
     active#(U12(X1,X2,X3)) -> active#(X1)
     active#(s(X)) -> active#(X) ->
     active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3)
     active#(s(X)) -> active#(X) ->
     active#(U11(X1,X2,X3)) -> active#(X1)
     active#(s(X)) -> active#(X) ->
     active#(U12(tt(),M,N)) -> s#(plus(N,M))
     active#(s(X)) -> active#(X) -> active#(U12(tt(),M,N)) -> plus#(N,M)
     active#(s(X)) -> active#(X) ->
     active#(U11(tt(),M,N)) -> U12#(tt(),M,N)
     active#(plus(X1,X2)) -> plus#(active(X1),X2) ->
     plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
     active#(plus(X1,X2)) -> plus#(active(X1),X2) ->
     plus#(X1,mark(X2)) -> plus#(X1,X2)
     active#(plus(X1,X2)) -> plus#(active(X1),X2) ->
     plus#(mark(X1),X2) -> plus#(X1,X2)
     active#(plus(X1,X2)) -> plus#(X1,active(X2)) ->
     plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
     active#(plus(X1,X2)) -> plus#(X1,active(X2)) ->
     plus#(X1,mark(X2)) -> plus#(X1,X2)
     active#(plus(X1,X2)) -> plus#(X1,active(X2)) ->
     plus#(mark(X1),X2) -> plus#(X1,X2)
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(plus(X1,X2)) -> plus#(X1,active(X2))
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(plus(X1,X2)) -> active#(X2)
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(plus(X1,X2)) -> plus#(active(X1),X2)
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(plus(X1,X2)) -> active#(X1)
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(s(X)) -> s#(active(X))
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(s(X)) -> active#(X)
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3)
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(U12(X1,X2,X3)) -> active#(X1)
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3)
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(U11(X1,X2,X3)) -> active#(X1)
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(U12(tt(),M,N)) -> s#(plus(N,M))
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(U12(tt(),M,N)) -> plus#(N,M)
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(U11(tt(),M,N)) -> U12#(tt(),M,N)
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(plus(X1,X2)) -> plus#(X1,active(X2))
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(plus(X1,X2)) -> active#(X2)
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(plus(X1,X2)) -> plus#(active(X1),X2)
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(plus(X1,X2)) -> active#(X1)
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(s(X)) -> s#(active(X))
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(s(X)) -> active#(X)
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3)
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(U12(X1,X2,X3)) -> active#(X1)
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3)
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(U11(X1,X2,X3)) -> active#(X1)
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(U12(tt(),M,N)) -> s#(plus(N,M))
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(U12(tt(),M,N)) -> plus#(N,M)
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(U11(tt(),M,N)) -> U12#(tt(),M,N)
     active#(U12(tt(),M,N)) -> s#(plus(N,M)) ->
     s#(ok(X)) -> s#(X)
     active#(U12(tt(),M,N)) -> s#(plus(N,M)) ->
     s#(mark(X)) -> s#(X)
     active#(U12(tt(),M,N)) -> plus#(N,M) ->
     plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
     active#(U12(tt(),M,N)) -> plus#(N,M) ->
     plus#(X1,mark(X2)) -> plus#(X1,X2)
     active#(U12(tt(),M,N)) -> plus#(N,M) ->
     plus#(mark(X1),X2) -> plus#(X1,X2)
     active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) ->
     U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3)
     active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) ->
     U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
     active#(U12(X1,X2,X3)) -> active#(X1) ->
     active#(plus(X1,X2)) -> plus#(X1,active(X2))
     active#(U12(X1,X2,X3)) -> active#(X1) ->
     active#(plus(X1,X2)) -> active#(X2)
     active#(U12(X1,X2,X3)) -> active#(X1) ->
     active#(plus(X1,X2)) -> plus#(active(X1),X2)
     active#(U12(X1,X2,X3)) -> active#(X1) ->
     active#(plus(X1,X2)) -> active#(X1)
     active#(U12(X1,X2,X3)) -> active#(X1) ->
     active#(s(X)) -> s#(active(X))
     active#(U12(X1,X2,X3)) -> active#(X1) ->
     active#(s(X)) -> active#(X)
     active#(U12(X1,X2,X3)) -> active#(X1) ->
     active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3)
     active#(U12(X1,X2,X3)) -> active#(X1) ->
     active#(U12(X1,X2,X3)) -> active#(X1)
     active#(U12(X1,X2,X3)) -> active#(X1) ->
     active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3)
     active#(U12(X1,X2,X3)) -> active#(X1) ->
     active#(U11(X1,X2,X3)) -> active#(X1)
     active#(U12(X1,X2,X3)) -> active#(X1) ->
     active#(U12(tt(),M,N)) -> s#(plus(N,M))
     active#(U12(X1,X2,X3)) -> active#(X1) ->
