Problem TCT 09 nonmultrec

Tool CaT

Execution TimeUnknown
Answer
MAYBE
InputTCT 09 nonmultrec

stdout:

MAYBE

Problem:
 battle(H(0(),x),n) -> battle(x,s(n))
 battle(H(H(0(),x),y),n) -> battle(f(x,y,n),s(n))
 battle(H(H(H(0(),x),y),z),n) -> battle(H(f(x,y,n),z),s(n))
 f(x,y,o()) -> y
 f(x,y,s(n)) -> H(x,f(x,y,n))

Proof:
 Open

Tool IRC1

Execution TimeUnknown
Answer
MAYBE
InputTCT 09 nonmultrec

stdout:

MAYBE

Tool IRC2

Execution TimeUnknown
Answer
MAYBE
InputTCT 09 nonmultrec

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  battle(H(0(), x), n) -> battle(x, s(n))
     , battle(H(H(0(), x), y), n) -> battle(f(x, y, n), s(n))
     , battle(H(H(H(0(), x), y), z), n) ->
       battle(H(f(x, y, n), z), s(n))
     , f(x, y, o()) -> y
     , f(x, y, s(n)) -> H(x, f(x, y, n))}

Proof Output:    
  None of the processors succeeded.
  
  Details of failed attempt(s):
  -----------------------------
    1) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:
           
             {  1: battle^#(H(0(), x), n) -> c_0(battle^#(x, s(n)))
              , 2: battle^#(H(H(0(), x), y), n) ->
                   c_1(battle^#(f(x, y, n), s(n)))
              , 3: battle^#(H(H(H(0(), x), y), z), n) ->
                   c_2(battle^#(H(f(x, y, n), z), s(n)))
              , 4: f^#(x, y, o()) -> c_3()
              , 5: f^#(x, y, s(n)) -> c_4(f^#(x, y, n))}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{5}                                                       [   YES(?,O(n^2))    ]
                |
                `->{4}                                                   [   YES(?,O(n^2))    ]
             
             ->{1,3,2}                                                   [         NA         ]
             
           
         
         Sub-problems:
         -------------
           * Path {1,3,2}: NA
             ----------------
             
             The usable rules for this path are:
             
               {  f(x, y, o()) -> y
                , f(x, y, s(n)) -> H(x, f(x, y, n))}
             
             The weight gap principle does not apply:
               The input cannot be shown compatible
             Complexity induced by the adequate RMI: MAYBE
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {5}: YES(?,O(n^2))
             -----------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(battle) = {}, Uargs(H) = {}, Uargs(s) = {}, Uargs(f) = {},
                 Uargs(battle^#) = {}, Uargs(c_0) = {}, Uargs(c_1) = {},
                 Uargs(c_2) = {}, Uargs(f^#) = {}, Uargs(c_4) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                battle(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                H(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                            [0 0 0]      [0 0 0]      [0]
                            [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                s(x1) = [1 3 0] x1 + [0]
                        [0 1 0]      [0]
                        [0 0 0]      [0]
                f(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
                                [0 0 0]      [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0 0 0]      [0]
                o() = [0]
                      [0]
                      [0]
                battle^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                   [0 0 0]      [0 0 0]      [0]
                                   [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_2(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                f^#(x1, x2, x3) = [3 3 3] x1 + [3 3 3] x2 + [0 0 0] x3 + [0]
                                  [3 3 3]      [3 3 3]      [3 3 3]      [0]
                                  [3 3 3]      [3 3 3]      [3 3 3]      [0]
                c_3() = [0]
                        [0]
                        [0]
                c_4(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 3'
             --------------------------------------
             Answer:           YES(?,O(n^2))
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {f^#(x, y, s(n)) -> c_4(f^#(x, y, n))}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_4) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s(x1) = [1 2 2] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 1]      [4]
                f^#(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 1] x3 + [0]
                                  [0 4 0]      [0 0 0]      [4 0 0]      [0]
                                  [4 4 0]      [0 0 2]      [0 0 0]      [0]
                c_4(x1) = [1 0 0] x1 + [3]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
           
