Problem Maude 06 LengthOfFiniteLists nokinds-noand

Tool IRC1

Execution TimeUnknown
Answer
MAYBE
InputMaude 06 LengthOfFiniteLists nokinds-noand

stdout:

MAYBE

Tool IRC2

Execution TimeUnknown
Answer
MAYBE
InputMaude 06 LengthOfFiniteLists nokinds-noand

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  zeros() -> cons(0(), zeros())
     , U11(tt()) -> tt()
     , U21(tt()) -> tt()
     , U31(tt()) -> tt()
     , U41(tt(), V2) -> U42(isNatIList(V2))
     , U42(tt()) -> tt()
     , U51(tt(), V2) -> U52(isNatList(V2))
     , U52(tt()) -> tt()
     , U61(tt(), L, N) -> U62(isNat(N), L)
     , U62(tt(), L) -> s(length(L))
     , isNat(0()) -> tt()
     , isNat(length(V1)) -> U11(isNatList(V1))
     , isNat(s(V1)) -> U21(isNat(V1))
     , isNatIList(V) -> U31(isNatList(V))
     , isNatIList(zeros()) -> tt()
     , isNatIList(cons(V1, V2)) -> U41(isNat(V1), V2)
     , isNatList(nil()) -> tt()
     , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
     , length(nil()) -> 0()
     , length(cons(N, L)) -> U61(isNatList(L), L, 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: zeros^#() -> c_0(zeros^#())
              , 2: U11^#(tt()) -> c_1()
              , 3: U21^#(tt()) -> c_2()
              , 4: U31^#(tt()) -> c_3()
              , 5: U41^#(tt(), V2) -> c_4(U42^#(isNatIList(V2)))
              , 6: U42^#(tt()) -> c_5()
              , 7: U51^#(tt(), V2) -> c_6(U52^#(isNatList(V2)))
              , 8: U52^#(tt()) -> c_7()
              , 9: U61^#(tt(), L, N) -> c_8(U62^#(isNat(N), L))
              , 10: U62^#(tt(), L) -> c_9(length^#(L))
              , 11: isNat^#(0()) -> c_10()
              , 12: isNat^#(length(V1)) -> c_11(U11^#(isNatList(V1)))
              , 13: isNat^#(s(V1)) -> c_12(U21^#(isNat(V1)))
              , 14: isNatIList^#(V) -> c_13(U31^#(isNatList(V)))
              , 15: isNatIList^#(zeros()) -> c_14()
              , 16: isNatIList^#(cons(V1, V2)) -> c_15(U41^#(isNat(V1), V2))
              , 17: isNatList^#(nil()) -> c_16()
              , 18: isNatList^#(cons(V1, V2)) -> c_17(U51^#(isNat(V1), V2))
              , 19: length^#(nil()) -> c_18()
              , 20: length^#(cons(N, L)) -> c_19(U61^#(isNatList(L), L, N))}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{18}                                                      [         NA         ]
                |
                `->{7}                                                   [         NA         ]
                    |
                    `->{8}                                               [         NA         ]
             
             ->{17}                                                      [         NA         ]
             
             ->{16}                                                      [         NA         ]
                |
                `->{5}                                                   [         NA         ]
                    |
                    `->{6}                                               [         NA         ]
             
             ->{15}                                                      [         NA         ]
             
             ->{14}                                                      [         NA         ]
                |
                `->{4}                                                   [         NA         ]
             
             ->{13}                                                      [         NA         ]
                |
                `->{3}                                                   [         NA         ]
             
             ->{12}                                                      [         NA         ]
                |
                `->{2}                                                   [         NA         ]
             
             ->{11}                                                      [         NA         ]
             
             ->{9,20,10}                                                 [         NA         ]
                |
                `->{19}                                                  [         NA         ]
             
