YES

Problem:
 active(and(tt(),X)) -> mark(X)
 active(plus(N,0())) -> mark(N)
 active(plus(N,s(M))) -> mark(s(plus(N,M)))
 active(and(X1,X2)) -> and(active(X1),X2)
 active(plus(X1,X2)) -> plus(active(X1),X2)
 active(plus(X1,X2)) -> plus(X1,active(X2))
 active(s(X)) -> s(active(X))
 and(mark(X1),X2) -> mark(and(X1,X2))
 plus(mark(X1),X2) -> mark(plus(X1,X2))
 plus(X1,mark(X2)) -> mark(plus(X1,X2))
 s(mark(X)) -> mark(s(X))
 proper(and(X1,X2)) -> and(proper(X1),proper(X2))
 proper(tt()) -> ok(tt())
 proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
 proper(0()) -> ok(0())
 proper(s(X)) -> s(proper(X))
 and(ok(X1),ok(X2)) -> ok(and(X1,X2))
 plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
 s(ok(X)) -> ok(s(X))
 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,
   
   [s](x0) = x0,
   
   [plus](x0, x1) = 2x0 + x1,
   
   [0] = 1,
   
   [mark](x0) = x0,
   
   [active](x0) = x0,
   
   [and](x0, x1) = 4x0 + 2x1 + 3,
   
   [tt] = 0
  orientation:
   active(and(tt(),X)) = 2X + 3 >= X = mark(X)
   
   active(plus(N,0())) = 2N + 1 >= N = mark(N)
   
   active(plus(N,s(M))) = M + 2N >= M + 2N = mark(s(plus(N,M)))
   
   active(and(X1,X2)) = 4X1 + 2X2 + 3 >= 4X1 + 2X2 + 3 = and(active(X1),X2)
   
   active(plus(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = plus(active(X1),X2)
   
   active(plus(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = plus(X1,active(X2))
   
   active(s(X)) = X >= X = s(active(X))
   
   and(mark(X1),X2) = 4X1 + 2X2 + 3 >= 4X1 + 2X2 + 3 = mark(and(X1,X2))
   
   plus(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = mark(plus(X1,X2))
   
   plus(X1,mark(X2)) = 2X1 + X2 >= 2X1 + X2 = mark(plus(X1,X2))
   
   s(mark(X)) = X >= X = mark(s(X))
   
   proper(and(X1,X2)) = 4X1 + 2X2 + 3 >= 4X1 + 2X2 + 3 = and(proper(X1),proper(X2))
   
   proper(tt()) = 0 >= 0 = ok(tt())
   
   proper(plus(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = plus(proper(X1),proper(X2))
   
   proper(0()) = 1 >= 1 = ok(0())
   
   proper(s(X)) = X >= X = s(proper(X))
   
   and(ok(X1),ok(X2)) = 4X1 + 2X2 + 3 >= 4X1 + 2X2 + 3 = ok(and(X1,X2))
   
   plus(ok(X1),ok(X2)) = 2X1 + X2 >= 2X1 + X2 = ok(plus(X1,X2))
   
   s(ok(X)) = X >= X = ok(s(X))
   
   top(mark(X)) = X >= X = top(proper(X))
   