     active#(U12(tt(),M,N)) -> plus#(N,M)
     active#(U12(X1,X2,X3)) -> active#(X1) ->
     active#(U11(tt(),M,N)) -> U12#(tt(),M,N)
     active#(U11(tt(),M,N)) -> U12#(tt(),M,N) ->
     U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3)
     active#(U11(tt(),M,N)) -> U12#(tt(),M,N) ->
     U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
     active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) ->
     U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3)
     active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) ->
     U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
     active#(U11(X1,X2,X3)) -> active#(X1) ->
     active#(plus(X1,X2)) -> plus#(X1,active(X2))
     active#(U11(X1,X2,X3)) -> active#(X1) ->
     active#(plus(X1,X2)) -> active#(X2)
     active#(U11(X1,X2,X3)) -> active#(X1) ->
     active#(plus(X1,X2)) -> plus#(active(X1),X2)
     active#(U11(X1,X2,X3)) -> active#(X1) ->
     active#(plus(X1,X2)) -> active#(X1)
     active#(U11(X1,X2,X3)) -> active#(X1) ->
     active#(s(X)) -> s#(active(X))
     active#(U11(X1,X2,X3)) -> active#(X1) ->
     active#(s(X)) -> active#(X)
     active#(U11(X1,X2,X3)) -> active#(X1) ->
     active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3)
     active#(U11(X1,X2,X3)) -> active#(X1) ->
     active#(U12(X1,X2,X3)) -> active#(X1)
     active#(U11(X1,X2,X3)) -> active#(X1) ->
     active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3)
     active#(U11(X1,X2,X3)) -> active#(X1) ->
     active#(U11(X1,X2,X3)) -> active#(X1)
     active#(U11(X1,X2,X3)) -> active#(X1) ->
     active#(U12(tt(),M,N)) -> s#(plus(N,M))
     active#(U11(X1,X2,X3)) -> active#(X1) ->
     active#(U12(tt(),M,N)) -> plus#(N,M)
     active#(U11(X1,X2,X3)) -> active#(X1) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,N)
    SCC Processor:
     #sccs: 7
     #rules: 25
     #arcs: 265/1521
     DPs:
      top#(ok(X)) -> top#(active(X))
      top#(mark(X)) -> top#(proper(X))
     TRS:
      active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
      active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
      active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
      active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
      active(s(X)) -> s(active(X))
      active(plus(X1,X2)) -> plus(active(X1),X2)
      active(plus(X1,X2)) -> plus(X1,active(X2))
      U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
      U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
      s(mark(X)) -> mark(s(X))
      plus(mark(X1),X2) -> mark(plus(X1,X2))
      plus(X1,mark(X2)) -> mark(plus(X1,X2))
      proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
      proper(s(X)) -> s(proper(X))
      proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
      U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
      s(ok(X)) -> ok(s(X))
      plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     KBO Processor:
      argument filtering:
       pi(tt) = []
       pi(U11) = [0,1,2]
       pi(active) = 0
       pi(U12) = [0,1,2]
       pi(mark) = [0]
       pi(plus) = [0,1]
       pi(s) = 0
       pi(0) = []
       pi(proper) = 0
       pi(ok) = 0
       pi(top) = []
       pi(top#) = 0
      weight function:
       w0 = 1
       w(top#) = w(top) = w(0) = w(mark) = w(U11) = w(tt) = 1
       w(ok) = w(proper) = w(s) = w(plus) = w(U12) = w(active) = 0
      precedence:
       top ~ plus ~ U12 ~ U11 > top# ~ ok ~ proper ~ 0 ~ s ~ mark ~ active ~ tt
      problem:
       DPs:
        top#(ok(X)) -> top#(active(X))
       TRS:
        active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
        active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
        active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
        active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
        active(s(X)) -> s(active(X))
        active(plus(X1,X2)) -> plus(active(X1),X2)
        active(plus(X1,X2)) -> plus(X1,active(X2))
        U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
        U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
        s(mark(X)) -> mark(s(X))
        plus(mark(X1),X2) -> mark(plus(X1,X2))
        plus(X1,mark(X2)) -> mark(plus(X1,X2))
        proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
        proper(tt()) -> ok(tt())
        proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
        proper(s(X)) -> s(proper(X))
        proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
        proper(0()) -> ok(0())
        U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
        U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
        s(ok(X)) -> ok(s(X))
        plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Arctic Interpretation Processor:
       dimension: 1
       interpretation:
        [top#](x0) = x0,
        