           * Path {5}->{4}: YES(?,O(n^2))
             ----------------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(battle) = {}, Uargs(H) = {}, Uargs(s) = {}, Uargs(f) = {},
                 Uargs(battle^#) = {}, Uargs(c_0) = {}, Uargs(c_1) = {},
                 Uargs(c_2) = {}, Uargs(f^#) = {}, Uargs(c_4) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                battle(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                H(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                            [0 0 0]      [0 0 0]      [0]
                            [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                f(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
                                [0 0 0]      [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0 0 0]      [0]
                o() = [0]
                      [0]
                      [0]
                battle^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                   [0 0 0]      [0 0 0]      [0]
                                   [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_2(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                f^#(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 0 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 0]      [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                c_4(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 3'
             --------------------------------------
             Answer:           YES(?,O(n^2))
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {f^#(x, y, o()) -> c_3()}
               Weak Rules: {f^#(x, y, s(n)) -> c_4(f^#(x, y, n))}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_4) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s(x1) = [1 4 0] x1 + [0]
                        [0 1 2]      [2]
                        [0 0 0]      [0]
                o() = [2]
                      [0]
                      [2]
                f^#(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [2 4 2] x3 + [0]
                                  [4 0 0]      [4 0 4]      [2 4 0]      [0]
                                  [4 4 4]      [0 0 4]      [2 2 2]      [4]
                c_3() = [1]
                        [0]
                        [0]
                c_4(x1) = [1 0 0] x1 + [7]
                          [0 0 0]      [7]
                          [0 0 0]      [7]
    
    2) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:
           
             {  1: battle^#(H(0(), x), n) -> c_0(battle^#(x, s(n)))
              , 2: battle^#(H(H(0(), x), y), n) ->
                   c_1(battle^#(f(x, y, n), s(n)))
              , 3: battle^#(H(H(H(0(), x), y), z), n) ->
                   c_2(battle^#(H(f(x, y, n), z), s(n)))
              , 4: f^#(x, y, o()) -> c_3()
              , 5: f^#(x, y, s(n)) -> c_4(f^#(x, y, n))}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{5}                                                       [   YES(?,O(n^2))    ]
                |
                `->{4}                                                   [   YES(?,O(n^1))    ]
             
             ->{1,3,2}                                                   [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * Path {1,3,2}: MAYBE
             -------------------
             
             The usable rules for this path are:
             
               {  f(x, y, o()) -> y
                , f(x, y, s(n)) -> H(x, f(x, y, n))}
             
             The weight gap principle does not apply:
               The input cannot be shown compatible
             Complexity induced by the adequate RMI: MAYBE
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    innermost runtime-complexity with respect to
               Rules:
                 {  battle^#(H(0(), x), n) -> c_0(battle^#(x, s(n)))
                  , battle^#(H(H(H(0(), x), y), z), n) ->
                    c_2(battle^#(H(f(x, y, n), z), s(n)))
                  , battle^#(H(H(0(), x), y), n) -> c_1(battle^#(f(x, y, n), s(n)))
                  , f(x, y, o()) -> y
                  , f(x, y, s(n)) -> H(x, f(x, y, n))}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {5}: YES(?,O(n^2))
             -----------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(battle) = {}, Uargs(H) = {}, Uargs(s) = {}, Uargs(f) = {},
                 Uargs(battle^#) = {}, Uargs(c_0) = {}, Uargs(c_1) = {},
                 Uargs(c_2) = {}, Uargs(f^#) = {}, Uargs(c_4) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                battle(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                H(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                            [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                s(x1) = [1 2] x1 + [0]
                        [0 0]      [0]
                f(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                [0 0]      [0 0]      [0 0]      [0]
                o() = [0]
                      [0]
                battle^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_2(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                f^#(x1, x2, x3) = [3 3] x1 + [3 3] x2 + [3 3] x3 + [0]
                                  [3 3]      [3 3]      [3 3]      [0]
                c_3() = [0]
                        [0]
                c_4(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           YES(?,O(n^2))
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {f^#(x, y, s(n)) -> c_4(f^#(x, y, n))}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_4) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s(x1) = [1 6] x1 + [2]
                        [0 1]      [2]
                f^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 5] x3 + [2]
                                  [0 4]      [4 4]      [2 2]      [0]
                c_4(x1) = [1 0] x1 + [7]
                          [2 0]      [3]
           