   top(ok(X)) = X >= X = top(active(X))
  problem:
   active(plus(N,s(M))) -> mark(s(plus(N,M)))
   active(and(X1,X2)) -> and(active(X1),X2)
   active(plus(X1,X2)) -> plus(active(X1),X2)
   active(plus(X1,X2)) -> plus(X1,active(X2))
   active(s(X)) -> s(active(X))
   and(mark(X1),X2) -> mark(and(X1,X2))
   plus(mark(X1),X2) -> mark(plus(X1,X2))
   plus(X1,mark(X2)) -> mark(plus(X1,X2))
   s(mark(X)) -> mark(s(X))
   proper(and(X1,X2)) -> and(proper(X1),proper(X2))
   proper(tt()) -> ok(tt())
   proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
   proper(0()) -> ok(0())
   proper(s(X)) -> s(proper(X))
   and(ok(X1),ok(X2)) -> ok(and(X1,X2))
   plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
   s(ok(X)) -> ok(s(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  DP Processor:
   DPs:
    active#(plus(N,s(M))) -> plus#(N,M)
    active#(plus(N,s(M))) -> s#(plus(N,M))
    active#(and(X1,X2)) -> active#(X1)
    active#(and(X1,X2)) -> and#(active(X1),X2)
    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))
    active#(s(X)) -> active#(X)
    active#(s(X)) -> s#(active(X))
    and#(mark(X1),X2) -> and#(X1,X2)
    plus#(mark(X1),X2) -> plus#(X1,X2)
    plus#(X1,mark(X2)) -> plus#(X1,X2)
    s#(mark(X)) -> s#(X)
    proper#(and(X1,X2)) -> proper#(X2)
    proper#(and(X1,X2)) -> proper#(X1)
    proper#(and(X1,X2)) -> and#(proper(X1),proper(X2))
    proper#(plus(X1,X2)) -> proper#(X2)
    proper#(plus(X1,X2)) -> proper#(X1)
    proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X))
    and#(ok(X1),ok(X2)) -> and#(X1,X2)
    plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
    s#(ok(X)) -> s#(X)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    active(plus(N,s(M))) -> mark(s(plus(N,M)))
    active(and(X1,X2)) -> and(active(X1),X2)
    active(plus(X1,X2)) -> plus(active(X1),X2)
    active(plus(X1,X2)) -> plus(X1,active(X2))
    active(s(X)) -> s(active(X))
    and(mark(X1),X2) -> mark(and(X1,X2))
    plus(mark(X1),X2) -> mark(plus(X1,X2))
    plus(X1,mark(X2)) -> mark(plus(X1,X2))
    s(mark(X)) -> mark(s(X))
    proper(and(X1,X2)) -> and(proper(X1),proper(X2))
    proper(tt()) -> ok(tt())
    proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
    proper(0()) -> ok(0())
    proper(s(X)) -> s(proper(X))
    and(ok(X1),ok(X2)) -> ok(and(X1,X2))
    plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
    s(ok(X)) -> ok(s(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X))
   TDG Processor:
    DPs:
     active#(plus(N,s(M))) -> plus#(N,M)
     active#(plus(N,s(M))) -> s#(plus(N,M))
     active#(and(X1,X2)) -> active#(X1)
     active#(and(X1,X2)) -> and#(active(X1),X2)
     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))
     active#(s(X)) -> active#(X)
     active#(s(X)) -> s#(active(X))
     and#(mark(X1),X2) -> and#(X1,X2)
     plus#(mark(X1),X2) -> plus#(X1,X2)
     plus#(X1,mark(X2)) -> plus#(X1,X2)
     s#(mark(X)) -> s#(X)
     proper#(and(X1,X2)) -> proper#(X2)
     proper#(and(X1,X2)) -> proper#(X1)
     proper#(and(X1,X2)) -> and#(proper(X1),proper(X2))
     proper#(plus(X1,X2)) -> proper#(X2)
     proper#(plus(X1,X2)) -> proper#(X1)
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
     proper#(s(X)) -> proper#(X)
     proper#(s(X)) -> s#(proper(X))
     and#(ok(X1),ok(X2)) -> and#(X1,X2)
     plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
     s#(ok(X)) -> s#(X)
     top#(mark(X)) -> proper#(X)
     top#(mark(X)) -> top#(proper(X))
     top#(ok(X)) -> active#(X)
     top#(ok(X)) -> top#(active(X))
    TRS:
     active(plus(N,s(M))) -> mark(s(plus(N,M)))
     active(and(X1,X2)) -> and(active(X1),X2)
     active(plus(X1,X2)) -> plus(active(X1),X2)
     active(plus(X1,X2)) -> plus(X1,active(X2))
     active(s(X)) -> s(active(X))
     and(mark(X1),X2) -> mark(and(X1,X2))
     plus(mark(X1),X2) -> mark(plus(X1,X2))
     plus(X1,mark(X2)) -> mark(plus(X1,X2))
     s(mark(X)) -> mark(s(X))
     proper(and(X1,X2)) -> and(proper(X1),proper(X2))
     proper(tt()) -> ok(tt())
     proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     and(ok(X1),ok(X2)) -> ok(and(X1,X2))
     plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
     s(ok(X)) -> ok(s(X))
     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#(s(X)) -> s#(active(X))