             ->{1}                                                       [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * Path {1}: MAYBE
             ---------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {1}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(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]
                U11(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(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]
                U52(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                length(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                nil() = [0]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 3'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {zeros^#() -> c_0(zeros^#())}
               Weak Rules: {}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {9,20,10}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {1}, Uargs(c_8) = {1},
                 Uargs(U62^#) = {1}, Uargs(c_9) = {1}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 0 0] x1 + [1 2 2] x2 + [0]
                               [0 1 3]      [0 1 3]      [2]
                               [0 0 1]      [0 0 1]      [2]
                0() = [0]
                      [2]
                      [0]
                U11(x1) = [2 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [2]
                tt() = [0]
                       [0]
                       [2]
                U21(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 0]      [2]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [2 0 2] x1 + [0 2 2] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [1 0 0]      [0 3 3]      [3]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [2]
                isNatList(x1) = [0 2 2] x1 + [0]
                                [0 0 0]      [0]
                                [0 3 0]      [2]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 2] x1 + [1]
                            [0 0 0]      [0]
                            [0 1 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 0 0]      [2]
                        [0 0 1]      [2]
                length(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [2]
                             [2 2 2]      [2]
                nil() = [0]
                        [0]
                        [2]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(x1, x2, x3) = [1 0 0] x1 + [1 0 2] x2 + [1 0 2] x3 + [0]
                                    [3 3 3]      [3 3 3]      [3 3 3]      [0]
                                    [3 3 3]      [3 3 3]      [3 3 3]      [0]
                c_8(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                U62^#(x1, x2) = [1 0 0] x1 + [1 0 2] x2 + [0]
                                [3 3 3]      [3 3 3]      [0]
                                [3 3 3]      [3 3 3]      [0]
                c_9(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                length^#(x1) = [1 0 2] x1 + [0]
                               [3 3 3]      [0]
                               [3 3 3]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {9,20,10}->{19}: NA
             ------------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {1}, Uargs(c_8) = {1},
                 Uargs(U62^#) = {1}, Uargs(c_9) = {1}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
                               [0 1 1]      [0 1 0]      [2]
                               [0 0 0]      [0 0 0]      [3]
                0() = [0]
                      [0]
                      [2]
                U11(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [1 0 0] x1 + [0 2 0] x2 + [3]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                U52(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [0 2 0] x1 + [0]
                                [0 0 3]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 2 2] x1 + [0]
                            [0 0 3]      [2]
                            [0 0 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 1 1]      [2]
                        [0 0 0]      [2]
                length(x1) = [0 0 0] x1 + [0]
                             [0 1 0]      [0]
                             [0 0 0]      [3]
                nil() = [0]
                        [2]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(x1, x2, x3) = [3 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_8(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                U62^#(x1, x2) = [3 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_9(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(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]
                U11(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(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]
                U52(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                length(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                nil() = [0]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {12}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {1}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [3]
                               [0 0 2]      [0 1 0]      [0]
                               [0 0 1]      [0 0 0]      [0]
                0() = [2]
                      [0]
                      [0]
                U11(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                tt() = [0]
                       [1]
                       [0]
                U21(x1) = [1 1 0] x1 + [0]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [1 2 0] x1 + [2 0 0] x2 + [2]
                              [0 0 0]      [1 1 0]      [1]
                              [0 0 0]      [0 2 0]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                isNatList(x1) = [2 0 0] x1 + [2]
                                [1 3 2]      [2]
                                [0 2 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [2 0 0] x1 + [0]
                            [0 0 0]      [1]
                            [0 0 0]      [0]
                s(x1) = [1 2 2] x1 + [2]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                length(x1) = [1 2 0] x1 + [2]
                             [2 2 0]      [0]
                             [0 0 0]      [0]
                nil() = [0]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [2 0 0] x1 + [0]
                            [3 3 3]      [0]
                            [3 3 3]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [2 2 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {12}->{2}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {1}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 2 2] x1 + [1 0 0] x2 + [0]
                               [0 0 3]      [0 1 2]      [0]
                               [0 0 0]      [0 0 0]      [2]
                0() = [0]
                      [3]
                      [3]
                U11(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [2]
                       [0]
                       [0]
                U21(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [2 0 0] x1 + [0 2 3] x2 + [0]
                              [3 0 0]      [0 3 0]      [2]
                              [0 0 0]      [0 0 3]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [0 2 1] x1 + [0]
                                [0 3 0]      [2]
                                [2 2 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 3] x1 + [0]
                            [0 0 0]      [0]
                            [2 3 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 1]      [1]
                length(x1) = [0 0 2] x1 + [0]
                             [0 0 0]      [0]
                             [0 2 2]      [2]
                nil() = [1]
                        [3]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [3 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {13}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {1},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {1},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 2 3] x1 + [1 0 0] x2 + [3]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 1]      [0 0 0]      [2]
                0() = [0]
                      [0]
                      [0]
                U11(x1) = [2 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [1 0 0] x1 + [2 0 0] x2 + [3]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [2 0 0] x1 + [0]
                                [2 0 2]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [2 0 2] x1 + [1]
                            [0 0 2]      [0]
                            [0 0 0]      [0]
                s(x1) = [1 2 1] x1 + [2]
                        [0 0 1]      [0]
                        [0 0 0]      [2]
                length(x1) = [0 0 0] x1 + [2]
                             [0 0 0]      [0]
                             [2 0 0]      [0]
                nil() = [1]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [1 0 0] x1 + [0]
                            [3 3 3]      [0]
                            [3 3 3]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [2 2 3] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {13}->{3}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {1},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {1},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
                               [0 1 3]      [0 1 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [1]
                U11(x1) = [1 0 0] x1 + [2]
                          [0 1 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [2]
                       [0]
                U21(x1) = [1 2 0] x1 + [0]
                          [0 0 0]      [2]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [1 2 0] x1 + [0 2 0] x2 + [0]
                              [0 2 0]      [1 2 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [1 0 0]      [2]
                          [0 0 0]      [0]
                isNatList(x1) = [0 2 0] x1 + [2]
                                [1 2 0]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 2 1] x1 + [0]
                            [0 0 2]      [0]
                            [0 0 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 1 2]      [0]
                        [0 0 1]      [1]
                length(x1) = [0 0 0] x1 + [0]
                             [3 1 0]      [3]
                             [2 2 0]      [0]
                nil() = [2]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [3 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {14}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {1}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {1}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 1 2] x1 + [1 2 0] x2 + [2]
                               [0 0 0]      [0 0 0]      [2]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [2]
                U11(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [1]
                tt() = [0]
                       [0]
                       [1]
                U21(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [1]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [1 0 3] x1 + [1 2 0] x2 + [3]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [1]
                U52(x1) = [1 3 1] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [1]
                isNatList(x1) = [1 2 0] x1 + [1]
                                [0 0 0]      [1]
                                [0 0 0]      [1]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 1] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [1]
                s(x1) = [1 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 1]      [2]
                length(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [1 2 0]      [3]
                nil() = [0]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [1 2 2] x1 + [0]
                            [3 3 3]      [0]
                            [3 3 3]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [3 3 3] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {14}->{4}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {1}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {1}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 2 2] x1 + [1 0 0] x2 + [0]
                               [0 0 3]      [0 1 2]      [0]
                               [0 0 0]      [0 0 0]      [2]
                0() = [0]
                      [3]
                      [3]
                U11(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [2]
                       [0]
                       [0]
                U21(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [2 0 0] x1 + [0 2 3] x2 + [0]
                              [3 0 0]      [0 3 0]      [2]
                              [0 0 0]      [0 0 3]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [0 2 1] x1 + [0]
                                [0 3 0]      [2]
                                [2 2 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 3] x1 + [0]
                            [0 0 0]      [0]
                            [2 3 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 1]      [1]
                length(x1) = [0 0 2] x1 + [0]
                             [0 0 0]      [0]
                             [0 2 2]      [2]
                nil() = [1]
                        [3]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [3 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {15}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(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]
                U11(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(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]
                U52(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                length(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                nil() = [0]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 3 0] x1 + [1 0 0] x2 + [1]
                               [0 1 2]      [0 1 0]      [1]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [2]
                      [0]
                U11(x1) = [2 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [2 0 0] x1 + [1 2 0] x2 + [2]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [1 2 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 2 0] x1 + [0]
                            [0 0 3]      [1]
                            [1 3 0]      [1]
                s(x1) = [1 1 0] x1 + [0]
                        [0 1 0]      [1]
                        [0 0 0]      [1]
                length(x1) = [2 0 0] x1 + [0]
                             [1 2 0]      [2]
                             [0 0 0]      [0]
                nil() = [0]
                        [2]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(x1, x2) = [1 0 2] x1 + [1 0 0] x2 + [0]
                                [3 3 3]      [3 3 3]      [0]
                                [3 3 3]      [3 3 3]      [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [3 0 3] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}->{5}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()
                , isNatIList(V) -> U31(isNatList(V))
                , isNatIList(zeros()) -> tt()
                , isNatIList(cons(V1, V2)) -> U41(isNat(V1), V2)
                , U31(tt()) -> tt()
                , U41(tt(), V2) -> U42(isNatIList(V2))
                , U42(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {1}, Uargs(U41) = {1}, Uargs(U42) = {1},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {1},
                 Uargs(U42^#) = {1}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [1]
                          [0]
                          [0]
                cons(x1, x2) = [1 3 3] x1 + [1 3 1] x2 + [3]
                               [0 1 3]      [0 0 1]      [1]
                               [0 0 1]      [0 0 0]      [3]
                0() = [0]
                      [0]
                      [0]
                U11(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [1]
                          [0 0 0]      [2]
                tt() = [0]
                       [1]
                       [2]
                U21(x1) = [1 0 1] x1 + [0]
                          [0 0 0]      [1]
                          [0 0 0]      [2]
                U31(x1) = [1 0 0] x1 + [1]
                          [0 0 2]      [0]
                          [0 0 1]      [0]
                U41(x1, x2) = [2 2 3] x1 + [1 3 3] x2 + [0]
                              [0 0 0]      [2 2 0]      [0]
                              [0 1 2]      [1 1 1]      [0]
                U42(x1) = [1 0 0] x1 + [2]
                          [0 1 0]      [0]
                          [0 0 0]      [2]
                isNatIList(x1) = [1 3 3] x1 + [3]
                                 [2 0 0]      [0]
                                 [1 1 1]      [1]
                U51(x1, x2) = [1 0 0] x1 + [1 3 1] x2 + [3]
                              [0 0 0]      [0 0 0]      [1]
                              [0 0 0]      [1 1 1]      [0]
                U52(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [1]
                          [0 0 1]      [0]
                isNatList(x1) = [1 0 1] x1 + [0]
                                [0 0 0]      [2]
                                [1 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 2] x1 + [2]
                            [0 3 0]      [2]
                            [0 0 0]      [3]
                s(x1) = [1 0 0] x1 + [0]
                        [0 1 0]      [3]
                        [0 0 1]      [2]
                length(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [2 0 2]      [1]
                nil() = [2]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(x1, x2) = [3 0 0] x1 + [3 3 3] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_4(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                U42^#(x1) = [1 0 0] x1 + [0]
                            [3 3 3]      [0]
                            [3 3 3]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}->{5}->{6}: NA
             -----------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()
                , isNatIList(V) -> U31(isNatList(V))
                , isNatIList(zeros()) -> tt()
                , isNatIList(cons(V1, V2)) -> U41(isNat(V1), V2)
                , U31(tt()) -> tt()
                , U41(tt(), V2) -> U42(isNatIList(V2))
                , U42(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {1}, Uargs(U41) = {1}, Uargs(U42) = {1},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {1},
                 Uargs(U42^#) = {1}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [1]
                          [0]
                          [0]
                cons(x1, x2) = [1 2 2] x1 + [1 3 0] x2 + [2]
                               [0 1 2]      [0 1 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [3]
                      [0]
                U11(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                tt() = [2]
                       [1]
                       [0]
                U21(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                U31(x1) = [1 1 0] x1 + [0]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                U41(x1, x2) = [2 1 0] x1 + [2 3 0] x2 + [0]
                              [0 1 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                U42(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                isNatIList(x1) = [2 3 0] x1 + [2]
                                 [0 0 0]      [1]
                                 [0 0 0]      [0]
                U51(x1, x2) = [2 0 0] x1 + [1 3 0] x2 + [0]
                              [0 0 0]      [1 3 0]      [1]
                              [0 0 0]      [0 0 0]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                isNatList(x1) = [1 1 0] x1 + [0]
                                [1 2 0]      [0]
                                [0 0 3]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 1 0] x1 + [0]
                            [0 0 0]      [1]
                            [0 0 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 1 0]      [3]
                        [0 0 0]      [0]
                length(x1) = [0 0 0] x1 + [0]
                             [2 2 0]      [2]
                             [0 0 0]      [0]
                nil() = [1]
                        [2]
                        [3]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(x1, x2) = [3 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_4(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                U42^#(x1) = [3 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {17}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(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]
                U11(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(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]
                U52(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                length(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                nil() = [0]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 3 0] x1 + [1 0 0] x2 + [1]
                               [0 1 2]      [0 1 0]      [1]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [2]
                      [0]
                U11(x1) = [2 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [2 0 0] x1 + [1 2 0] x2 + [2]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [1 2 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 2 0] x1 + [0]
                            [0 0 3]      [1]
                            [1 3 0]      [1]
                s(x1) = [1 1 0] x1 + [0]
                        [0 1 0]      [1]
                        [0 0 0]      [1]
                length(x1) = [2 0 0] x1 + [0]
                             [1 2 0]      [2]
                             [0 0 0]      [0]
                nil() = [0]
                        [2]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(x1, x2) = [1 0 2] x1 + [1 0 0] x2 + [0]
                                [3 3 3]      [3 3 3]      [0]
                                [3 3 3]      [3 3 3]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [3 0 3] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}->{7}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {1},
                 Uargs(U52^#) = {1}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 0 3] x1 + [1 2 0] x2 + [1]
                               [0 1 3]      [0 0 0]      [0]
                               [0 0 1]      [0 0 1]      [0]
                0() = [2]
                      [2]
                      [0]
                U11(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [2]
                tt() = [0]
                       [0]
                       [2]
                U21(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 0]      [2]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [1 0 2] x1 + [2 3 1] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 1]      [1 2 0]      [2]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [2]
                isNatList(x1) = [2 3 1] x1 + [0]
                                [0 0 0]      [0]
                                [1 0 0]      [2]
                U61(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]
                U62(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]
                isNat(x1) = [0 2 1] x1 + [0]
                            [0 0 3]      [0]
                            [1 0 0]      [0]
                s(x1) = [1 0 0] x1 + [2]
                        [0 1 0]      [2]
                        [0 0 1]      [0]
                length(x1) = [0 0 0] x1 + [2]
                             [2 0 0]      [3]
                             [0 3 3]      [3]
                nil() = [0]
                        [0]
                        [1]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(x1, x2) = [3 0 0] x1 + [3 3 3] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_6(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                U52^#(x1) = [1 2 0] x1 + [0]
                            [3 3 3]      [0]
                            [3 3 3]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}->{7}->{8}: NA
             -----------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {1},
                 Uargs(U52^#) = {1}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 1 1] x1 + [1 0 0] x2 + [2]
                               [0 1 0]      [0 1 0]      [3]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                U11(x1) = [1 1 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 0]      [1]
                tt() = [0]
                       [0]
                       [1]
                U21(x1) = [1 0 1] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [1]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [1 0 3] x1 + [1 3 0] x2 + [3]
                              [0 0 0]      [1 0 0]      [0]
                              [0 0 0]      [0 1 0]      [0]
                U52(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 1]      [0]
                isNatList(x1) = [1 3 0] x1 + [0]
                                [1 0 0]      [0]
                                [0 1 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 3 1] x1 + [2]
                            [2 1 1]      [0]
                            [0 0 0]      [1]
                s(x1) = [1 2 3] x1 + [0]
                        [0 1 1]      [2]
                        [0 0 1]      [2]
                length(x1) = [0 2 3] x1 + [0]
                             [0 2 3]      [3]
                             [2 2 0]      [0]
                nil() = [0]
                        [1]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(x1, x2) = [3 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_6(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                U52^#(x1) = [3 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
    
    2) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:
           
             {  1: zeros^#() -> c_0(zeros^#())
              , 2: U11^#(tt()) -> c_1()
              , 3: U21^#(tt()) -> c_2()
              , 4: U31^#(tt()) -> c_3()
              , 5: U41^#(tt(), V2) -> c_4(U42^#(isNatIList(V2)))
              , 6: U42^#(tt()) -> c_5()
              , 7: U51^#(tt(), V2) -> c_6(U52^#(isNatList(V2)))
              , 8: U52^#(tt()) -> c_7()
              , 9: U61^#(tt(), L, N) -> c_8(U62^#(isNat(N), L))
              , 10: U62^#(tt(), L) -> c_9(length^#(L))
              , 11: isNat^#(0()) -> c_10()
              , 12: isNat^#(length(V1)) -> c_11(U11^#(isNatList(V1)))
              , 13: isNat^#(s(V1)) -> c_12(U21^#(isNat(V1)))
              , 14: isNatIList^#(V) -> c_13(U31^#(isNatList(V)))
              , 15: isNatIList^#(zeros()) -> c_14()
              , 16: isNatIList^#(cons(V1, V2)) -> c_15(U41^#(isNat(V1), V2))
              , 17: isNatList^#(nil()) -> c_16()
              , 18: isNatList^#(cons(V1, V2)) -> c_17(U51^#(isNat(V1), V2))
              , 19: length^#(nil()) -> c_18()
              , 20: length^#(cons(N, L)) -> c_19(U61^#(isNatList(L), L, N))}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{18}                                                      [         NA         ]
                |
                `->{7}                                                   [         NA         ]
                    |
                    `->{8}                                               [         NA         ]
             