           * Path {5}->{4}: YES(?,O(n^1))
             ----------------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(battle) = {}, Uargs(H) = {}, Uargs(s) = {}, Uargs(f) = {},
                 Uargs(battle^#) = {}, Uargs(c_0) = {}, Uargs(c_1) = {},
                 Uargs(c_2) = {}, Uargs(f^#) = {}, Uargs(c_4) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                battle(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                H(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                            [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                f(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                [0 0]      [0 0]      [0 0]      [0]
                o() = [0]
                      [0]
                battle^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_2(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                f^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_3() = [0]
                        [0]
                c_4(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           YES(?,O(n^1))
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {f^#(x, y, o()) -> c_3()}
               Weak Rules: {f^#(x, y, s(n)) -> c_4(f^#(x, y, n))}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_4) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s(x1) = [1 0] x1 + [2]
                        [0 1]      [2]
                o() = [2]
                      [2]
                f^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [2 2] x3 + [0]
                                  [0 4]      [4 4]      [2 2]      [0]
                c_3() = [1]
                        [0]
                c_4(x1) = [1 0] x1 + [3]
                          [0 0]      [7]
    
    3) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:
           
             {  1: battle^#(H(0(), x), n) -> c_0(battle^#(x, s(n)))
              , 2: battle^#(H(H(0(), x), y), n) ->
                   c_1(battle^#(f(x, y, n), s(n)))
              , 3: battle^#(H(H(H(0(), x), y), z), n) ->
                   c_2(battle^#(H(f(x, y, n), z), s(n)))
              , 4: f^#(x, y, o()) -> c_3()
              , 5: f^#(x, y, s(n)) -> c_4(f^#(x, y, n))}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{5}                                                       [   YES(?,O(n^1))    ]
                |
                `->{4}                                                   [   YES(?,O(n^1))    ]
             
             ->{1,3,2}                                                   [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * Path {1,3,2}: MAYBE
             -------------------
             
             The usable rules for this path are:
             
               {  f(x, y, o()) -> y
                , f(x, y, s(n)) -> H(x, f(x, y, n))}
             
             The weight gap principle does not apply:
               The input cannot be shown compatible
             Complexity induced by the adequate RMI: MAYBE
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 1'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    innermost runtime-complexity with respect to
               Rules:
                 {  battle^#(H(0(), x), n) -> c_0(battle^#(x, s(n)))
                  , battle^#(H(H(H(0(), x), y), z), n) ->
                    c_2(battle^#(H(f(x, y, n), z), s(n)))
                  , battle^#(H(H(0(), x), y), n) -> c_1(battle^#(f(x, y, n), s(n)))
                  , f(x, y, o()) -> y
                  , f(x, y, s(n)) -> H(x, f(x, y, n))}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {5}: YES(?,O(n^1))
             -----------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(battle) = {}, Uargs(H) = {}, Uargs(s) = {}, Uargs(f) = {},
                 Uargs(battle^#) = {}, Uargs(c_0) = {}, Uargs(c_1) = {},
                 Uargs(c_2) = {}, Uargs(f^#) = {}, Uargs(c_4) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                battle(x1, x2) = [0] x1 + [0] x2 + [0]
                H(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                s(x1) = [1] x1 + [0]
                f(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                o() = [0]
                battle^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                c_2(x1) = [0] x1 + [0]
                f^#(x1, x2, x3) = [3] x1 + [3] x2 + [3] x3 + [0]
                c_3() = [0]
                c_4(x1) = [1] x1 + [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 1'
             --------------------------------------
             Answer:           YES(?,O(n^1))
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {f^#(x, y, s(n)) -> c_4(f^#(x, y, n))}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_4) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s(x1) = [1] x1 + [2]
                f^#(x1, x2, x3) = [7] x1 + [7] x2 + [6] x3 + [0]
                c_4(x1) = [1] x1 + [3]
           