     top#(ok(X)) -> active#(X) -> active#(s(X)) -> active#(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#(and(X1,X2)) -> and#(active(X1),X2)
     top#(ok(X)) -> active#(X) -> active#(and(X1,X2)) -> active#(X1)
     top#(ok(X)) -> active#(X) -> active#(plus(N,s(M))) -> s#(plus(N,M))
     top#(ok(X)) -> active#(X) ->
     active#(plus(N,s(M))) -> plus#(N,M)
     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#(s(X)) -> s#(proper(X))
     top#(mark(X)) -> proper#(X) -> proper#(s(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#(and(X1,X2)) -> and#(proper(X1),proper(X2))
     top#(mark(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X1)
     top#(mark(X)) -> proper#(X) -> proper#(and(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#(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#(and(X1,X2)) -> and#(proper(X1),proper(X2))
     proper#(s(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X1)
     proper#(s(X)) -> proper#(X) ->
     proper#(and(X1,X2)) -> proper#(X2)
     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#(s(X)) -> s#(proper(X))
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(s(X)) -> proper#(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#(and(X1,X2)) -> and#(proper(X1),proper(X2))
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(and(X1,X2)) -> proper#(X1)
     proper#(plus(X1,X2)) -> proper#(X2) ->
     proper#(and(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#(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#(and(X1,X2)) -> and#(proper(X1),proper(X2))
     proper#(plus(X1,X2)) -> proper#(X1) ->
     proper#(and(X1,X2)) -> proper#(X1)
     proper#(plus(X1,X2)) -> proper#(X1) ->
     proper#(and(X1,X2)) -> proper#(X2)
     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#(and(X1,X2)) -> proper#(X2) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(and(X1,X2)) -> proper#(X2) ->
     proper#(s(X)) -> proper#(X)
     proper#(and(X1,X2)) -> proper#(X2) ->
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
     proper#(and(X1,X2)) -> proper#(X2) ->
     proper#(plus(X1,X2)) -> proper#(X1)
     proper#(and(X1,X2)) -> proper#(X2) ->
     proper#(plus(X1,X2)) -> proper#(X2)
     proper#(and(X1,X2)) -> proper#(X2) ->
     proper#(and(X1,X2)) -> and#(proper(X1),proper(X2))
     proper#(and(X1,X2)) -> proper#(X2) ->
     proper#(and(X1,X2)) -> proper#(X1)
     proper#(and(X1,X2)) -> proper#(X2) ->
     proper#(and(X1,X2)) -> proper#(X2)
     proper#(and(X1,X2)) -> proper#(X1) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(and(X1,X2)) -> proper#(X1) ->
     proper#(s(X)) -> proper#(X)
     proper#(and(X1,X2)) -> proper#(X1) ->
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
     proper#(and(X1,X2)) -> proper#(X1) ->
     proper#(plus(X1,X2)) -> proper#(X1)
     proper#(and(X1,X2)) -> proper#(X1) ->
     proper#(plus(X1,X2)) -> proper#(X2)
     proper#(and(X1,X2)) -> proper#(X1) ->
     proper#(and(X1,X2)) -> and#(proper(X1),proper(X2))
     proper#(and(X1,X2)) -> proper#(X1) ->
     proper#(and(X1,X2)) -> proper#(X1)
     proper#(and(X1,X2)) -> proper#(X1) ->
     proper#(and(X1,X2)) -> proper#(X2)
     proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) ->
     and#(ok(X1),ok(X2)) -> and#(X1,X2)
     proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) ->
     and#(mark(X1),X2) -> and#(X1,X2)
     and#(ok(X1),ok(X2)) -> and#(X1,X2) ->
     and#(ok(X1),ok(X2)) -> and#(X1,X2)
     and#(ok(X1),ok(X2)) -> and#(X1,X2) ->
     and#(mark(X1),X2) -> and#(X1,X2)
     and#(mark(X1),X2) -> and#(X1,X2) ->
     and#(ok(X1),ok(X2)) -> and#(X1,X2)
     and#(mark(X1),X2) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2)
     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)
     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#(s(X)) -> s#(active(X))
     active#(s(X)) -> active#(X) -> active#(s(X)) -> active#(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#(and(X1,X2)) -> and#(active(X1),X2)
     active#(s(X)) -> active#(X) -> active#(and(X1,X2)) -> active#(X1)
     active#(s(X)) -> active#(X) ->
     active#(plus(N,s(M))) -> s#(plus(N,M))
     active#(s(X)) -> active#(X) ->
     active#(plus(N,s(M))) -> plus#(N,M)
     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#(s(X)) -> s#(active(X))
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(s(X)) -> active#(X)
     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#(and(X1,X2)) -> and#(active(X1),X2)