        [top](x0) = 0,
        
        [ok](x0) = 1x0,
        
        [proper](x0) = 1x0 + 0,
        
        [0] = 6,
        
        [s](x0) = x0,
        
        [plus](x0, x1) = x1,
        
        [mark](x0) = x0,
        
        [U12](x0, x1, x2) = x0 + x1,
        
        [active](x0) = x0,
        
        [U11](x0, x1, x2) = x0 + x1 + x2,
        
        [tt] = 0
       orientation:
        top#(ok(X)) = 1X >= X = top#(active(X))
        
        active(U11(tt(),M,N)) = M + N + 0 >= M + 0 = mark(U12(tt(),M,N))
        
        active(U12(tt(),M,N)) = M + 0 >= M = mark(s(plus(N,M)))
        
        active(U11(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U11(active(X1),X2,X3)
        
        active(U12(X1,X2,X3)) = X1 + X2 >= X1 + X2 = U12(active(X1),X2,X3)
        
        active(s(X)) = X >= X = s(active(X))
        
        active(plus(X1,X2)) = X2 >= X2 = plus(active(X1),X2)
        
        active(plus(X1,X2)) = X2 >= X2 = plus(X1,active(X2))
        
        U11(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = mark(U11(X1,X2,X3))
        
        U12(mark(X1),X2,X3) = X1 + X2 >= X1 + X2 = mark(U12(X1,X2,X3))
        
        s(mark(X)) = X >= X = mark(s(X))
        
        plus(mark(X1),X2) = X2 >= X2 = mark(plus(X1,X2))
        
        plus(X1,mark(X2)) = X2 >= X2 = mark(plus(X1,X2))
        
        proper(U11(X1,X2,X3)) = 1X1 + 1X2 + 1X3 + 0 >= 1X1 + 1X2 + 1X3 + 0 = U11(proper(X1),proper(X2),proper(X3))
        
        proper(tt()) = 1 >= 1 = ok(tt())
        
        proper(U12(X1,X2,X3)) = 1X1 + 1X2 + 0 >= 1X1 + 1X2 + 0 = U12(proper(X1),proper(X2),proper(X3))
        
        proper(s(X)) = 1X + 0 >= 1X + 0 = s(proper(X))
        
        proper(plus(X1,X2)) = 1X2 + 0 >= 1X2 + 0 = plus(proper(X1),proper(X2))
        
        proper(0()) = 7 >= 7 = ok(0())
        
        U11(ok(X1),ok(X2),ok(X3)) = 1X1 + 1X2 + 1X3 >= 1X1 + 1X2 + 1X3 = ok(U11(X1,X2,X3))
        
        U12(ok(X1),ok(X2),ok(X3)) = 1X1 + 1X2 >= 1X1 + 1X2 = ok(U12(X1,X2,X3))
        
        s(ok(X)) = 1X >= 1X = ok(s(X))
        
        plus(ok(X1),ok(X2)) = 1X2 >= 1X2 = ok(plus(X1,X2))
        
        top(mark(X)) = 0 >= 0 = top(proper(X))
        
        top(ok(X)) = 0 >= 0 = top(active(X))
       problem:
        DPs:
         