             ->{17}                                                      [         NA         ]
             
             ->{16}                                                      [         NA         ]
                |
                `->{5}                                                   [         NA         ]
                    |
                    `->{6}                                               [         NA         ]
             
             ->{15}                                                      [         NA         ]
             
             ->{14}                                                      [         NA         ]
                |
                `->{4}                                                   [         NA         ]
             
             ->{13}                                                      [         NA         ]
                |
                `->{3}                                                   [         NA         ]
             
             ->{12}                                                      [         NA         ]
                |
                `->{2}                                                   [         NA         ]
             
             ->{11}                                                      [         NA         ]
             
             ->{9,20,10}                                                 [         NA         ]
                |
                `->{19}                                                  [         NA         ]
             
             ->{1}                                                       [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * Path {1}: MAYBE
             ---------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {1}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                U11(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                tt() = [0]
                       [0]
                U21(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U52(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatList(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                length(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {zeros^#() -> c_0(zeros^#())}
               Weak Rules: {}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {9,20,10}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {1}, Uargs(c_8) = {1},
                 Uargs(U62^#) = {1}, Uargs(c_9) = {1}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
                               [0 1]      [0 1]      [2]
                0() = [0]
                      [1]
                U11(x1) = [1 0] x1 + [1]
                          [0 0]      [1]
                tt() = [0]
                       [1]
                U21(x1) = [1 2] x1 + [0]
                          [0 0]      [1]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 0] x1 + [0 3] x2 + [2]
                              [0 0]      [0 0]      [1]
                U52(x1) = [1 0] x1 + [1]
                          [0 0]      [1]
                isNatList(x1) = [0 3] x1 + [0]
                                [0 0]      [1]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 3] x1 + [0]
                            [0 0]      [2]
                s(x1) = [1 0] x1 + [0]
                        [0 1]      [3]
                length(x1) = [0 0] x1 + [0]
                             [3 1]      [2]
                nil() = [0]
                        [3]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [2 0] x1 + [3 0] x2 + [1 3] x3 + [0]
                                    [3 3]      [3 3]      [3 3]      [0]
                c_8(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                U62^#(x1, x2) = [1 0] x1 + [3 0] x2 + [0]
                                [3 3]      [3 3]      [0]
                c_9(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                length^#(x1) = [3 0] x1 + [0]
                               [3 3]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {9,20,10}->{19}: NA
             ------------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {1}, Uargs(c_8) = {1},
                 Uargs(U62^#) = {1}, Uargs(c_9) = {1}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [3]
                0() = [0]
                      [0]
                U11(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                tt() = [0]
                       [0]
                U21(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [2 0] x1 + [0 2] x2 + [3]
                              [0 0]      [0 0]      [0]
                U52(x1) = [1 0] x1 + [2]
                          [0 0]      [0]
                isNatList(x1) = [0 2] x1 + [0]
                                [0 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 1] x1 + [1]
                            [2 0]      [0]
                s(x1) = [1 0] x1 + [0]
                        [0 1]      [2]
                length(x1) = [0 2] x1 + [0]
                             [0 2]      [3]
                nil() = [0]
                        [2]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [3 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                U62^#(x1, x2) = [3 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                U11(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                tt() = [0]
                       [0]
                U21(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U52(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatList(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                length(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {12}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {1}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 2] x1 + [1 2] x2 + [2]
                               [0 0]      [0 1]      [2]
                0() = [0]
                      [0]
                U11(x1) = [1 0] x1 + [1]
                          [0 0]      [1]
                tt() = [0]
                       [1]
                U21(x1) = [1 0] x1 + [1]
                          [0 0]      [1]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [2 3] x1 + [2 3] x2 + [3]
                              [0 1]      [0 0]      [0]
                U52(x1) = [1 3] x1 + [0]
                          [0 0]      [1]
                isNatList(x1) = [2 3] x1 + [1]
                                [0 0]      [1]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 0] x1 + [2]
                            [0 0]      [1]
                s(x1) = [1 0] x1 + [2]
                        [0 0]      [0]
                length(x1) = [3 3] x1 + [2]
                             [3 0]      [0]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [2 0] x1 + [0]
                            [3 3]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [3 3] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {12}->{2}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {1}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 1] x1 + [1 2] x2 + [0]
                               [0 0]      [0 1]      [3]
                0() = [2]
                      [0]
                U11(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                tt() = [1]
                       [0]
                U21(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 0] x1 + [2 3] x2 + [3]
                              [0 0]      [1 2]      [0]
                U52(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                isNatList(x1) = [2 1] x1 + [2]
                                [1 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 0] x1 + [1]
                            [0 0]      [0]
                s(x1) = [1 1] x1 + [2]
                        [0 0]      [0]
                length(x1) = [2 1] x1 + [3]
                             [0 0]      [0]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [3 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {13}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {1},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {1},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [3]
                0() = [0]
                      [0]
                U11(x1) = [2 2] x1 + [0]
                          [0 0]      [0]
                tt() = [1]
                       [0]
                U21(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 0] x1 + [0 3] x2 + [3]
                              [0 0]      [0 1]      [0]
                U52(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                isNatList(x1) = [0 3] x1 + [2]
                                [0 1]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 3] x1 + [2]
                            [2 0]      [0]
                s(x1) = [1 2] x1 + [0]
                        [0 1]      [2]
                length(x1) = [0 0] x1 + [0]
                             [0 3]      [1]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [1 0] x1 + [0]
                            [3 3]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 3] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {13}->{3}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {1},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {1},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [3]
                0() = [0]
                      [0]
                U11(x1) = [1 0] x1 + [2]
                          [0 0]      [0]
                tt() = [0]
                       [0]
                U21(x1) = [1 0] x1 + [2]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 2] x1 + [0 3] x2 + [2]
                              [0 0]      [0 0]      [0]
                U52(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                isNatList(x1) = [0 3] x1 + [0]
                                [0 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 3] x1 + [2]
                            [0 0]      [1]
                s(x1) = [1 0] x1 + [0]
                        [0 1]      [3]
                length(x1) = [0 0] x1 + [0]
                             [0 1]      [3]
                nil() = [0]
                        [3]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [3 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {14}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {1}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {1}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 0] x1 + [1 2] x2 + [0]
                               [0 1]      [0 1]      [3]
                0() = [0]
                      [0]
                U11(x1) = [3 0] x1 + [2]
                          [0 0]      [1]
                tt() = [0]
                       [1]
                U21(x1) = [1 0] x1 + [2]
                          [0 0]      [1]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 1] x1 + [2 3] x2 + [3]
                              [0 0]      [0 1]      [1]
                U52(x1) = [1 0] x1 + [1]
                          [0 1]      [0]
                isNatList(x1) = [2 3] x1 + [1]
                                [0 1]      [1]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [2 2] x1 + [1]
                            [0 0]      [1]
                s(x1) = [1 0] x1 + [2]
                        [0 1]      [0]
                length(x1) = [3 3] x1 + [2]
                             [0 3]      [2]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [1 0] x1 + [0]
                            [3 3]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [3 3] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {14}->{4}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {1}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {1}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 1] x1 + [1 2] x2 + [0]
                               [0 0]      [0 1]      [3]
                0() = [2]
                      [0]
                U11(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                tt() = [1]
                       [0]
                U21(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 0] x1 + [2 3] x2 + [3]
                              [0 0]      [1 2]      [0]
                U52(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                isNatList(x1) = [2 1] x1 + [2]
                                [1 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 0] x1 + [1]
                            [0 0]      [0]
                s(x1) = [1 1] x1 + [2]
                        [0 0]      [0]
                length(x1) = [2 1] x1 + [3]
                             [0 0]      [0]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [3 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {15}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                U11(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                tt() = [0]
                       [0]
                U21(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U52(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatList(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                length(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 3] x1 + [1 2] x2 + [3]
                               [0 1]      [0 1]      [0]
                0() = [0]
                      [0]
                U11(x1) = [1 0] x1 + [2]
                          [0 1]      [3]
                tt() = [0]
                       [1]
                U21(x1) = [1 0] x1 + [3]
                          [0 0]      [1]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 0] x1 + [1 3] x2 + [1]
                              [0 0]      [0 2]      [0]
                U52(x1) = [1 1] x1 + [0]
                          [0 1]      [0]
                isNatList(x1) = [1 1] x1 + [0]
                                [0 2]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 2] x1 + [1]
                            [1 0]      [1]
                s(x1) = [1 2] x1 + [2]
                        [0 1]      [3]
                length(x1) = [0 2] x1 + [2]
                             [2 3]      [2]
                nil() = [2]
                        [2]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [2 0] x1 + [1 0] x2 + [0]
                                [3 3]      [3 3]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [2 2] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}->{5}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()
                , isNatIList(V) -> U31(isNatList(V))
                , isNatIList(zeros()) -> tt()
                , isNatIList(cons(V1, V2)) -> U41(isNat(V1), V2)
                , U31(tt()) -> tt()
                , U41(tt(), V2) -> U42(isNatIList(V2))
                , U42(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {1}, Uargs(U41) = {1}, Uargs(U42) = {1},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {1},
                 Uargs(U42^#) = {1}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 1] x1 + [1 3] x2 + [3]
                               [0 1]      [0 1]      [0]
                0() = [0]
                      [2]
                U11(x1) = [1 0] x1 + [1]
                          [0 0]      [2]
                tt() = [0]
                       [2]
                U21(x1) = [1 2] x1 + [0]
                          [0 1]      [0]
                U31(x1) = [1 0] x1 + [2]
                          [0 0]      [2]
                U41(x1, x2) = [2 2] x1 + [3 3] x2 + [2]
                              [0 0]      [0 1]      [2]
                U42(x1) = [1 1] x1 + [0]
                          [0 1]      [0]
                isNatIList(x1) = [3 0] x1 + [3]
                                 [0 1]      [2]
                U51(x1, x2) = [1 2] x1 + [3 3] x2 + [0]
                              [0 0]      [2 0]      [2]
                U52(x1) = [1 0] x1 + [1]
                          [0 1]      [2]
                isNatList(x1) = [3 0] x1 + [0]
                                [2 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 0] x1 + [1]
                            [0 1]      [0]
                s(x1) = [1 2] x1 + [2]
                        [0 1]      [0]
                length(x1) = [3 0] x1 + [2]
                             [0 0]      [2]
                nil() = [2]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [3 0] x1 + [3 3] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                U42^#(x1) = [1 3] x1 + [0]
                            [3 3]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}->{5}->{6}: NA
             -----------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()
                , isNatIList(V) -> U31(isNatList(V))
                , isNatIList(zeros()) -> tt()
                , isNatIList(cons(V1, V2)) -> U41(isNat(V1), V2)
                , U31(tt()) -> tt()
                , U41(tt(), V2) -> U42(isNatIList(V2))
                , U42(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {1}, Uargs(U41) = {1}, Uargs(U42) = {1},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {1},
                 Uargs(U42^#) = {1}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [2]
                          [0]
                cons(x1, x2) = [1 3] x1 + [1 2] x2 + [2]
                               [0 1]      [0 0]      [2]
                0() = [0]
                      [1]
                U11(x1) = [1 0] x1 + [1]
                          [0 0]      [1]
                tt() = [1]
                       [1]
                U21(x1) = [1 1] x1 + [0]
                          [0 1]      [0]
                U31(x1) = [2 0] x1 + [0]
                          [0 0]      [1]
                U41(x1, x2) = [2 1] x1 + [2 3] x2 + [3]
                              [0 0]      [0 0]      [1]
                U42(x1) = [1 2] x1 + [0]
                          [0 0]      [1]
                isNatIList(x1) = [2 2] x1 + [1]
                                 [0 0]      [2]
                U51(x1, x2) = [1 0] x1 + [1 2] x2 + [1]
                              [0 0]      [0 0]      [1]
                U52(x1) = [1 1] x1 + [0]
                          [0 0]      [1]
                isNatList(x1) = [1 1] x1 + [0]
                                [0 0]      [1]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 0] x1 + [2]
                            [0 1]      [0]
                s(x1) = [1 1] x1 + [1]
                        [0 1]      [0]
                length(x1) = [2 2] x1 + [2]
                             [0 0]      [2]
                nil() = [2]
                        [2]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [3 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                U42^#(x1) = [3 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {17}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                U11(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                tt() = [0]
                       [0]
                U21(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U52(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatList(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                length(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 3] x1 + [1 2] x2 + [3]
                               [0 1]      [0 1]      [0]
                0() = [0]
                      [0]
                U11(x1) = [1 0] x1 + [2]
                          [0 1]      [3]
                tt() = [0]
                       [1]
                U21(x1) = [1 0] x1 + [3]
                          [0 0]      [1]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 0] x1 + [1 3] x2 + [1]
                              [0 0]      [0 2]      [0]
                U52(x1) = [1 1] x1 + [0]
                          [0 1]      [0]
                isNatList(x1) = [1 1] x1 + [0]
                                [0 2]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 2] x1 + [1]
                            [1 0]      [1]
                s(x1) = [1 2] x1 + [2]
                        [0 1]      [3]
                length(x1) = [0 2] x1 + [2]
                             [2 3]      [2]
                nil() = [2]
                        [2]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [2 0] x1 + [1 0] x2 + [0]
                                [3 3]      [3 3]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [2 2] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}->{7}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {1},
                 Uargs(U52^#) = {1}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 2] x1 + [1 3] x2 + [3]
                               [0 0]      [0 0]      [1]
                0() = [1]
                      [0]
                U11(x1) = [2 0] x1 + [0]
                          [1 0]      [0]
                tt() = [2]
                       [2]
                U21(x1) = [1 0] x1 + [1]
                          [0 0]      [2]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 1] x1 + [3 3] x2 + [0]
                              [0 0]      [1 1]      [2]
                U52(x1) = [1 0] x1 + [1]
                          [0 0]      [2]
                isNatList(x1) = [3 0] x1 + [0]
                                [1 1]      [2]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 1] x1 + [2]
                            [1 0]      [1]
                s(x1) = [1 3] x1 + [2]
                        [0 1]      [0]
                length(x1) = [3 0] x1 + [0]
                             [3 0]      [0]
                nil() = [3]
                        [3]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [3 0] x1 + [3 3] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                U52^#(x1) = [1 0] x1 + [0]
                            [3 3]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}->{7}->{8}: NA
             -----------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {1},
                 Uargs(U52^#) = {1}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 3] x1 + [1 0] x2 + [2]
                               [0 0]      [0 1]      [2]
                0() = [0]
                      [0]
                U11(x1) = [1 1] x1 + [0]
                          [0 0]      [3]
                tt() = [0]
                       [3]
                U21(x1) = [1 3] x1 + [0]
                          [0 0]      [3]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 0] x1 + [3 1] x2 + [3]
                              [0 0]      [1 0]      [0]
                U52(x1) = [1 0] x1 + [2]
                          [0 1]      [0]
                isNatList(x1) = [3 1] x1 + [0]
                                [1 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [3 2] x1 + [3]
                            [0 0]      [3]
                s(x1) = [1 0] x1 + [2]
                        [0 1]      [2]
                length(x1) = [0 0] x1 + [3]
                             [2 2]      [2]
                nil() = [3]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [3 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                U52^#(x1) = [3 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
    