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(and(X1,X2)) -> active#(X1)
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(plus(N,s(M))) -> s#(plus(N,M))
     active#(plus(X1,X2)) -> active#(X2) ->
     active#(plus(N,s(M))) -> plus#(N,M)
     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#(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#(and(X1,X2)) -> and#(active(X1),X2)
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(and(X1,X2)) -> active#(X1)
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(plus(N,s(M))) -> s#(plus(N,M))
     active#(plus(X1,X2)) -> active#(X1) ->
     active#(plus(N,s(M))) -> plus#(N,M)
     active#(plus(N,s(M))) -> s#(plus(N,M)) ->
     s#(ok(X)) -> s#(X)
     active#(plus(N,s(M))) -> s#(plus(N,M)) ->
     s#(mark(X)) -> s#(X)
     active#(plus(N,s(M))) -> plus#(N,M) ->
     plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
     active#(plus(N,s(M))) -> plus#(N,M) ->
     plus#(X1,mark(X2)) -> plus#(X1,X2)
     active#(plus(N,s(M))) -> plus#(N,M) ->
     plus#(mark(X1),X2) -> plus#(X1,X2)
     active#(and(X1,X2)) -> and#(active(X1),X2) ->
     and#(ok(X1),ok(X2)) -> and#(X1,X2)
     active#(and(X1,X2)) -> and#(active(X1),X2) ->
     and#(mark(X1),X2) -> and#(X1,X2)
     active#(and(X1,X2)) -> active#(X1) ->
     active#(s(X)) -> s#(active(X))
     active#(and(X1,X2)) -> active#(X1) ->
     active#(s(X)) -> active#(X)
     active#(and(X1,X2)) -> active#(X1) ->
     active#(plus(X1,X2)) -> plus#(X1,active(X2))
     active#(and(X1,X2)) -> active#(X1) ->
     active#(plus(X1,X2)) -> active#(X2)
     active#(and(X1,X2)) -> active#(X1) ->
     active#(plus(X1,X2)) -> plus#(active(X1),X2)
     active#(and(X1,X2)) -> active#(X1) ->
     active#(plus(X1,X2)) -> active#(X1)
     active#(and(X1,X2)) -> active#(X1) ->
     active#(and(X1,X2)) -> and#(active(X1),X2)
     active#(and(X1,X2)) -> active#(X1) ->
     active#(and(X1,X2)) -> active#(X1)
     active#(and(X1,X2)) -> active#(X1) ->
     active#(plus(N,s(M))) -> s#(plus(N,M))
     active#(and(X1,X2)) -> active#(X1) -> active#(plus(N,s(M))) -> plus#(N,M)
    SCC Processor:
     #sccs: 6
     #rules: 18
     #arcs: 145/841
     DPs:
      top#(ok(X)) -> top#(active(X))
      top#(mark(X)) -> top#(proper(X))
     TRS:
      active(plus(N,s(M))) -> mark(s(plus(N,M)))
      active(and(X1,X2)) -> and(active(X1),X2)
      active(plus(X1,X2)) -> plus(active(X1),X2)
      active(plus(X1,X2)) -> plus(X1,active(X2))
      active(s(X)) -> s(active(X))
      and(mark(X1),X2) -> mark(and(X1,X2))
      plus(mark(X1),X2) -> mark(plus(X1,X2))
      plus(X1,mark(X2)) -> mark(plus(X1,X2))
      s(mark(X)) -> mark(s(X))
      proper(and(X1,X2)) -> and(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(s(X)) -> s(proper(X))
      and(ok(X1),ok(X2)) -> ok(and(X1,X2))
      plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
      s(ok(X)) -> ok(s(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     LPO Processor:
      argument filtering:
       pi(tt) = []
       pi(and) = 0
       pi(active) = 0
       pi(mark) = [0]
       pi(0) = []
       pi(plus) = [0,1]
       pi(s) = [0]
       pi(proper) = 0
       pi(ok) = 0
       pi(top) = 0
       pi(top#) = 0
      precedence:
       plus > s > top# ~ top ~ ok ~ proper ~ 0 ~ mark ~ active ~ and ~ tt
      problem:
       DPs:
        top#(ok(X)) -> top#(active(X))
       TRS:
        active(plus(N,s(M))) -> mark(s(plus(N,M)))
        active(and(X1,X2)) -> and(active(X1),X2)
        active(plus(X1,X2)) -> plus(active(X1),X2)
        active(plus(X1,X2)) -> plus(X1,active(X2))
        active(s(X)) -> s(active(X))
        and(mark(X1),X2) -> mark(and(X1,X2))
        plus(mark(X1),X2) -> mark(plus(X1,X2))
        plus(X1,mark(X2)) -> mark(plus(X1,X2))
        s(mark(X)) -> mark(s(X))
        proper(and(X1,X2)) -> and(proper(X1),proper(X2))
        proper(tt()) -> ok(tt())
        proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
        proper(0()) -> ok(0())
        proper(s(X)) -> s(proper(X))
        and(ok(X1),ok(X2)) -> ok(and(X1,X2))
        plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
        s(ok(X)) -> ok(s(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Arctic Interpretation Processor:
       dimension: 1
       interpretation:
        [top#](x0) = 2x0 + 0,
        