           * Path {5}->{4}: YES(?,O(n^1))
             ----------------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(battle) = {}, Uargs(H) = {}, Uargs(s) = {}, Uargs(f) = {},
                 Uargs(battle^#) = {}, Uargs(c_0) = {}, Uargs(c_1) = {},
                 Uargs(c_2) = {}, Uargs(f^#) = {}, Uargs(c_4) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                battle(x1, x2) = [0] x1 + [0] x2 + [0]
                H(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                s(x1) = [0] x1 + [0]
                f(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                o() = [0]
                battle^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                c_2(x1) = [0] x1 + [0]
                f^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_3() = [0]
                c_4(x1) = [1] x1 + [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 1'
             --------------------------------------
             Answer:           YES(?,O(n^1))
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {f^#(x, y, o()) -> c_3()}
               Weak Rules: {f^#(x, y, s(n)) -> c_4(f^#(x, y, n))}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_4) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s(x1) = [1] x1 + [2]
                o() = [0]
                f^#(x1, x2, x3) = [7] x1 + [7] x2 + [2] x3 + [1]
                c_3() = [0]
                c_4(x1) = [1] x1 + [4]
    
    4) 'matrix-interpretation of dimension 1' failed due to the following reason:
         The input cannot be shown compatible
    
    5) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
         match-boundness of the problem could not be verified.
    
    6) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
         match-boundness of the problem could not be verified.
    

Tool RC1

Execution TimeUnknown
Answer
MAYBE
InputTCT 09 nonmultrec

stdout:

MAYBE

Tool RC2

Execution TimeUnknown
Answer
MAYBE
InputTCT 09 nonmultrec

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    runtime-complexity with respect to
  Rules:
    {  battle(H(0(), x), n) -> battle(x, s(n))
     , battle(H(H(0(), x), y), n) -> battle(f(x, y, n), s(n))
     , battle(H(H(H(0(), x), y), z), n) ->
       battle(H(f(x, y, n), z), s(n))
     , f(x, y, o()) -> y
     , f(x, y, s(n)) -> H(x, f(x, y, n))}

Proof Output:    
  None of the processors succeeded.
  
  Details of failed attempt(s):
  -----------------------------
    1) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:
           
             {  1: battle^#(H(0(), x), n) -> c_0(battle^#(x, s(n)))
              , 2: battle^#(H(H(0(), x), y), n) ->
                   c_1(battle^#(f(x, y, n), s(n)))
              , 3: battle^#(H(H(H(0(), x), y), z), n) ->
                   c_2(battle^#(H(f(x, y, n), z), s(n)))
              , 4: f^#(x, y, o()) -> c_3(y)
              , 5: f^#(x, y, s(n)) -> c_4(x, f^#(x, y, n))}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{5}                                                       [   YES(?,O(n^2))    ]
                |
                `->{4}                                                   [   YES(?,O(n^2))    ]
             
             ->{1,3,2}                                                   [         NA         ]
             
           
         
         Sub-problems:
         -------------
           * Path {1,3,2}: NA
             ----------------
             
             The usable rules for this path are:
             