        TRS:
         active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
         active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
         active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
         active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
         active(s(X)) -> s(active(X))
         active(plus(X1,X2)) -> plus(active(X1),X2)
         active(plus(X1,X2)) -> plus(X1,active(X2))
         U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
         U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
         s(mark(X)) -> mark(s(X))
         plus(mark(X1),X2) -> mark(plus(X1,X2))
         plus(X1,mark(X2)) -> mark(plus(X1,X2))
         proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
         proper(tt()) -> ok(tt())
         proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
         proper(s(X)) -> s(proper(X))
         proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
         proper(0()) -> ok(0())
         U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
         U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
         s(ok(X)) -> ok(s(X))
         plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
         top(mark(X)) -> top(proper(X))
         top(ok(X)) -> top(active(X))
       Qed
     
     DPs:
      active#(U11(X1,X2,X3)) -> active#(X1)
      active#(U12(X1,X2,X3)) -> active#(X1)
      active#(s(X)) -> active#(X)
      active#(plus(X1,X2)) -> active#(X1)
      active#(plus(X1,X2)) -> active#(X2)
     TRS:
      active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
      active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
      active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
      active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
      active(s(X)) -> s(active(X))
      active(plus(X1,X2)) -> plus(active(X1),X2)
      active(plus(X1,X2)) -> plus(X1,active(X2))
      U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
      U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
      s(mark(X)) -> mark(s(X))
      plus(mark(X1),X2) -> mark(plus(X1,X2))
      plus(X1,mark(X2)) -> mark(plus(X1,X2))
      proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
      proper(s(X)) -> s(proper(X))
      proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
      U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
      s(ok(X)) -> ok(s(X))
      plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(active#) = 0
      problem:
       DPs:
        
       TRS:
        active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
        active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
        active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
        active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
        active(s(X)) -> s(active(X))
        active(plus(X1,X2)) -> plus(active(X1),X2)
        active(plus(X1,X2)) -> plus(X1,active(X2))
        U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
        U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
        s(mark(X)) -> mark(s(X))
        plus(mark(X1),X2) -> mark(plus(X1,X2))
        plus(X1,mark(X2)) -> mark(plus(X1,X2))
        proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
        proper(tt()) -> ok(tt())
        proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
        proper(s(X)) -> s(proper(X))
        proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
        proper(0()) -> ok(0())
        U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
        U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
        s(ok(X)) -> ok(s(X))
        plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
     
     DPs:
      proper#(U11(X1,X2,X3)) -> proper#(X3)
      proper#(U11(X1,X2,X3)) -> proper#(X2)
      proper#(U11(X1,X2,X3)) -> proper#(X1)
      proper#(U12(X1,X2,X3)) -> proper#(X3)
      proper#(U12(X1,X2,X3)) -> proper#(X2)
      proper#(U12(X1,X2,X3)) -> proper#(X1)
      proper#(s(X)) -> proper#(X)
      proper#(plus(X1,X2)) -> proper#(X2)
      proper#(plus(X1,X2)) -> proper#(X1)
     TRS:
      active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
      active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
      active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
      active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
      active(s(X)) -> s(active(X))
      active(plus(X1,X2)) -> plus(active(X1),X2)
      active(plus(X1,X2)) -> plus(X1,active(X2))
      U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
      U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
      s(mark(X)) -> mark(s(X))
      plus(mark(X1),X2) -> mark(plus(X1,X2))
      plus(X1,mark(X2)) -> mark(plus(X1,X2))
      proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
      proper(s(X)) -> s(proper(X))
      proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
      U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
      s(ok(X)) -> ok(s(X))
      plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(proper#) = 0
      problem:
       DPs:
        
       TRS:
        active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
        active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
        active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
        active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
        active(s(X)) -> s(active(X))
        active(plus(X1,X2)) -> plus(active(X1),X2)
        active(plus(X1,X2)) -> plus(X1,active(X2))
        U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
        U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
        s(mark(X)) -> mark(s(X))
        plus(mark(X1),X2) -> mark(plus(X1,X2))
        plus(X1,mark(X2)) -> mark(plus(X1,X2))
        proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
        proper(tt()) -> ok(tt())
        proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
        proper(s(X)) -> s(proper(X))
        proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
        proper(0()) -> ok(0())
        U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
        U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
        s(ok(X)) -> ok(s(X))
        plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
     