    3) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:
           
             {  1: zeros^#() -> c_0(zeros^#())
              , 2: U11^#(tt()) -> c_1()
              , 3: U21^#(tt()) -> c_2()
              , 4: U31^#(tt()) -> c_3()
              , 5: U41^#(tt(), V2) -> c_4(U42^#(isNatIList(V2)))
              , 6: U42^#(tt()) -> c_5()
              , 7: U51^#(tt(), V2) -> c_6(U52^#(isNatList(V2)))
              , 8: U52^#(tt()) -> c_7()
              , 9: U61^#(tt(), L, N) -> c_8(U62^#(isNat(N), L))
              , 10: U62^#(tt(), L) -> c_9(length^#(L))
              , 11: isNat^#(0()) -> c_10()
              , 12: isNat^#(length(V1)) -> c_11(U11^#(isNatList(V1)))
              , 13: isNat^#(s(V1)) -> c_12(U21^#(isNat(V1)))
              , 14: isNatIList^#(V) -> c_13(U31^#(isNatList(V)))
              , 15: isNatIList^#(zeros()) -> c_14()
              , 16: isNatIList^#(cons(V1, V2)) -> c_15(U41^#(isNat(V1), V2))
              , 17: isNatList^#(nil()) -> c_16()
              , 18: isNatList^#(cons(V1, V2)) -> c_17(U51^#(isNat(V1), V2))
              , 19: length^#(nil()) -> c_18()
              , 20: length^#(cons(N, L)) -> c_19(U61^#(isNatList(L), L, N))}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{18}                                                      [         NA         ]
                |
                `->{7}                                                   [         NA         ]
                    |
                    `->{8}                                               [         NA         ]
             
             ->{17}                                                      [         NA         ]
             
             ->{16}                                                      [         NA         ]
                |
                `->{5}                                                   [         NA         ]
                    |
                    `->{6}                                               [         NA         ]
             
             ->{15}                                                      [         NA         ]
             
             ->{14}                                                      [         NA         ]
                |
                `->{4}                                                   [         NA         ]
             
             ->{13}                                                      [         NA         ]
                |
                `->{3}                                                   [         NA         ]
             
             ->{12}                                                      [         NA         ]
                |
                `->{2}                                                   [         NA         ]
             
             ->{11}                                                      [         NA         ]
             
             ->{9,20,10}                                                 [         NA         ]
                |
                `->{19}                                                  [         NA         ]
             