        [top](x0) = 0,
        
        [ok](x0) = 2x0 + 4,
        
        [proper](x0) = 3x0 + 4,
        
        [s](x0) = x0 + 2,
        
        [plus](x0, x1) = x0,
        
        [0] = 0,
        
        [mark](x0) = x0,
        
        [active](x0) = x0 + 2,
        
        [and](x0, x1) = x0 + 1x1 + 2,
        
        [tt] = 4
       orientation:
        top#(ok(X)) = 4X + 6 >= 2X + 4 = top#(active(X))
        
        active(plus(N,s(M))) = N + 2 >= N + 2 = mark(s(plus(N,M)))
        
        active(and(X1,X2)) = X1 + 1X2 + 2 >= X1 + 1X2 + 2 = and(active(X1),X2)
        
        active(plus(X1,X2)) = X1 + 2 >= X1 + 2 = plus(active(X1),X2)
        
        active(plus(X1,X2)) = X1 + 2 >= X1 = plus(X1,active(X2))
        
        active(s(X)) = X + 2 >= X + 2 = s(active(X))
        
        and(mark(X1),X2) = X1 + 1X2 + 2 >= X1 + 1X2 + 2 = mark(and(X1,X2))
        
        plus(mark(X1),X2) = X1 >= X1 = mark(plus(X1,X2))
        
        plus(X1,mark(X2)) = X1 >= X1 = mark(plus(X1,X2))
        
        s(mark(X)) = X + 2 >= X + 2 = mark(s(X))
        
        proper(and(X1,X2)) = 3X1 + 4X2 + 5 >= 3X1 + 4X2 + 5 = and(proper(X1),proper(X2))
        
        proper(tt()) = 7 >= 6 = ok(tt())
        
        proper(plus(X1,X2)) = 3X1 + 4 >= 3X1 + 4 = plus(proper(X1),proper(X2))
        
        proper(0()) = 4 >= 4 = ok(0())
        
        proper(s(X)) = 3X + 5 >= 3X + 4 = s(proper(X))
        
        and(ok(X1),ok(X2)) = 2X1 + 3X2 + 5 >= 2X1 + 3X2 + 4 = ok(and(X1,X2))
        
        plus(ok(X1),ok(X2)) = 2X1 + 4 >= 2X1 + 4 = ok(plus(X1,X2))
        
        s(ok(X)) = 2X + 4 >= 2X + 4 = ok(s(X))
        
        top(mark(X)) = 0 >= 0 = top(proper(X))
        
        top(ok(X)) = 0 >= 0 = top(active(X))
       problem:
        DPs:
         