     DPs:
      plus#(mark(X1),X2) -> plus#(X1,X2)
      plus#(X1,mark(X2)) -> plus#(X1,X2)
      plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
     TRS:
      active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
      active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
      active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
      active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
      active(s(X)) -> s(active(X))
      active(plus(X1,X2)) -> plus(active(X1),X2)
      active(plus(X1,X2)) -> plus(X1,active(X2))
      U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
      U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
      s(mark(X)) -> mark(s(X))
      plus(mark(X1),X2) -> mark(plus(X1,X2))
      plus(X1,mark(X2)) -> mark(plus(X1,X2))
      proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
      proper(s(X)) -> s(proper(X))
      proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
      U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
      s(ok(X)) -> ok(s(X))
      plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(plus#) = 1
      problem:
       DPs:
        plus#(mark(X1),X2) -> plus#(X1,X2)
       TRS:
        active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
        active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
        active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
        active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
        active(s(X)) -> s(active(X))
        active(plus(X1,X2)) -> plus(active(X1),X2)
        active(plus(X1,X2)) -> plus(X1,active(X2))
        U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
        U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
        s(mark(X)) -> mark(s(X))
        plus(mark(X1),X2) -> mark(plus(X1,X2))
        plus(X1,mark(X2)) -> mark(plus(X1,X2))
        proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
        proper(tt()) -> ok(tt())
        proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
        proper(s(X)) -> s(proper(X))
        proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
        proper(0()) -> ok(0())
        U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
        U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
        s(ok(X)) -> ok(s(X))
        plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Subterm Criterion Processor:
       simple projection:
        pi(plus#) = 0
       problem:
        DPs:
         
        TRS:
         active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
         active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
         active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
         active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
         active(s(X)) -> s(active(X))
         active(plus(X1,X2)) -> plus(active(X1),X2)
         active(plus(X1,X2)) -> plus(X1,active(X2))
         U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
         U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
         s(mark(X)) -> mark(s(X))
         plus(mark(X1),X2) -> mark(plus(X1,X2))
         plus(X1,mark(X2)) -> mark(plus(X1,X2))
         proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
         proper(tt()) -> ok(tt())
         proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
         proper(s(X)) -> s(proper(X))
         proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
         proper(0()) -> ok(0())
         U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
         U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
         s(ok(X)) -> ok(s(X))
         plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
         top(mark(X)) -> top(proper(X))
         top(ok(X)) -> top(active(X))
       Qed
     
     DPs:
      s#(mark(X)) -> s#(X)
      s#(ok(X)) -> s#(X)
     TRS:
      active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
      active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
      active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
      active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
      active(s(X)) -> s(active(X))
      active(plus(X1,X2)) -> plus(active(X1),X2)
      active(plus(X1,X2)) -> plus(X1,active(X2))
      U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
      U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
      s(mark(X)) -> mark(s(X))
      plus(mark(X1),X2) -> mark(plus(X1,X2))
      plus(X1,mark(X2)) -> mark(plus(X1,X2))
      proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
      proper(s(X)) -> s(proper(X))
      proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
      U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
      s(ok(X)) -> ok(s(X))
      plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(s#) = 0
      problem:
       DPs:
        
       TRS:
        active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
        active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
        active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
        active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
        active(s(X)) -> s(active(X))
        active(plus(X1,X2)) -> plus(active(X1),X2)
        active(plus(X1,X2)) -> plus(X1,active(X2))
        U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
        U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
        s(mark(X)) -> mark(s(X))
        plus(mark(X1),X2) -> mark(plus(X1,X2))
        plus(X1,mark(X2)) -> mark(plus(X1,X2))
        proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
        proper(tt()) -> ok(tt())
        proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
        proper(s(X)) -> s(proper(X))
        proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
        proper(0()) -> ok(0())
        U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
        U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
        s(ok(X)) -> ok(s(X))
        plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
     