               {  f(x, y, o()) -> y
                , f(x, y, s(n)) -> H(x, f(x, y, n))}
             
             The weight gap principle does not apply:
               The input cannot be shown compatible
             Complexity induced by the adequate RMI: MAYBE
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {5}: YES(?,O(n^2))
             -----------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(battle) = {}, Uargs(H) = {}, Uargs(s) = {}, Uargs(f) = {},
                 Uargs(battle^#) = {}, Uargs(c_0) = {}, Uargs(c_1) = {},
                 Uargs(c_2) = {}, Uargs(f^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                battle(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                H(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                            [0 0 0]      [0 0 0]      [0]
                            [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                s(x1) = [1 3 0] x1 + [0]
                        [0 1 0]      [0]
                        [0 0 0]      [0]
                f(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
                                [0 0 0]      [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0 0 0]      [0]
                o() = [0]
                      [0]
                      [0]
                battle^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                   [0 0 0]      [0 0 0]      [0]
                                   [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_2(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                f^#(x1, x2, x3) = [2 3 3] x1 + [3 3 3] x2 + [0 0 0] x3 + [0]
                                  [3 3 3]      [3 3 3]      [3 3 3]      [0]
                                  [3 3 3]      [3 3 3]      [3 3 3]      [0]
                c_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_4(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
                              [0 0 0]      [0 1 0]      [0]
                              [0 0 0]      [0 0 1]      [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 3'
             --------------------------------------
             Answer:           YES(?,O(n^2))
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {f^#(x, y, s(n)) -> c_4(x, f^#(x, y, n))}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_4) = {2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s(x1) = [1 2 1] x1 + [0]
                        [0 1 2]      [2]
                        [0 0 0]      [1]
                f^#(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 5 0] x3 + [0]
                                  [0 0 0]      [0 0 0]      [0 4 0]      [2]
                                  [0 0 0]      [0 4 4]      [4 2 4]      [0]
                c_4(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [7]
                              [0 0 0]      [0 0 0]      [6]
                              [0 0 0]      [0 2 0]      [3]
           
           * Path {5}->{4}: YES(?,O(n^2))
             ----------------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(battle) = {}, Uargs(H) = {}, Uargs(s) = {}, Uargs(f) = {},
                 Uargs(battle^#) = {}, Uargs(c_0) = {}, Uargs(c_1) = {},
                 Uargs(c_2) = {}, Uargs(f^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                battle(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                H(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                            [0 0 0]      [0 0 0]      [0]
                            [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                f(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
                                [0 0 0]      [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0 0 0]      [0]
                o() = [0]
                      [0]
                      [0]
                battle^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                   [0 0 0]      [0 0 0]      [0]
                                   [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_2(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                f^#(x1, x2, x3) = [3 3 3] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 0 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 0]      [0 0 0]      [0]
                c_3(x1) = [1 1 1] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_4(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
                              [0 0 0]      [0 1 0]      [0]
                              [0 0 0]      [0 0 1]      [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 3'
             --------------------------------------
             Answer:           YES(?,O(n^2))
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {f^#(x, y, o()) -> c_3(y)}
               Weak Rules: {f^#(x, y, s(n)) -> c_4(x, f^#(x, y, n))}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s(x1) = [1 0 2] x1 + [2]
                        [0 1 0]      [2]
                        [0 0 0]      [2]
                o() = [2]
                      [2]
                      [2]
                f^#(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [2 2 0] x3 + [0]
                                  [4 0 0]      [4 0 0]      [2 2 0]      [0]
                                  [4 4 0]      [4 0 4]      [2 2 2]      [0]
                c_3(x1) = [0 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_4(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [7]
                              [3 0 0]      [0 0 0]      [7]
                              [3 3 0]      [0 0 0]      [7]
    
    2) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:
           
             {  1: battle^#(H(0(), x), n) -> c_0(battle^#(x, s(n)))
              , 2: battle^#(H(H(0(), x), y), n) ->
                   c_1(battle^#(f(x, y, n), s(n)))
              , 3: battle^#(H(H(H(0(), x), y), z), n) ->
                   c_2(battle^#(H(f(x, y, n), z), s(n)))
              , 4: f^#(x, y, o()) -> c_3(y)
              , 5: f^#(x, y, s(n)) -> c_4(x, f^#(x, y, n))}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{5}                                                       [   YES(?,O(n^1))    ]
                |
                `->{4}                                                   [   YES(?,O(n^1))    ]
             
