Problem Maude 06 MYNAT nosorts-noand-peanoSimple

Tool Bounds

Execution Time	60.030712ms
Answer	TIMEOUT
Input	Maude 06 MYNAT nosorts-noand-peanoSimple

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.4690318ms
Answer	YES(?,O(n^2))
Input	Maude 06 MYNAT nosorts-noand-peanoSimple

stdout:

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

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

Time: 0.430276 seconds
Statistics:
Number of monomials: 288
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.28485298ms
Answer	YES(?,O(n^2))
Input	Maude 06 MYNAT nosorts-noand-peanoSimple

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	0.54398584ms
Answer	YES(?,O(n^2))
Input	Maude 06 MYNAT nosorts-noand-peanoSimple

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  plus(N, s(M)) -> U11(tt(), M, N)
     , plus(N, 0()) -> N
     , U12(tt(), M, N) -> s(plus(N, M))
     , U11(tt(), M, N) -> U12(tt(), M, 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:
   U11(x1, x2, x3) = [1 0] x1 + [1 1] x2 + [1 2] x3 + [3]
                     [0 1]      [0 1]      [0 1]      [3]
   tt() = [0]
          [2]
   U12(x1, x2, x3) = [1 0] x1 + [1 1] x2 + [1 2] x3 + [2]
                     [0 1]      [0 1]      [0 1]      [3]
   s(x1) = [1 0] x1 + [0]
           [0 1]      [3]
   plus(x1, x2) = [1 2] x1 + [1 1] x2 + [1]
                  [0 1]      [0 1]      [2]
   0() = [3]
         [3]

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

Tool TRI

Execution Time	0.15011382ms
Answer	YES(?,O(n^2))
Input	Maude 06 MYNAT nosorts-noand-peanoSimple

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	8.4245205e-2ms
Answer	YES(?,O(n^2))
Input	Maude 06 MYNAT nosorts-noand-peanoSimple

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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