             ->{1}                                                       [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * Path {1}: MAYBE
             ---------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {1}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                U11(x1) = [0] x1 + [0]
                tt() = [0]
                U21(x1) = [0] x1 + [0]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [0] x1 + [0] x2 + [0]
                U52(x1) = [0] x1 + [0]
                isNatList(x1) = [0] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                length(x1) = [0] x1 + [0]
                nil() = [0]
                zeros^#() = [0]
                c_0(x1) = [1] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 1'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {zeros^#() -> c_0(zeros^#())}
               Weak Rules: {}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {9,20,10}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             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 {9,20,10}->{19}: NA
             ------------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {1}, Uargs(c_8) = {1},
                 Uargs(U62^#) = {1}, Uargs(c_9) = {1}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [1]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [2]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [2] x2 + [0]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [2] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [2] x1 + [0]
                s(x1) = [1] x1 + [1]
                length(x1) = [2] x1 + [2]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [3] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [1] x1 + [0]
                U62^#(x1, x2) = [3] x1 + [0] x2 + [0]
                c_9(x1) = [1] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [1] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                U11(x1) = [0] x1 + [0]
                tt() = [0]
                U21(x1) = [0] x1 + [0]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [0] x1 + [0] x2 + [0]
                U52(x1) = [0] x1 + [0]
                isNatList(x1) = [0] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                length(x1) = [0] x1 + [0]
                nil() = [0]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {12}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {1}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [2]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [2] x1 + [2] x2 + [0]
                U52(x1) = [1] x1 + [2]
                isNatList(x1) = [2] x1 + [1]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [1] x1 + [0]
                s(x1) = [1] x1 + [2]
                length(x1) = [2] x1 + [3]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [3] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [3] x1 + [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {12}->{2}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {1}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [2]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [2] x1 + [2] x2 + [0]
                U52(x1) = [1] x1 + [2]
                isNatList(x1) = [2] x1 + [1]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [1] x1 + [0]
                s(x1) = [1] x1 + [2]
                length(x1) = [2] x1 + [3]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [3] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {13}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {1},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {1},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [2]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [0]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [2] x2 + [2]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [2] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [2] x1 + [0]
                s(x1) = [1] x1 + [1]
                length(x1) = [2] x1 + [1]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [1] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [3] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [1] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {13}->{3}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {1},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {1},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [2]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [0]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [2] x2 + [2]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [2] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [2] x1 + [0]
                s(x1) = [1] x1 + [2]
                length(x1) = [2] x1 + [2]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [3] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [1] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {14}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {1}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {1}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [2]
                U11(x1) = [2] x1 + [3]
                tt() = [3]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [3] x2 + [0]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [3] x1 + [1]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [3] x1 + [0]
                s(x1) = [1] x1 + [3]
                length(x1) = [2] x1 + [3]
                nil() = [1]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [1] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [3] x1 + [0]
                c_13(x1) = [1] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {14}->{4}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {1}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {1}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [2]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [2] x1 + [2] x2 + [0]
                U52(x1) = [1] x1 + [2]
                isNatList(x1) = [2] x1 + [1]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [1] x1 + [0]
                s(x1) = [1] x1 + [2]
                length(x1) = [2] x1 + [3]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [3] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [1] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {15}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                U11(x1) = [0] x1 + [0]
                tt() = [0]
                U21(x1) = [0] x1 + [0]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [0] x1 + [0] x2 + [0]
                U52(x1) = [0] x1 + [0]
                isNatList(x1) = [0] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                length(x1) = [0] x1 + [0]
                nil() = [0]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [2]
                0() = [3]
                U11(x1) = [2] x1 + [1]
                tt() = [0]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [2] x2 + [2]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [2] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [2] x1 + [0]
                s(x1) = [1] x1 + [1]
                length(x1) = [2] x1 + [2]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [1] x1 + [3] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [3] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [1] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}->{5}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()
                , isNatIList(V) -> U31(isNatList(V))
                , isNatIList(zeros()) -> tt()
                , isNatIList(cons(V1, V2)) -> U41(isNat(V1), V2)
                , U31(tt()) -> tt()
                , U41(tt(), V2) -> U42(isNatIList(V2))
                , U42(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {1}, Uargs(U41) = {1}, Uargs(U42) = {1},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {1},
                 Uargs(U42^#) = {1}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [3]
                cons(x1, x2) = [1] x1 + [1] x2 + [3]
                0() = [1]
                U11(x1) = [1] x1 + [1]
                tt() = [2]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [2] x1 + [0]
                U41(x1, x2) = [2] x1 + [2] x2 + [1]
                U42(x1) = [1] x1 + [2]
                isNatIList(x1) = [2] x1 + [2]
                U51(x1, x2) = [1] x1 + [1] x2 + [0]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [1] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [1] x1 + [2]
                s(x1) = [1] x1 + [2]
                length(x1) = [1] x1 + [0]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_4(x1) = [1] x1 + [0]
                U42^#(x1) = [1] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [1] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}->{5}->{6}: NA
             -----------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()
                , isNatIList(V) -> U31(isNatList(V))
                , isNatIList(zeros()) -> tt()
                , isNatIList(cons(V1, V2)) -> U41(isNat(V1), V2)
                , U31(tt()) -> tt()
                , U41(tt(), V2) -> U42(isNatIList(V2))
                , U42(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {1}, Uargs(U41) = {1}, Uargs(U42) = {1},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {1},
                 Uargs(U42^#) = {1}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [3]
                cons(x1, x2) = [1] x1 + [1] x2 + [2]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [1]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [1] x1 + [1]
                U41(x1, x2) = [1] x1 + [2] x2 + [3]
                U42(x1) = [1] x1 + [1]
                isNatIList(x1) = [2] x1 + [2]
                U51(x1, x2) = [1] x1 + [2] x2 + [1]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [2] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [2] x1 + [0]
                s(x1) = [1] x1 + [1]
                length(x1) = [2] x1 + [2]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [3] x1 + [0] x2 + [0]
                c_4(x1) = [1] x1 + [0]
                U42^#(x1) = [3] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [1] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {17}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                U11(x1) = [0] x1 + [0]
                tt() = [0]
                U21(x1) = [0] x1 + [0]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [0] x1 + [0] x2 + [0]
                U52(x1) = [0] x1 + [0]
                isNatList(x1) = [0] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                length(x1) = [0] x1 + [0]
                nil() = [0]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [2]
                0() = [3]
                U11(x1) = [2] x1 + [1]
                tt() = [0]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [2] x2 + [2]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [2] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [2] x1 + [0]
                s(x1) = [1] x1 + [1]
                length(x1) = [2] x1 + [2]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [1] x1 + [3] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [3] x1 + [0]
                c_16() = [0]
                c_17(x1) = [1] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}->{7}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {1},
                 Uargs(U52^#) = {1}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [2]
                0() = [1]
                U11(x1) = [1] x1 + [1]
                tt() = [2]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [2] x2 + [0]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [2] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [1] x1 + [2]
                s(x1) = [1] x1 + [2]
                length(x1) = [2] x1 + [0]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_6(x1) = [1] x1 + [0]
                U52^#(x1) = [1] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [1] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}->{7}->{8}: NA
             -----------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {1},
                 Uargs(U52^#) = {1}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [3]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [0]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [1] x2 + [2]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [1] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [1] x1 + [0]
                s(x1) = [1] x1 + [2]
                length(x1) = [2] x1 + [2]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [3] x1 + [0] x2 + [0]
                c_6(x1) = [1] x1 + [0]
                U52^#(x1) = [3] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [1] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
    
    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
InputMaude 06 LengthOfFiniteLists nokinds-noand

stdout:

MAYBE

Tool RC2

Execution TimeUnknown
Answer
MAYBE
InputMaude 06 LengthOfFiniteLists nokinds-noand

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    runtime-complexity with respect to
  Rules:
    {  zeros() -> cons(0(), zeros())
     , U11(tt()) -> tt()
     , U21(tt()) -> tt()
     , U31(tt()) -> tt()
     , U41(tt(), V2) -> U42(isNatIList(V2))
     , U42(tt()) -> tt()
     , U51(tt(), V2) -> U52(isNatList(V2))
     , U52(tt()) -> tt()
     , U61(tt(), L, N) -> U62(isNat(N), L)
     , U62(tt(), L) -> s(length(L))
     , isNat(0()) -> tt()
     , isNat(length(V1)) -> U11(isNatList(V1))
     , isNat(s(V1)) -> U21(isNat(V1))
     , isNatIList(V) -> U31(isNatList(V))
     , isNatIList(zeros()) -> tt()
     , isNatIList(cons(V1, V2)) -> U41(isNat(V1), V2)
     , isNatList(nil()) -> tt()
     , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
     , length(nil()) -> 0()
     , length(cons(N, L)) -> U61(isNatList(L), L, 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: zeros^#() -> c_0(zeros^#())
              , 2: U11^#(tt()) -> c_1()
              , 3: U21^#(tt()) -> c_2()
              , 4: U31^#(tt()) -> c_3()
              , 5: U41^#(tt(), V2) -> c_4(U42^#(isNatIList(V2)))
              , 6: U42^#(tt()) -> c_5()
              , 7: U51^#(tt(), V2) -> c_6(U52^#(isNatList(V2)))
              , 8: U52^#(tt()) -> c_7()
              , 9: U61^#(tt(), L, N) -> c_8(U62^#(isNat(N), L))
              , 10: U62^#(tt(), L) -> c_9(length^#(L))
              , 11: isNat^#(0()) -> c_10()
              , 12: isNat^#(length(V1)) -> c_11(U11^#(isNatList(V1)))
              , 13: isNat^#(s(V1)) -> c_12(U21^#(isNat(V1)))
              , 14: isNatIList^#(V) -> c_13(U31^#(isNatList(V)))
              , 15: isNatIList^#(zeros()) -> c_14()
              , 16: isNatIList^#(cons(V1, V2)) -> c_15(U41^#(isNat(V1), V2))
              , 17: isNatList^#(nil()) -> c_16()
              , 18: isNatList^#(cons(V1, V2)) -> c_17(U51^#(isNat(V1), V2))
              , 19: length^#(nil()) -> c_18()
              , 20: length^#(cons(N, L)) -> c_19(U61^#(isNatList(L), L, N))}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{18}                                                      [         NA         ]
                |
                `->{7}                                                   [         NA         ]
                    |
                    `->{8}                                               [         NA         ]
             
             ->{17}                                                      [         NA         ]
             
             ->{16}                                                      [         NA         ]
                |
                `->{5}                                                   [         NA         ]
                    |
                    `->{6}                                               [         NA         ]
             
             ->{15}                                                      [         NA         ]
             
             ->{14}                                                      [         NA         ]
                |
                `->{4}                                                   [         NA         ]
             
             ->{13}                                                      [         NA         ]
                |
                `->{3}                                                   [         NA         ]
             
             ->{12}                                                      [         NA         ]
                |
                `->{2}                                                   [         NA         ]
             
             ->{11}                                                      [         NA         ]
             
             ->{9,20,10}                                                 [         NA         ]
                |
                `->{19}                                                  [         NA         ]
             