             ->{1,3,2}                                                   [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * Path {1,3,2}: MAYBE
             -------------------
             
             The usable rules for this path are:
             
               {  f(x, y, o()) -> y
                , f(x, y, s(n)) -> H(x, f(x, y, n))}
             
             The weight gap principle does not apply:
               The input cannot be shown compatible
             Complexity induced by the adequate RMI: MAYBE
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    runtime-complexity with respect to
               Rules:
                 {  battle^#(H(0(), x), n) -> c_0(battle^#(x, s(n)))
                  , battle^#(H(H(H(0(), x), y), z), n) ->
                    c_2(battle^#(H(f(x, y, n), z), s(n)))
                  , battle^#(H(H(0(), x), y), n) -> c_1(battle^#(f(x, y, n), s(n)))
                  , f(x, y, o()) -> y
                  , f(x, y, s(n)) -> H(x, f(x, y, n))}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {5}: YES(?,O(n^1))
             -----------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(battle) = {}, Uargs(H) = {}, Uargs(s) = {}, Uargs(f) = {},
                 Uargs(battle^#) = {}, Uargs(c_0) = {}, Uargs(c_1) = {},
                 Uargs(c_2) = {}, Uargs(f^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                battle(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                H(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                            [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                s(x1) = [1 2] x1 + [0]
                        [0 0]      [0]
                f(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                [0 0]      [0 0]      [0 0]      [0]
                o() = [0]
                      [0]
                battle^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_2(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                f^#(x1, x2, x3) = [3 3] x1 + [3 3] x2 + [3 3] x3 + [0]
                                  [3 3]      [3 3]      [3 3]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                              [0 0]      [0 1]      [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           YES(?,O(n^1))
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {f^#(x, y, s(n)) -> c_4(x, f^#(x, y, n))}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_4) = {2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s(x1) = [1 3] x1 + [2]
                        [0 0]      [0]
                f^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [2 0] x3 + [0]
                                  [0 0]      [0 4]      [3 0]      [4]
                c_4(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
                              [0 0]      [0 0]      [7]
           
           * Path {5}->{4}: YES(?,O(n^1))
             ----------------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(battle) = {}, Uargs(H) = {}, Uargs(s) = {}, Uargs(f) = {},
                 Uargs(battle^#) = {}, Uargs(c_0) = {}, Uargs(c_1) = {},
                 Uargs(c_2) = {}, Uargs(f^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                battle(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                H(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                            [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                f(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                [0 0]      [0 0]      [0 0]      [0]
                o() = [0]
                      [0]
                battle^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_2(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                f^#(x1, x2, x3) = [3 3] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_3(x1) = [1 1] x1 + [0]
                          [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                              [0 0]      [0 1]      [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           YES(?,O(n^1))
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {f^#(x, y, o()) -> c_3(y)}
               Weak Rules: {f^#(x, y, s(n)) -> c_4(x, f^#(x, y, n))}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s(x1) = [1 0] x1 + [2]
                        [0 1]      [2]
                o() = [2]
                      [2]
                f^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [2 2] x3 + [0]
                                  [0 0]      [4 0]      [2 2]      [0]
                c_3(x1) = [0 0] x1 + [1]
                          [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [1 0] x2 + [7]
                              [0 0]      [0 0]      [6]
    
    3) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:
           
             {  1: battle^#(H(0(), x), n) -> c_0(battle^#(x, s(n)))
              , 2: battle^#(H(H(0(), x), y), n) ->
                   c_1(battle^#(f(x, y, n), s(n)))
              , 3: battle^#(H(H(H(0(), x), y), z), n) ->
                   c_2(battle^#(H(f(x, y, n), z), s(n)))
              , 4: f^#(x, y, o()) -> c_3(y)
              , 5: f^#(x, y, s(n)) -> c_4(x, f^#(x, y, n))}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{5}                                                       [   YES(?,O(n^1))    ]
                |
                `->{4}                                                   [   YES(?,O(n^1))    ]
             
