Problem Transformed CSR 04 PEANO nosorts-noand FR

Tool Bounds

Execution Time	60.035236ms
Answer	TIMEOUT
Input	Transformed CSR 04 PEANO nosorts-noand FR

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , plus(N, s(M)) -> U11(tt(), M, N)
     , plus(N, 0()) -> N
     , U12(tt(), M, N) -> s(plus(activate(N), activate(M)))
     , U11(tt(), M, N) -> U12(tt(), activate(M), activate(N))}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	15.491066ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 PEANO nosorts-noand FR

stdout:

YES(?,O(n^2))
QUADRATIC upper bound on the derivational complexity

This TRS is terminating using the deltarestricted interpretation
0(delta) =  + 3 + 3*delta
plus(delta, X1, X0) =  + 1*X0 + 1*X1 + 0 + 3*X0*delta + 0*X1*delta + 0*delta
s(delta, X0) =  + 1*X0 + 3 + 0*X0*delta + 0*delta
U11(delta, X2, X1, X0) =  + 1*X0 + 1*X1 + 1*X2 + 3 + 0*X0*delta + 3*X1*delta + 0*X2*delta + 3*delta
activate(delta, X0) =  + 1*X0 + 0 + 0*X0*delta + 1*delta
tt(delta) =  + 0 + 3*delta
U12(delta, X2, X1, X0) =  + 1*X0 + 1*X1 + 0*X2 + 3 + 0*X0*delta + 3*X1*delta + 2*X2*delta + 0*delta
plus_tau_1(delta) = delta/(1 + 0 * delta)
plus_tau_2(delta) = delta/(1 + 3 * delta)
s_tau_1(delta) = delta/(1 + 0 * delta)
U11_tau_1(delta) = delta/(1 + 0 * delta)
U11_tau_2(delta) = delta/(1 + 3 * delta)
U11_tau_3(delta) = delta/(1 + 0 * delta)
activate_tau_1(delta) = delta/(1 + 0 * delta)
U12_tau_1(delta) = delta/(0 + 2 * delta)
U12_tau_2(delta) = delta/(1 + 3 * delta)
U12_tau_3(delta) = delta/(1 + 0 * delta)

Time: 15.451405 seconds
Statistics:
Number of monomials: 1072
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.49274898ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 PEANO nosorts-noand FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , plus(N, s(M)) -> U11(tt(), M, N)
     , plus(N, 0()) -> N
     , U12(tt(), M, N) -> s(plus(activate(N), activate(M)))
     , U11(tt(), M, N) -> U12(tt(), activate(M), activate(N))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   tt() = [0]
          [2]
   U11(x1, x2, x3) = [1 3] x1 + [1 3] x2 + [1 0] x3 + [2]
                     [0 0]      [0 1]      [0 1]      [3]
   activate(x1) = [1 0] x1 + [1]
                  [0 1]      [0]
   U12(x1, x2, x3) = [1 2] x1 + [1 3] x2 + [1 0] x3 + [0]
                     [0 1]      [0 1]      [0 1]      [1]
   plus(x1, x2) = [1 0] x1 + [1 3] x2 + [0]
                  [0 1]      [0 1]      [0]
   s(x1) = [1 0] x1 + [0]
           [0 1]      [3]
   0() = [3]
         [3]

Hurray, we answered YES(?,O(n^2))

Tool IDA

Execution Time	0.85442615ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 PEANO nosorts-noand FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , plus(N, s(M)) -> U11(tt(), M, N)
     , plus(N, 0()) -> N
     , U12(tt(), M, N) -> s(plus(activate(N), activate(M)))
     , U11(tt(), M, N) -> U12(tt(), activate(M), activate(N))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following EDA-non-satisfying and IDA(2)-non-satisfying matrix interpretation:
  Interpretation Functions:
   tt() = [0]
          [2]
   U11(x1, x2, x3) = [1 2] x1 + [1 3] x2 + [1 0] x3 + [3]
                     [0 0]      [0 1]      [0 1]      [3]
   activate(x1) = [1 0] x1 + [1]
                  [0 1]      [0]
   U12(x1, x2, x3) = [1 2] x1 + [1 3] x2 + [1 0] x3 + [0]
                     [0 1]      [0 1]      [0 1]      [1]
   plus(x1, x2) = [1 0] x1 + [1 3] x2 + [0]
                  [0 1]      [0 1]      [0]
   s(x1) = [1 0] x1 + [0]
           [0 1]      [3]
   0() = [2]
         [0]

Hurray, we answered YES(?,O(n^2))

Tool TRI

Execution Time	0.21220899ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 PEANO nosorts-noand FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , plus(N, s(M)) -> U11(tt(), M, N)
     , plus(N, 0()) -> N
     , U12(tt(), M, N) -> s(plus(activate(N), activate(M)))
     , U11(tt(), M, N) -> U12(tt(), activate(M), activate(N))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   tt() = [2]
          [2]
   U11(x1, x2, x3) = [1 2] x1 + [1 3] x2 + [1 0] x3 + [1]
                     [0 1]      [0 1]      [0 1]      [1]
   activate(x1) = [1 0] x1 + [1]
                  [0 1]      [0]
   U12(x1, x2, x3) = [1 0] x1 + [1 3] x2 + [1 0] x3 + [2]
                     [0 0]      [0 1]      [0 1]      [3]
   plus(x1, x2) = [1 0] x1 + [1 3] x2 + [0]
                  [0 1]      [0 1]      [0]
   s(x1) = [1 0] x1 + [0]
           [0 1]      [3]
   0() = [3]
         [3]

Hurray, we answered YES(?,O(n^2))

Tool TRI2

Execution Time	0.162642ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 PEANO nosorts-noand FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , plus(N, s(M)) -> U11(tt(), M, N)
     , plus(N, 0()) -> N
     , U12(tt(), M, N) -> s(plus(activate(N), activate(M)))
     , U11(tt(), M, N) -> U12(tt(), activate(M), activate(N))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   tt() = [0]
          [2]
   U11(x1, x2, x3) = [1 2] x1 + [1 3] x2 + [1 0] x3 + [3]
                     [0 1]      [0 1]      [0 1]      [3]
   activate(x1) = [1 0] x1 + [1]
                  [0 1]      [0]
   U12(x1, x2, x3) = [1 2] x1 + [1 3] x2 + [1 0] x3 + [0]
                     [0 1]      [0 1]      [0 1]      [3]
   plus(x1, x2) = [1 0] x1 + [1 3] x2 + [0]
                  [0 1]      [0 1]      [2]
   s(x1) = [1 0] x1 + [0]
           [0 1]      [3]
   0() = [3]
         [3]

Hurray, we answered YES(?,O(n^2))