        TRS:
         active(plus(N,s(M))) -> mark(s(plus(N,M)))
         active(and(X1,X2)) -> and(active(X1),X2)
         active(plus(X1,X2)) -> plus(active(X1),X2)
         active(plus(X1,X2)) -> plus(X1,active(X2))
         active(s(X)) -> s(active(X))
         and(mark(X1),X2) -> mark(and(X1,X2))
         plus(mark(X1),X2) -> mark(plus(X1,X2))
         plus(X1,mark(X2)) -> mark(plus(X1,X2))
         s(mark(X)) -> mark(s(X))
         proper(and(X1,X2)) -> and(proper(X1),proper(X2))
         proper(tt()) -> ok(tt())
         proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
         proper(0()) -> ok(0())
         proper(s(X)) -> s(proper(X))
         and(ok(X1),ok(X2)) -> ok(and(X1,X2))
         plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
         s(ok(X)) -> ok(s(X))
         top(mark(X)) -> top(proper(X))
         top(ok(X)) -> top(active(X))
       Qed
     
     DPs:
      active#(and(X1,X2)) -> active#(X1)
      active#(plus(X1,X2)) -> active#(X1)
      active#(plus(X1,X2)) -> active#(X2)
      active#(s(X)) -> active#(X)
     TRS:
      active(plus(N,s(M))) -> mark(s(plus(N,M)))
      active(and(X1,X2)) -> and(active(X1),X2)
      active(plus(X1,X2)) -> plus(active(X1),X2)
      active(plus(X1,X2)) -> plus(X1,active(X2))
      active(s(X)) -> s(active(X))
      and(mark(X1),X2) -> mark(and(X1,X2))
      plus(mark(X1),X2) -> mark(plus(X1,X2))
      plus(X1,mark(X2)) -> mark(plus(X1,X2))
      s(mark(X)) -> mark(s(X))
      proper(and(X1,X2)) -> and(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(s(X)) -> s(proper(X))
      and(ok(X1),ok(X2)) -> ok(and(X1,X2))
      plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
      s(ok(X)) -> ok(s(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(active#) = 0
      problem:
       DPs:
        
       TRS:
        active(plus(N,s(M))) -> mark(s(plus(N,M)))
        active(and(X1,X2)) -> and(active(X1),X2)
        active(plus(X1,X2)) -> plus(active(X1),X2)
        active(plus(X1,X2)) -> plus(X1,active(X2))
        active(s(X)) -> s(active(X))
        and(mark(X1),X2) -> mark(and(X1,X2))
        plus(mark(X1),X2) -> mark(plus(X1,X2))
        plus(X1,mark(X2)) -> mark(plus(X1,X2))
        s(mark(X)) -> mark(s(X))
        proper(and(X1,X2)) -> and(proper(X1),proper(X2))
        proper(tt()) -> ok(tt())
        proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
        proper(0()) -> ok(0())
        proper(s(X)) -> s(proper(X))
        and(ok(X1),ok(X2)) -> ok(and(X1,X2))
        plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
        s(ok(X)) -> ok(s(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
     
     DPs:
      proper#(and(X1,X2)) -> proper#(X2)
      proper#(and(X1,X2)) -> proper#(X1)
      proper#(plus(X1,X2)) -> proper#(X2)
      proper#(plus(X1,X2)) -> proper#(X1)
      proper#(s(X)) -> proper#(X)
     TRS:
      active(plus(N,s(M))) -> mark(s(plus(N,M)))
      active(and(X1,X2)) -> and(active(X1),X2)
      active(plus(X1,X2)) -> plus(active(X1),X2)
      active(plus(X1,X2)) -> plus(X1,active(X2))
      active(s(X)) -> s(active(X))
      and(mark(X1),X2) -> mark(and(X1,X2))
      plus(mark(X1),X2) -> mark(plus(X1,X2))
      plus(X1,mark(X2)) -> mark(plus(X1,X2))
      s(mark(X)) -> mark(s(X))
      proper(and(X1,X2)) -> and(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(s(X)) -> s(proper(X))
      and(ok(X1),ok(X2)) -> ok(and(X1,X2))
      plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
      s(ok(X)) -> ok(s(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(proper#) = 0
      problem:
       DPs:
        