             ->{1}                                                       [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * Path {1}: MAYBE
             ---------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {1}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(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]
                U11(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(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]
                U52(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                length(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                nil() = [0]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 3'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {zeros^#() -> c_0(zeros^#())}
               Weak Rules: {}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {9,20,10}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {1}, Uargs(c_8) = {1},
                 Uargs(U62^#) = {1}, Uargs(c_9) = {1}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 0 0] x1 + [1 2 2] x2 + [0]
                               [0 1 3]      [0 1 3]      [2]
                               [0 0 1]      [0 0 1]      [2]
                0() = [0]
                      [2]
                      [0]
                U11(x1) = [2 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [2]
                tt() = [0]
                       [0]
                       [2]
                U21(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 0]      [2]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [2 0 2] x1 + [0 2 2] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [1 0 0]      [0 3 3]      [3]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [2]
                isNatList(x1) = [0 2 2] x1 + [0]
                                [0 0 0]      [0]
                                [0 3 0]      [2]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 2] x1 + [1]
                            [0 0 0]      [0]
                            [0 1 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 0 0]      [2]
                        [0 0 1]      [2]
                length(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [2]
                             [2 2 2]      [2]
                nil() = [0]
                        [0]
                        [2]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(x1, x2, x3) = [1 0 0] x1 + [1 0 2] x2 + [1 0 2] x3 + [0]
                                    [3 3 3]      [3 3 3]      [3 3 3]      [0]
                                    [3 3 3]      [3 3 3]      [3 3 3]      [0]
                c_8(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                U62^#(x1, x2) = [1 0 0] x1 + [1 0 2] x2 + [0]
                                [3 3 3]      [3 3 3]      [0]
                                [3 3 3]      [3 3 3]      [0]
                c_9(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                length^#(x1) = [1 0 2] x1 + [0]
                               [3 3 3]      [0]
                               [3 3 3]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {9,20,10}->{19}: NA
             ------------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {1}, Uargs(c_8) = {1},
                 Uargs(U62^#) = {1}, Uargs(c_9) = {1}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
                               [0 1 1]      [0 1 0]      [2]
                               [0 0 0]      [0 0 0]      [3]
                0() = [0]
                      [0]
                      [2]
                U11(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [1 0 0] x1 + [0 2 0] x2 + [3]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                U52(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [0 2 0] x1 + [0]
                                [0 0 3]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 2 2] x1 + [0]
                            [0 0 3]      [2]
                            [0 0 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 1 1]      [2]
                        [0 0 0]      [2]
                length(x1) = [0 0 0] x1 + [0]
                             [0 1 0]      [0]
                             [0 0 0]      [3]
                nil() = [0]
                        [2]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(x1, x2, x3) = [3 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_8(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                U62^#(x1, x2) = [3 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_9(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(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]
                U11(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(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]
                U52(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                length(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                nil() = [0]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {12}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {1}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [3]
                               [0 0 2]      [0 1 0]      [0]
                               [0 0 1]      [0 0 0]      [0]
                0() = [2]
                      [0]
                      [0]
                U11(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                tt() = [0]
                       [1]
                       [0]
                U21(x1) = [1 1 0] x1 + [0]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [1 2 0] x1 + [2 0 0] x2 + [2]
                              [0 0 0]      [1 1 0]      [1]
                              [0 0 0]      [0 2 0]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                isNatList(x1) = [2 0 0] x1 + [2]
                                [1 3 2]      [2]
                                [0 2 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [2 0 0] x1 + [0]
                            [0 0 0]      [1]
                            [0 0 0]      [0]
                s(x1) = [1 2 2] x1 + [2]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                length(x1) = [1 2 0] x1 + [2]
                             [2 2 0]      [0]
                             [0 0 0]      [0]
                nil() = [0]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [2 0 0] x1 + [0]
                            [3 3 3]      [0]
                            [3 3 3]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [2 2 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {12}->{2}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {1}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 2 2] x1 + [1 0 0] x2 + [0]
                               [0 0 3]      [0 1 2]      [0]
                               [0 0 0]      [0 0 0]      [2]
                0() = [0]
                      [3]
                      [3]
                U11(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [2]
                       [0]
                       [0]
                U21(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [2 0 0] x1 + [0 2 3] x2 + [0]
                              [3 0 0]      [0 3 0]      [2]
                              [0 0 0]      [0 0 3]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [0 2 1] x1 + [0]
                                [0 3 0]      [2]
                                [2 2 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 3] x1 + [0]
                            [0 0 0]      [0]
                            [2 3 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 1]      [1]
                length(x1) = [0 0 2] x1 + [0]
                             [0 0 0]      [0]
                             [0 2 2]      [2]
                nil() = [1]
                        [3]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [3 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {13}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {1},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {1},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 2 3] x1 + [1 0 0] x2 + [3]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 1]      [0 0 0]      [2]
                0() = [0]
                      [0]
                      [0]
                U11(x1) = [2 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [1 0 0] x1 + [2 0 0] x2 + [3]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [2 0 0] x1 + [0]
                                [2 0 2]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [2 0 2] x1 + [1]
                            [0 0 2]      [0]
                            [0 0 0]      [0]
                s(x1) = [1 2 1] x1 + [2]
                        [0 0 1]      [0]
                        [0 0 0]      [2]
                length(x1) = [0 0 0] x1 + [2]
                             [0 0 0]      [0]
                             [2 0 0]      [0]
                nil() = [1]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [1 0 0] x1 + [0]
                            [3 3 3]      [0]
                            [3 3 3]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [2 2 3] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {13}->{3}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {1},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {1},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
                               [0 1 3]      [0 1 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [1]
                U11(x1) = [1 0 0] x1 + [2]
                          [0 1 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [2]
                       [0]
                U21(x1) = [1 2 0] x1 + [0]
                          [0 0 0]      [2]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [1 2 0] x1 + [0 2 0] x2 + [0]
                              [0 2 0]      [1 2 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [1 0 0]      [2]
                          [0 0 0]      [0]
                isNatList(x1) = [0 2 0] x1 + [2]
                                [1 2 0]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 2 1] x1 + [0]
                            [0 0 2]      [0]
                            [0 0 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 1 2]      [0]
                        [0 0 1]      [1]
                length(x1) = [0 0 0] x1 + [0]
                             [3 1 0]      [3]
                             [2 2 0]      [0]
                nil() = [2]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [3 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {14}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {1}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {1}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 1 2] x1 + [1 2 0] x2 + [2]
                               [0 0 0]      [0 0 0]      [2]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [2]
                U11(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [1]
                tt() = [0]
                       [0]
                       [1]
                U21(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [1]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [1 0 3] x1 + [1 2 0] x2 + [3]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [1]
                U52(x1) = [1 3 1] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [1]
                isNatList(x1) = [1 2 0] x1 + [1]
                                [0 0 0]      [1]
                                [0 0 0]      [1]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 1] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [1]
                s(x1) = [1 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 1]      [2]
                length(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [1 2 0]      [3]
                nil() = [0]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [1 2 2] x1 + [0]
                            [3 3 3]      [0]
                            [3 3 3]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [3 3 3] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {14}->{4}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {1}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {1}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 2 2] x1 + [1 0 0] x2 + [0]
                               [0 0 3]      [0 1 2]      [0]
                               [0 0 0]      [0 0 0]      [2]
                0() = [0]
                      [3]
                      [3]
                U11(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [2]
                       [0]
                       [0]
                U21(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [2 0 0] x1 + [0 2 3] x2 + [0]
                              [3 0 0]      [0 3 0]      [2]
                              [0 0 0]      [0 0 3]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [0 2 1] x1 + [0]
                                [0 3 0]      [2]
                                [2 2 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 3] x1 + [0]
                            [0 0 0]      [0]
                            [2 3 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 1]      [1]
                length(x1) = [0 0 2] x1 + [0]
                             [0 0 0]      [0]
                             [0 2 2]      [2]
                nil() = [1]
                        [3]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [3 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {15}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(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]
                U11(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(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]
                U52(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                length(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                nil() = [0]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 3 0] x1 + [1 0 0] x2 + [1]
                               [0 1 2]      [0 1 0]      [1]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [2]
                      [0]
                U11(x1) = [2 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [2 0 0] x1 + [1 2 0] x2 + [2]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [1 2 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 2 0] x1 + [0]
                            [0 0 3]      [1]
                            [1 3 0]      [1]
                s(x1) = [1 1 0] x1 + [0]
                        [0 1 0]      [1]
                        [0 0 0]      [1]
                length(x1) = [2 0 0] x1 + [0]
                             [1 2 0]      [2]
                             [0 0 0]      [0]
                nil() = [0]
                        [2]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(x1, x2) = [1 0 2] x1 + [1 0 0] x2 + [0]
                                [3 3 3]      [3 3 3]      [0]
                                [3 3 3]      [3 3 3]      [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [3 0 3] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}->{5}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()
                , isNatIList(V) -> U31(isNatList(V))
                , isNatIList(zeros()) -> tt()
                , isNatIList(cons(V1, V2)) -> U41(isNat(V1), V2)
                , U31(tt()) -> tt()
                , U41(tt(), V2) -> U42(isNatIList(V2))
                , U42(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {1}, Uargs(U41) = {1}, Uargs(U42) = {1},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {1},
                 Uargs(U42^#) = {1}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [1]
                          [0]
                          [0]
                cons(x1, x2) = [1 3 3] x1 + [1 3 1] x2 + [3]
                               [0 1 3]      [0 0 1]      [1]
                               [0 0 1]      [0 0 0]      [3]
                0() = [0]
                      [0]
                      [0]
                U11(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [1]
                          [0 0 0]      [2]
                tt() = [0]
                       [1]
                       [2]
                U21(x1) = [1 0 1] x1 + [0]
                          [0 0 0]      [1]
                          [0 0 0]      [2]
                U31(x1) = [1 0 0] x1 + [1]
                          [0 0 2]      [0]
                          [0 0 1]      [0]
                U41(x1, x2) = [2 2 3] x1 + [1 3 3] x2 + [0]
                              [0 0 0]      [2 2 0]      [0]
                              [0 1 2]      [1 1 1]      [0]
                U42(x1) = [1 0 0] x1 + [2]
                          [0 1 0]      [0]
                          [0 0 0]      [2]
                isNatIList(x1) = [1 3 3] x1 + [3]
                                 [2 0 0]      [0]
                                 [1 1 1]      [1]
                U51(x1, x2) = [1 0 0] x1 + [1 3 1] x2 + [3]
                              [0 0 0]      [0 0 0]      [1]
                              [0 0 0]      [1 1 1]      [0]
                U52(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [1]
                          [0 0 1]      [0]
                isNatList(x1) = [1 0 1] x1 + [0]
                                [0 0 0]      [2]
                                [1 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 2] x1 + [2]
                            [0 3 0]      [2]
                            [0 0 0]      [3]
                s(x1) = [1 0 0] x1 + [0]
                        [0 1 0]      [3]
                        [0 0 1]      [2]
                length(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [2 0 2]      [1]
                nil() = [2]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(x1, x2) = [3 0 0] x1 + [3 3 3] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_4(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                U42^#(x1) = [1 0 0] x1 + [0]
                            [3 3 3]      [0]
                            [3 3 3]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}->{5}->{6}: NA
             -----------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()
                , isNatIList(V) -> U31(isNatList(V))
                , isNatIList(zeros()) -> tt()
                , isNatIList(cons(V1, V2)) -> U41(isNat(V1), V2)
                , U31(tt()) -> tt()
                , U41(tt(), V2) -> U42(isNatIList(V2))
                , U42(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {1}, Uargs(U41) = {1}, Uargs(U42) = {1},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {1},
                 Uargs(U42^#) = {1}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [1]
                          [0]
                          [0]
                cons(x1, x2) = [1 2 2] x1 + [1 3 0] x2 + [2]
                               [0 1 2]      [0 1 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [3]
                      [0]
                U11(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                tt() = [2]
                       [1]
                       [0]
                U21(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                U31(x1) = [1 1 0] x1 + [0]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                U41(x1, x2) = [2 1 0] x1 + [2 3 0] x2 + [0]
                              [0 1 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                U42(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                isNatIList(x1) = [2 3 0] x1 + [2]
                                 [0 0 0]      [1]
                                 [0 0 0]      [0]
                U51(x1, x2) = [2 0 0] x1 + [1 3 0] x2 + [0]
                              [0 0 0]      [1 3 0]      [1]
                              [0 0 0]      [0 0 0]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [1]
                          [0 0 0]      [0]
                isNatList(x1) = [1 1 0] x1 + [0]
                                [1 2 0]      [0]
                                [0 0 3]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 1 0] x1 + [0]
                            [0 0 0]      [1]
                            [0 0 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 1 0]      [3]
                        [0 0 0]      [0]
                length(x1) = [0 0 0] x1 + [0]
                             [2 2 0]      [2]
                             [0 0 0]      [0]
                nil() = [1]
                        [2]
                        [3]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(x1, x2) = [3 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_4(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                U42^#(x1) = [3 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {17}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(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]
                U11(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(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]
                U52(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                length(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                nil() = [0]
                        [0]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(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_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 3 0] x1 + [1 0 0] x2 + [1]
                               [0 1 2]      [0 1 0]      [1]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [2]
                      [0]
                U11(x1) = [2 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                tt() = [0]
                       [0]
                       [0]
                U21(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [2 0 0] x1 + [1 2 0] x2 + [2]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatList(x1) = [1 2 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 2 0] x1 + [0]
                            [0 0 3]      [1]
                            [1 3 0]      [1]
                s(x1) = [1 1 0] x1 + [0]
                        [0 1 0]      [1]
                        [0 0 0]      [1]
                length(x1) = [2 0 0] x1 + [0]
                             [1 2 0]      [2]
                             [0 0 0]      [0]
                nil() = [0]
                        [2]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(x1, x2) = [1 0 2] x1 + [1 0 0] x2 + [0]
                                [3 3 3]      [3 3 3]      [0]
                                [3 3 3]      [3 3 3]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U52^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [3 0 3] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}->{7}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {1},
                 Uargs(U52^#) = {1}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 0 3] x1 + [1 2 0] x2 + [1]
                               [0 1 3]      [0 0 0]      [0]
                               [0 0 1]      [0 0 1]      [0]
                0() = [2]
                      [2]
                      [0]
                U11(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [2]
                tt() = [0]
                       [0]
                       [2]
                U21(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 0]      [2]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [1 0 2] x1 + [2 3 1] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 1]      [1 2 0]      [2]
                U52(x1) = [1 0 0] x1 + [1]
                          [0 0 0]      [0]
                          [0 0 0]      [2]
                isNatList(x1) = [2 3 1] x1 + [0]
                                [0 0 0]      [0]
                                [1 0 0]      [2]
                U61(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]
                U62(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]
                isNat(x1) = [0 2 1] x1 + [0]
                            [0 0 3]      [0]
                            [1 0 0]      [0]
                s(x1) = [1 0 0] x1 + [2]
                        [0 1 0]      [2]
                        [0 0 1]      [0]
                length(x1) = [0 0 0] x1 + [2]
                             [2 0 0]      [3]
                             [0 3 3]      [3]
                nil() = [0]
                        [0]
                        [1]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(x1, x2) = [3 0 0] x1 + [3 3 3] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_6(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                U52^#(x1) = [1 2 0] x1 + [0]
                            [3 3 3]      [0]
                            [3 3 3]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}->{7}->{8}: NA
             -----------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {1},
                 Uargs(U52^#) = {1}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                          [0]
                cons(x1, x2) = [1 1 1] x1 + [1 0 0] x2 + [2]
                               [0 1 0]      [0 1 0]      [3]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                U11(x1) = [1 1 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 0]      [1]
                tt() = [0]
                       [0]
                       [1]
                U21(x1) = [1 0 1] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [1]
                U31(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U41(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]
                U42(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                isNatIList(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                U51(x1, x2) = [1 0 3] x1 + [1 3 0] x2 + [3]
                              [0 0 0]      [1 0 0]      [0]
                              [0 0 0]      [0 1 0]      [0]
                U52(x1) = [1 0 0] x1 + [2]
                          [0 0 0]      [0]
                          [0 0 1]      [0]
                isNatList(x1) = [1 3 0] x1 + [0]
                                [1 0 0]      [0]
                                [0 1 0]      [0]
                U61(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]
                U62(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]
                isNat(x1) = [0 3 1] x1 + [2]
                            [2 1 1]      [0]
                            [0 0 0]      [1]
                s(x1) = [1 2 3] x1 + [0]
                        [0 1 1]      [2]
                        [0 0 1]      [2]
                length(x1) = [0 2 3] x1 + [0]
                             [0 2 3]      [3]
                             [2 2 0]      [0]
                nil() = [0]
                        [1]
                        [0]
                zeros^#() = [0]
                            [0]
                            [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U11^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_1() = [0]
                        [0]
                        [0]
                U21^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                U31^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_3() = [0]
                        [0]
                        [0]
                U41^#(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U42^#(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_5() = [0]
                        [0]
                        [0]
                U51^#(x1, x2) = [3 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_6(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                U52^#(x1) = [3 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                c_7() = [0]
                        [0]
                        [0]
                U61^#(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                U62^#(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_9(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                length^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                isNat^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                c_10() = [0]
                         [0]
                         [0]
                c_11(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_12(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatIList^#(x1) = [0 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14() = [0]
                         [0]
                         [0]
                c_15(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                isNatList^#(x1) = [0 0 0] x1 + [0]
                                  [0 0 0]      [0]
                                  [0 0 0]      [0]
                c_16() = [0]
                         [0]
                         [0]
                c_17(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_18() = [0]
                         [0]
                         [0]
                c_19(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
    