             ->{1,3,2}                                                   [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * Path {1,3,2}: MAYBE
             -------------------
             
             The usable rules for this path are:
             
               {  f(x, y, o()) -> y
                , f(x, y, s(n)) -> H(x, f(x, y, n))}
             
             The weight gap principle does not apply:
               The input cannot be shown compatible
             Complexity induced by the adequate RMI: MAYBE
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 1'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    runtime-complexity with respect to
               Rules:
                 {  battle^#(H(0(), x), n) -> c_0(battle^#(x, s(n)))
                  , battle^#(H(H(H(0(), x), y), z), n) ->
                    c_2(battle^#(H(f(x, y, n), z), s(n)))
                  , battle^#(H(H(0(), x), y), n) -> c_1(battle^#(f(x, y, n), s(n)))
                  , f(x, y, o()) -> y
                  , f(x, y, s(n)) -> H(x, f(x, y, n))}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {5}: YES(?,O(n^1))
             -----------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(battle) = {}, Uargs(H) = {}, Uargs(s) = {}, Uargs(f) = {},
                 Uargs(battle^#) = {}, Uargs(c_0) = {}, Uargs(c_1) = {},
                 Uargs(c_2) = {}, Uargs(f^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                battle(x1, x2) = [0] x1 + [0] x2 + [0]
                H(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                s(x1) = [1] x1 + [0]
                f(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                o() = [0]
                battle^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                c_2(x1) = [0] x1 + [0]
                f^#(x1, x2, x3) = [3] x1 + [3] x2 + [3] x3 + [0]
                c_3(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [1] x2 + [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 1'
             --------------------------------------
             Answer:           YES(?,O(n^1))
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {f^#(x, y, s(n)) -> c_4(x, f^#(x, y, n))}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_4) = {2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s(x1) = [1] x1 + [4]
                f^#(x1, x2, x3) = [7] x1 + [7] x2 + [2] x3 + [0]
                c_4(x1, x2) = [0] x1 + [1] x2 + [7]
           
           * Path {5}->{4}: YES(?,O(n^1))
             ----------------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(battle) = {}, Uargs(H) = {}, Uargs(s) = {}, Uargs(f) = {},
                 Uargs(battle^#) = {}, Uargs(c_0) = {}, Uargs(c_1) = {},
                 Uargs(c_2) = {}, Uargs(f^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                battle(x1, x2) = [0] x1 + [0] x2 + [0]
                H(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                s(x1) = [0] x1 + [0]
                f(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                o() = [0]
                battle^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                c_2(x1) = [0] x1 + [0]
                f^#(x1, x2, x3) = [3] x1 + [0] x2 + [0] x3 + [0]
                c_3(x1) = [1] x1 + [0]
                c_4(x1, x2) = [0] x1 + [1] x2 + [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 1'
             --------------------------------------
             Answer:           YES(?,O(n^1))
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {f^#(x, y, o()) -> c_3(y)}
               Weak Rules: {f^#(x, y, s(n)) -> c_4(x, f^#(x, y, n))}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s(x1) = [1] x1 + [0]
                o() = [2]
                f^#(x1, x2, x3) = [7] x1 + [7] x2 + [3] x3 + [2]
                c_3(x1) = [1] x1 + [1]
                c_4(x1, x2) = [0] x1 + [1] x2 + [0]
    
    4) 'matrix-interpretation of dimension 1' failed due to the following reason:
         The input cannot be shown compatible
    
    5) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
         match-boundness of the problem could not be verified.
    
    6) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
         match-boundness of the problem could not be verified.
    