     DPs:
      U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
      U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3)
     TRS:
      active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
      active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
      active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
      active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
      active(s(X)) -> s(active(X))
      active(plus(X1,X2)) -> plus(active(X1),X2)
      active(plus(X1,X2)) -> plus(X1,active(X2))
      U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
      U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
      s(mark(X)) -> mark(s(X))
      plus(mark(X1),X2) -> mark(plus(X1,X2))
      plus(X1,mark(X2)) -> mark(plus(X1,X2))
      proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
      proper(s(X)) -> s(proper(X))
      proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
      U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
      s(ok(X)) -> ok(s(X))
      plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(U12#) = 2
      problem:
       DPs:
        U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
       TRS:
        active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
        active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
        active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
        active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
        active(s(X)) -> s(active(X))
        active(plus(X1,X2)) -> plus(active(X1),X2)
        active(plus(X1,X2)) -> plus(X1,active(X2))
        U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
        U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
        s(mark(X)) -> mark(s(X))
        plus(mark(X1),X2) -> mark(plus(X1,X2))
        plus(X1,mark(X2)) -> mark(plus(X1,X2))
        proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
        proper(tt()) -> ok(tt())
        proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
        proper(s(X)) -> s(proper(X))
        proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
        proper(0()) -> ok(0())
        U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
        U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
        s(ok(X)) -> ok(s(X))
        plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Subterm Criterion Processor:
       simple projection:
        pi(U12#) = 0
       problem:
        DPs:
         
        TRS:
         active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
         active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
         active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
         active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
         active(s(X)) -> s(active(X))
         active(plus(X1,X2)) -> plus(active(X1),X2)
         active(plus(X1,X2)) -> plus(X1,active(X2))
         U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
         U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
         s(mark(X)) -> mark(s(X))
         plus(mark(X1),X2) -> mark(plus(X1,X2))
         plus(X1,mark(X2)) -> mark(plus(X1,X2))
         proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
         proper(tt()) -> ok(tt())
         proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
         proper(s(X)) -> s(proper(X))
         proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
         proper(0()) -> ok(0())
         U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
         U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
         s(ok(X)) -> ok(s(X))
         plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
         top(mark(X)) -> top(proper(X))
         top(ok(X)) -> top(active(X))
       Qed
     
     DPs:
      U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
      U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3)
     TRS:
      active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
      active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
      active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
      active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
      active(s(X)) -> s(active(X))
      active(plus(X1,X2)) -> plus(active(X1),X2)
      active(plus(X1,X2)) -> plus(X1,active(X2))
      U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
      U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
      s(mark(X)) -> mark(s(X))
      plus(mark(X1),X2) -> mark(plus(X1,X2))
      plus(X1,mark(X2)) -> mark(plus(X1,X2))
      proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
      proper(s(X)) -> s(proper(X))
      proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
      U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
      s(ok(X)) -> ok(s(X))
      plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(U11#) = 2
      problem:
       DPs:
        U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
       TRS:
        active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
        active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
        active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
        active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
        active(s(X)) -> s(active(X))
        active(plus(X1,X2)) -> plus(active(X1),X2)
        active(plus(X1,X2)) -> plus(X1,active(X2))
        U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
        U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
        s(mark(X)) -> mark(s(X))
        plus(mark(X1),X2) -> mark(plus(X1,X2))
        plus(X1,mark(X2)) -> mark(plus(X1,X2))
        proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
        proper(tt()) -> ok(tt())
        proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
        proper(s(X)) -> s(proper(X))
        proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
        proper(0()) -> ok(0())
        U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
        U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
        s(ok(X)) -> ok(s(X))
        plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Subterm Criterion Processor:
       simple projection:
        pi(U11#) = 0
       problem:
        DPs:
         
        TRS:
         active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
         active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
         active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
         active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
         active(s(X)) -> s(active(X))
         active(plus(X1,X2)) -> plus(active(X1),X2)
         active(plus(X1,X2)) -> plus(X1,active(X2))
         U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
         U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
         s(mark(X)) -> mark(s(X))
         plus(mark(X1),X2) -> mark(plus(X1,X2))
         plus(X1,mark(X2)) -> mark(plus(X1,X2))
         proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
         proper(tt()) -> ok(tt())
         proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
         proper(s(X)) -> s(proper(X))
         proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
         proper(0()) -> ok(0())
         U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
         U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
         s(ok(X)) -> ok(s(X))
         plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
         top(mark(X)) -> top(proper(X))
         top(ok(X)) -> top(active(X))
       Qed