       TRS:
        active(plus(N,s(M))) -> mark(s(plus(N,M)))
        active(and(X1,X2)) -> and(active(X1),X2)
        active(plus(X1,X2)) -> plus(active(X1),X2)
        active(plus(X1,X2)) -> plus(X1,active(X2))
        active(s(X)) -> s(active(X))
        and(mark(X1),X2) -> mark(and(X1,X2))
        plus(mark(X1),X2) -> mark(plus(X1,X2))
        plus(X1,mark(X2)) -> mark(plus(X1,X2))
        s(mark(X)) -> mark(s(X))
        proper(and(X1,X2)) -> and(proper(X1),proper(X2))
        proper(tt()) -> ok(tt())
        proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
        proper(0()) -> ok(0())
        proper(s(X)) -> s(proper(X))
        and(ok(X1),ok(X2)) -> ok(and(X1,X2))
        plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
        s(ok(X)) -> ok(s(X))
        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(plus(N,s(M))) -> mark(s(plus(N,M)))
      active(and(X1,X2)) -> and(active(X1),X2)
      active(plus(X1,X2)) -> plus(active(X1),X2)
      active(plus(X1,X2)) -> plus(X1,active(X2))
      active(s(X)) -> s(active(X))
      and(mark(X1),X2) -> mark(and(X1,X2))
      plus(mark(X1),X2) -> mark(plus(X1,X2))
      plus(X1,mark(X2)) -> mark(plus(X1,X2))
      s(mark(X)) -> mark(s(X))
      proper(and(X1,X2)) -> and(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(s(X)) -> s(proper(X))
      and(ok(X1),ok(X2)) -> ok(and(X1,X2))
      plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
      s(ok(X)) -> ok(s(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(s#) = 0
      problem:
       DPs:
        
       TRS:
        active(plus(N,s(M))) -> mark(s(plus(N,M)))
        active(and(X1,X2)) -> and(active(X1),X2)
        active(plus(X1,X2)) -> plus(active(X1),X2)
        active(plus(X1,X2)) -> plus(X1,active(X2))
        active(s(X)) -> s(active(X))
        and(mark(X1),X2) -> mark(and(X1,X2))
        plus(mark(X1),X2) -> mark(plus(X1,X2))
        plus(X1,mark(X2)) -> mark(plus(X1,X2))
        s(mark(X)) -> mark(s(X))
        proper(and(X1,X2)) -> and(proper(X1),proper(X2))
        proper(tt()) -> ok(tt())
        proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
        proper(0()) -> ok(0())
        proper(s(X)) -> s(proper(X))
        and(ok(X1),ok(X2)) -> ok(and(X1,X2))
        plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
        s(ok(X)) -> ok(s(X))
        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(plus(N,s(M))) -> mark(s(plus(N,M)))
      active(and(X1,X2)) -> and(active(X1),X2)
      active(plus(X1,X2)) -> plus(active(X1),X2)
      active(plus(X1,X2)) -> plus(X1,active(X2))
      active(s(X)) -> s(active(X))
      and(mark(X1),X2) -> mark(and(X1,X2))
      plus(mark(X1),X2) -> mark(plus(X1,X2))
      plus(X1,mark(X2)) -> mark(plus(X1,X2))
      s(mark(X)) -> mark(s(X))
      proper(and(X1,X2)) -> and(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(s(X)) -> s(proper(X))
      and(ok(X1),ok(X2)) -> ok(and(X1,X2))
      plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
      s(ok(X)) -> ok(s(X))
      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(plus(N,s(M))) -> mark(s(plus(N,M)))
        active(and(X1,X2)) -> and(active(X1),X2)
        active(plus(X1,X2)) -> plus(active(X1),X2)
        active(plus(X1,X2)) -> plus(X1,active(X2))
        active(s(X)) -> s(active(X))
        and(mark(X1),X2) -> mark(and(X1,X2))
        plus(mark(X1),X2) -> mark(plus(X1,X2))
        plus(X1,mark(X2)) -> mark(plus(X1,X2))
        s(mark(X)) -> mark(s(X))
        proper(and(X1,X2)) -> and(proper(X1),proper(X2))
        proper(tt()) -> ok(tt())
        proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
        proper(0()) -> ok(0())
        proper(s(X)) -> s(proper(X))
        and(ok(X1),ok(X2)) -> ok(and(X1,X2))
        plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
        s(ok(X)) -> ok(s(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Subterm Criterion Processor:
       simple projection:
        pi(plus#) = 0
       problem:
        DPs:
         