    2) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:
           
             {  1: zeros^#() -> c_0(zeros^#())
              , 2: U11^#(tt()) -> c_1()
              , 3: U21^#(tt()) -> c_2()
              , 4: U31^#(tt()) -> c_3()
              , 5: U41^#(tt(), V2) -> c_4(U42^#(isNatIList(V2)))
              , 6: U42^#(tt()) -> c_5()
              , 7: U51^#(tt(), V2) -> c_6(U52^#(isNatList(V2)))
              , 8: U52^#(tt()) -> c_7()
              , 9: U61^#(tt(), L, N) -> c_8(U62^#(isNat(N), L))
              , 10: U62^#(tt(), L) -> c_9(length^#(L))
              , 11: isNat^#(0()) -> c_10()
              , 12: isNat^#(length(V1)) -> c_11(U11^#(isNatList(V1)))
              , 13: isNat^#(s(V1)) -> c_12(U21^#(isNat(V1)))
              , 14: isNatIList^#(V) -> c_13(U31^#(isNatList(V)))
              , 15: isNatIList^#(zeros()) -> c_14()
              , 16: isNatIList^#(cons(V1, V2)) -> c_15(U41^#(isNat(V1), V2))
              , 17: isNatList^#(nil()) -> c_16()
              , 18: isNatList^#(cons(V1, V2)) -> c_17(U51^#(isNat(V1), V2))
              , 19: length^#(nil()) -> c_18()
              , 20: length^#(cons(N, L)) -> c_19(U61^#(isNatList(L), L, N))}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{18}                                                      [         NA         ]
                |
                `->{7}                                                   [         NA         ]
                    |
                    `->{8}                                               [         NA         ]
             
             ->{17}                                                      [         NA         ]
             
             ->{16}                                                      [         NA         ]
                |
                `->{5}                                                   [         NA         ]
                    |
                    `->{6}                                               [         NA         ]
             
             ->{15}                                                      [         NA         ]
             
             ->{14}                                                      [         NA         ]
                |
                `->{4}                                                   [         NA         ]
             
             ->{13}                                                      [         NA         ]
                |
                `->{3}                                                   [         NA         ]
             
             ->{12}                                                      [         NA         ]
                |
                `->{2}                                                   [         NA         ]
             
             ->{11}                                                      [         NA         ]
             
             ->{9,20,10}                                                 [         NA         ]
                |
                `->{19}                                                  [         NA         ]
             