Tool pair1rc

Execution TimeUnknown
Answer
TIMEOUT
InputTCT 09 nonmultrec

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  battle(H(0(), x), n) -> battle(x, s(n))
     , battle(H(H(0(), x), y), n) -> battle(f(x, y, n), s(n))
     , battle(H(H(H(0(), x), y), z), n) ->
       battle(H(f(x, y, n), z), s(n))
     , f(x, y, o()) -> y
     , f(x, y, s(n)) -> H(x, f(x, y, n))}
  StartTerms: basic terms
  Strategy: none

Certificate: TIMEOUT

Application of 'pair1 (timeout of 60.0 seconds)':
-------------------------------------------------
  Computation stopped due to timeout after 60.0 seconds

Arrrr..

Tool pair2rc

Execution TimeUnknown
Answer
TIMEOUT
InputTCT 09 nonmultrec

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  battle(H(0(), x), n) -> battle(x, s(n))
     , battle(H(H(0(), x), y), n) -> battle(f(x, y, n), s(n))
     , battle(H(H(H(0(), x), y), z), n) ->
       battle(H(f(x, y, n), z), s(n))
     , f(x, y, o()) -> y
     , f(x, y, s(n)) -> H(x, f(x, y, n))}
  StartTerms: basic terms
  Strategy: none

Certificate: TIMEOUT

Application of 'pair2 (timeout of 60.0 seconds)':
-------------------------------------------------
  Computation stopped due to timeout after 60.0 seconds

Arrrr..

Tool pair3irc

Execution TimeUnknown
Answer
TIMEOUT
InputTCT 09 nonmultrec

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  battle(H(0(), x), n) -> battle(x, s(n))
     , battle(H(H(0(), x), y), n) -> battle(f(x, y, n), s(n))
     , battle(H(H(H(0(), x), y), z), n) ->
       battle(H(f(x, y, n), z), s(n))
     , f(x, y, o()) -> y
     , f(x, y, s(n)) -> H(x, f(x, y, n))}
  StartTerms: basic terms
  Strategy: innermost

Certificate: TIMEOUT

Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
  Computation stopped due to timeout after 60.0 seconds

Arrrr..

Tool pair3rc

Execution TimeUnknown
Answer
TIMEOUT
InputTCT 09 nonmultrec

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  battle(H(0(), x), n) -> battle(x, s(n))
     , battle(H(H(0(), x), y), n) -> battle(f(x, y, n), s(n))
     , battle(H(H(H(0(), x), y), z), n) ->
       battle(H(f(x, y, n), z), s(n))
     , f(x, y, o()) -> y
     , f(x, y, s(n)) -> H(x, f(x, y, n))}
  StartTerms: basic terms
  Strategy: none

Certificate: TIMEOUT

Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
  Computation stopped due to timeout after 60.0 seconds

Arrrr..

Tool rc

Execution TimeUnknown
Answer
TIMEOUT
InputTCT 09 nonmultrec

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  battle(H(0(), x), n) -> battle(x, s(n))
     , battle(H(H(0(), x), y), n) -> battle(f(x, y, n), s(n))
     , battle(H(H(H(0(), x), y), z), n) ->
       battle(H(f(x, y, n), z), s(n))
     , f(x, y, o()) -> y
     , f(x, y, s(n)) -> H(x, f(x, y, n))}
  StartTerms: basic terms
  Strategy: none

Certificate: TIMEOUT

Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
  Computation stopped due to timeout after 60.0 seconds

Arrrr..

Tool tup3irc

Execution Time75.62329ms
Answer
TIMEOUT
InputTCT 09 nonmultrec

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  battle(H(0(), x), n) -> battle(x, s(n))
     , battle(H(H(0(), x), y), n) -> battle(f(x, y, n), s(n))
     , battle(H(H(H(0(), x), y), z), n) ->
       battle(H(f(x, y, n), z), s(n))
     , f(x, y, o()) -> y
     , f(x, y, s(n)) -> H(x, f(x, y, n))}
  StartTerms: basic terms
  Strategy: innermost

Certificate: TIMEOUT

Application of 'tup3 (timeout of 60.0 seconds)':
------------------------------------------------
  Computation stopped due to timeout after 60.0 seconds

Arrrr..