        TRS:
         active(plus(N,s(M))) -> mark(s(plus(N,M)))
         active(and(X1,X2)) -> and(active(X1),X2)
         active(plus(X1,X2)) -> plus(active(X1),X2)
         active(plus(X1,X2)) -> plus(X1,active(X2))
         active(s(X)) -> s(active(X))
         and(mark(X1),X2) -> mark(and(X1,X2))
         plus(mark(X1),X2) -> mark(plus(X1,X2))
         plus(X1,mark(X2)) -> mark(plus(X1,X2))
         s(mark(X)) -> mark(s(X))
         proper(and(X1,X2)) -> and(proper(X1),proper(X2))
         proper(tt()) -> ok(tt())
         proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
         proper(0()) -> ok(0())
         proper(s(X)) -> s(proper(X))
         and(ok(X1),ok(X2)) -> ok(and(X1,X2))
         plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
         s(ok(X)) -> ok(s(X))
         top(mark(X)) -> top(proper(X))
         top(ok(X)) -> top(active(X))
       Qed
     
     DPs:
      and#(mark(X1),X2) -> and#(X1,X2)
      and#(ok(X1),ok(X2)) -> and#(X1,X2)
     TRS:
      active(plus(N,s(M))) -> mark(s(plus(N,M)))
      active(and(X1,X2)) -> and(active(X1),X2)
      active(plus(X1,X2)) -> plus(active(X1),X2)
      active(plus(X1,X2)) -> plus(X1,active(X2))
      active(s(X)) -> s(active(X))
      and(mark(X1),X2) -> mark(and(X1,X2))
      plus(mark(X1),X2) -> mark(plus(X1,X2))
      plus(X1,mark(X2)) -> mark(plus(X1,X2))
      s(mark(X)) -> mark(s(X))
      proper(and(X1,X2)) -> and(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(s(X)) -> s(proper(X))
      and(ok(X1),ok(X2)) -> ok(and(X1,X2))
      plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
      s(ok(X)) -> ok(s(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(and#) = 1
      problem:
       DPs:
        and#(mark(X1),X2) -> and#(X1,X2)
       TRS:
        active(plus(N,s(M))) -> mark(s(plus(N,M)))
        active(and(X1,X2)) -> and(active(X1),X2)
        active(plus(X1,X2)) -> plus(active(X1),X2)
        active(plus(X1,X2)) -> plus(X1,active(X2))
        active(s(X)) -> s(active(X))
        and(mark(X1),X2) -> mark(and(X1,X2))
        plus(mark(X1),X2) -> mark(plus(X1,X2))
        plus(X1,mark(X2)) -> mark(plus(X1,X2))
        s(mark(X)) -> mark(s(X))
        proper(and(X1,X2)) -> and(proper(X1),proper(X2))
        proper(tt()) -> ok(tt())
        proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
        proper(0()) -> ok(0())
        proper(s(X)) -> s(proper(X))
        and(ok(X1),ok(X2)) -> ok(and(X1,X2))
        plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
        s(ok(X)) -> ok(s(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Subterm Criterion Processor:
       simple projection:
        pi(and#) = 0
       problem:
        DPs:
         
        TRS:
         active(plus(N,s(M))) -> mark(s(plus(N,M)))
         active(and(X1,X2)) -> and(active(X1),X2)
         active(plus(X1,X2)) -> plus(active(X1),X2)
         active(plus(X1,X2)) -> plus(X1,active(X2))
         active(s(X)) -> s(active(X))
         and(mark(X1),X2) -> mark(and(X1,X2))
         plus(mark(X1),X2) -> mark(plus(X1,X2))
         plus(X1,mark(X2)) -> mark(plus(X1,X2))
         s(mark(X)) -> mark(s(X))
         proper(and(X1,X2)) -> and(proper(X1),proper(X2))
         proper(tt()) -> ok(tt())
         proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
         proper(0()) -> ok(0())
         proper(s(X)) -> s(proper(X))
         and(ok(X1),ok(X2)) -> ok(and(X1,X2))
         plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
         s(ok(X)) -> ok(s(X))
         top(mark(X)) -> top(proper(X))
         top(ok(X)) -> top(active(X))
       Qed