             ->{1}                                                       [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * Path {1}: MAYBE
             ---------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {1}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                U11(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                tt() = [0]
                       [0]
                U21(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U52(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatList(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                length(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {zeros^#() -> c_0(zeros^#())}
               Weak Rules: {}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {9,20,10}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {1}, Uargs(c_8) = {1},
                 Uargs(U62^#) = {1}, Uargs(c_9) = {1}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
                               [0 1]      [0 1]      [2]
                0() = [0]
                      [1]
                U11(x1) = [1 0] x1 + [1]
                          [0 0]      [1]
                tt() = [0]
                       [1]
                U21(x1) = [1 2] x1 + [0]
                          [0 0]      [1]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 0] x1 + [0 3] x2 + [2]
                              [0 0]      [0 0]      [1]
                U52(x1) = [1 0] x1 + [1]
                          [0 0]      [1]
                isNatList(x1) = [0 3] x1 + [0]
                                [0 0]      [1]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 3] x1 + [0]
                            [0 0]      [2]
                s(x1) = [1 0] x1 + [0]
                        [0 1]      [3]
                length(x1) = [0 0] x1 + [0]
                             [3 1]      [2]
                nil() = [0]
                        [3]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [2 0] x1 + [3 0] x2 + [1 3] x3 + [0]
                                    [3 3]      [3 3]      [3 3]      [0]
                c_8(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                U62^#(x1, x2) = [1 0] x1 + [3 0] x2 + [0]
                                [3 3]      [3 3]      [0]
                c_9(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                length^#(x1) = [3 0] x1 + [0]
                               [3 3]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {9,20,10}->{19}: NA
             ------------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {1}, Uargs(c_8) = {1},
                 Uargs(U62^#) = {1}, Uargs(c_9) = {1}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [3]
                0() = [0]
                      [0]
                U11(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                tt() = [0]
                       [0]
                U21(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [2 0] x1 + [0 2] x2 + [3]
                              [0 0]      [0 0]      [0]
                U52(x1) = [1 0] x1 + [2]
                          [0 0]      [0]
                isNatList(x1) = [0 2] x1 + [0]
                                [0 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 1] x1 + [1]
                            [2 0]      [0]
                s(x1) = [1 0] x1 + [0]
                        [0 1]      [2]
                length(x1) = [0 2] x1 + [0]
                             [0 2]      [3]
                nil() = [0]
                        [2]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [3 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                U62^#(x1, x2) = [3 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                U11(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                tt() = [0]
                       [0]
                U21(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U52(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatList(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                length(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {12}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {1}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 2] x1 + [1 2] x2 + [2]
                               [0 0]      [0 1]      [2]
                0() = [0]
                      [0]
                U11(x1) = [1 0] x1 + [1]
                          [0 0]      [1]
                tt() = [0]
                       [1]
                U21(x1) = [1 0] x1 + [1]
                          [0 0]      [1]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [2 3] x1 + [2 3] x2 + [3]
                              [0 1]      [0 0]      [0]
                U52(x1) = [1 3] x1 + [0]
                          [0 0]      [1]
                isNatList(x1) = [2 3] x1 + [1]
                                [0 0]      [1]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 0] x1 + [2]
                            [0 0]      [1]
                s(x1) = [1 0] x1 + [2]
                        [0 0]      [0]
                length(x1) = [3 3] x1 + [2]
                             [3 0]      [0]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [2 0] x1 + [0]
                            [3 3]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [3 3] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {12}->{2}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {1}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 1] x1 + [1 2] x2 + [0]
                               [0 0]      [0 1]      [3]
                0() = [2]
                      [0]
                U11(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                tt() = [1]
                       [0]
                U21(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 0] x1 + [2 3] x2 + [3]
                              [0 0]      [1 2]      [0]
                U52(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                isNatList(x1) = [2 1] x1 + [2]
                                [1 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 0] x1 + [1]
                            [0 0]      [0]
                s(x1) = [1 1] x1 + [2]
                        [0 0]      [0]
                length(x1) = [2 1] x1 + [3]
                             [0 0]      [0]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [3 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {13}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {1},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {1},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [3]
                0() = [0]
                      [0]
                U11(x1) = [2 2] x1 + [0]
                          [0 0]      [0]
                tt() = [1]
                       [0]
                U21(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 0] x1 + [0 3] x2 + [3]
                              [0 0]      [0 1]      [0]
                U52(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                isNatList(x1) = [0 3] x1 + [2]
                                [0 1]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 3] x1 + [2]
                            [2 0]      [0]
                s(x1) = [1 2] x1 + [0]
                        [0 1]      [2]
                length(x1) = [0 0] x1 + [0]
                             [0 3]      [1]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [1 0] x1 + [0]
                            [3 3]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 3] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {13}->{3}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {1},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {1},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [3]
                0() = [0]
                      [0]
                U11(x1) = [1 0] x1 + [2]
                          [0 0]      [0]
                tt() = [0]
                       [0]
                U21(x1) = [1 0] x1 + [2]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 2] x1 + [0 3] x2 + [2]
                              [0 0]      [0 0]      [0]
                U52(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                isNatList(x1) = [0 3] x1 + [0]
                                [0 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 3] x1 + [2]
                            [0 0]      [1]
                s(x1) = [1 0] x1 + [0]
                        [0 1]      [3]
                length(x1) = [0 0] x1 + [0]
                             [0 1]      [3]
                nil() = [0]
                        [3]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [3 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {14}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {1}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {1}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 0] x1 + [1 2] x2 + [0]
                               [0 1]      [0 1]      [3]
                0() = [0]
                      [0]
                U11(x1) = [3 0] x1 + [2]
                          [0 0]      [1]
                tt() = [0]
                       [1]
                U21(x1) = [1 0] x1 + [2]
                          [0 0]      [1]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 1] x1 + [2 3] x2 + [3]
                              [0 0]      [0 1]      [1]
                U52(x1) = [1 0] x1 + [1]
                          [0 1]      [0]
                isNatList(x1) = [2 3] x1 + [1]
                                [0 1]      [1]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [2 2] x1 + [1]
                            [0 0]      [1]
                s(x1) = [1 0] x1 + [2]
                        [0 1]      [0]
                length(x1) = [3 3] x1 + [2]
                             [0 3]      [2]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [1 0] x1 + [0]
                            [3 3]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [3 3] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {14}->{4}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {1}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {1}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 1] x1 + [1 2] x2 + [0]
                               [0 0]      [0 1]      [3]
                0() = [2]
                      [0]
                U11(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                tt() = [1]
                       [0]
                U21(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 0] x1 + [2 3] x2 + [3]
                              [0 0]      [1 2]      [0]
                U52(x1) = [1 0] x1 + [1]
                          [0 0]      [0]
                isNatList(x1) = [2 1] x1 + [2]
                                [1 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 0] x1 + [1]
                            [0 0]      [0]
                s(x1) = [1 1] x1 + [2]
                        [0 0]      [0]
                length(x1) = [2 1] x1 + [3]
                             [0 0]      [0]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [3 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {15}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                U11(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                tt() = [0]
                       [0]
                U21(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U52(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatList(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                length(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 3] x1 + [1 2] x2 + [3]
                               [0 1]      [0 1]      [0]
                0() = [0]
                      [0]
                U11(x1) = [1 0] x1 + [2]
                          [0 1]      [3]
                tt() = [0]
                       [1]
                U21(x1) = [1 0] x1 + [3]
                          [0 0]      [1]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 0] x1 + [1 3] x2 + [1]
                              [0 0]      [0 2]      [0]
                U52(x1) = [1 1] x1 + [0]
                          [0 1]      [0]
                isNatList(x1) = [1 1] x1 + [0]
                                [0 2]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 2] x1 + [1]
                            [1 0]      [1]
                s(x1) = [1 2] x1 + [2]
                        [0 1]      [3]
                length(x1) = [0 2] x1 + [2]
                             [2 3]      [2]
                nil() = [2]
                        [2]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [2 0] x1 + [1 0] x2 + [0]
                                [3 3]      [3 3]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [2 2] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}->{5}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()
                , isNatIList(V) -> U31(isNatList(V))
                , isNatIList(zeros()) -> tt()
                , isNatIList(cons(V1, V2)) -> U41(isNat(V1), V2)
                , U31(tt()) -> tt()
                , U41(tt(), V2) -> U42(isNatIList(V2))
                , U42(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {1}, Uargs(U41) = {1}, Uargs(U42) = {1},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {1},
                 Uargs(U42^#) = {1}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 1] x1 + [1 3] x2 + [3]
                               [0 1]      [0 1]      [0]
                0() = [0]
                      [2]
                U11(x1) = [1 0] x1 + [1]
                          [0 0]      [2]
                tt() = [0]
                       [2]
                U21(x1) = [1 2] x1 + [0]
                          [0 1]      [0]
                U31(x1) = [1 0] x1 + [2]
                          [0 0]      [2]
                U41(x1, x2) = [2 2] x1 + [3 3] x2 + [2]
                              [0 0]      [0 1]      [2]
                U42(x1) = [1 1] x1 + [0]
                          [0 1]      [0]
                isNatIList(x1) = [3 0] x1 + [3]
                                 [0 1]      [2]
                U51(x1, x2) = [1 2] x1 + [3 3] x2 + [0]
                              [0 0]      [2 0]      [2]
                U52(x1) = [1 0] x1 + [1]
                          [0 1]      [2]
                isNatList(x1) = [3 0] x1 + [0]
                                [2 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 0] x1 + [1]
                            [0 1]      [0]
                s(x1) = [1 2] x1 + [2]
                        [0 1]      [0]
                length(x1) = [3 0] x1 + [2]
                             [0 0]      [2]
                nil() = [2]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [3 0] x1 + [3 3] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                U42^#(x1) = [1 3] x1 + [0]
                            [3 3]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}->{5}->{6}: NA
             -----------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()
                , isNatIList(V) -> U31(isNatList(V))
                , isNatIList(zeros()) -> tt()
                , isNatIList(cons(V1, V2)) -> U41(isNat(V1), V2)
                , U31(tt()) -> tt()
                , U41(tt(), V2) -> U42(isNatIList(V2))
                , U42(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {1}, Uargs(U41) = {1}, Uargs(U42) = {1},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {1},
                 Uargs(U42^#) = {1}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [2]
                          [0]
                cons(x1, x2) = [1 3] x1 + [1 2] x2 + [2]
                               [0 1]      [0 0]      [2]
                0() = [0]
                      [1]
                U11(x1) = [1 0] x1 + [1]
                          [0 0]      [1]
                tt() = [1]
                       [1]
                U21(x1) = [1 1] x1 + [0]
                          [0 1]      [0]
                U31(x1) = [2 0] x1 + [0]
                          [0 0]      [1]
                U41(x1, x2) = [2 1] x1 + [2 3] x2 + [3]
                              [0 0]      [0 0]      [1]
                U42(x1) = [1 2] x1 + [0]
                          [0 0]      [1]
                isNatIList(x1) = [2 2] x1 + [1]
                                 [0 0]      [2]
                U51(x1, x2) = [1 0] x1 + [1 2] x2 + [1]
                              [0 0]      [0 0]      [1]
                U52(x1) = [1 1] x1 + [0]
                          [0 0]      [1]
                isNatList(x1) = [1 1] x1 + [0]
                                [0 0]      [1]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 0] x1 + [2]
                            [0 1]      [0]
                s(x1) = [1 1] x1 + [1]
                        [0 1]      [0]
                length(x1) = [2 2] x1 + [2]
                             [0 0]      [2]
                nil() = [2]
                        [2]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [3 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                U42^#(x1) = [3 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {17}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                U11(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                tt() = [0]
                       [0]
                U21(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U52(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatList(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                length(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                nil() = [0]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 3] x1 + [1 2] x2 + [3]
                               [0 1]      [0 1]      [0]
                0() = [0]
                      [0]
                U11(x1) = [1 0] x1 + [2]
                          [0 1]      [3]
                tt() = [0]
                       [1]
                U21(x1) = [1 0] x1 + [3]
                          [0 0]      [1]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 0] x1 + [1 3] x2 + [1]
                              [0 0]      [0 2]      [0]
                U52(x1) = [1 1] x1 + [0]
                          [0 1]      [0]
                isNatList(x1) = [1 1] x1 + [0]
                                [0 2]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 2] x1 + [1]
                            [1 0]      [1]
                s(x1) = [1 2] x1 + [2]
                        [0 1]      [3]
                length(x1) = [0 2] x1 + [2]
                             [2 3]      [2]
                nil() = [2]
                        [2]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [2 0] x1 + [1 0] x2 + [0]
                                [3 3]      [3 3]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U52^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [2 2] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}->{7}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {1},
                 Uargs(U52^#) = {1}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 2] x1 + [1 3] x2 + [3]
                               [0 0]      [0 0]      [1]
                0() = [1]
                      [0]
                U11(x1) = [2 0] x1 + [0]
                          [1 0]      [0]
                tt() = [2]
                       [2]
                U21(x1) = [1 0] x1 + [1]
                          [0 0]      [2]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 1] x1 + [3 3] x2 + [0]
                              [0 0]      [1 1]      [2]
                U52(x1) = [1 0] x1 + [1]
                          [0 0]      [2]
                isNatList(x1) = [3 0] x1 + [0]
                                [1 1]      [2]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [1 1] x1 + [2]
                            [1 0]      [1]
                s(x1) = [1 3] x1 + [2]
                        [0 1]      [0]
                length(x1) = [3 0] x1 + [0]
                             [3 0]      [0]
                nil() = [3]
                        [3]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [3 0] x1 + [3 3] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                U52^#(x1) = [1 0] x1 + [0]
                            [3 3]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}->{7}->{8}: NA
             -----------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {1},
                 Uargs(U52^#) = {1}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                          [0]
                cons(x1, x2) = [1 3] x1 + [1 0] x2 + [2]
                               [0 0]      [0 1]      [2]
                0() = [0]
                      [0]
                U11(x1) = [1 1] x1 + [0]
                          [0 0]      [3]
                tt() = [0]
                       [3]
                U21(x1) = [1 3] x1 + [0]
                          [0 0]      [3]
                U31(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U41(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                U42(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                isNatIList(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                U51(x1, x2) = [1 0] x1 + [3 1] x2 + [3]
                              [0 0]      [1 0]      [0]
                U52(x1) = [1 0] x1 + [2]
                          [0 1]      [0]
                isNatList(x1) = [3 1] x1 + [0]
                                [1 0]      [0]
                U61(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                U62(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                isNat(x1) = [3 2] x1 + [3]
                            [0 0]      [3]
                s(x1) = [1 0] x1 + [2]
                        [0 1]      [2]
                length(x1) = [0 0] x1 + [3]
                             [2 2]      [2]
                nil() = [3]
                        [0]
                zeros^#() = [0]
                            [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U11^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_1() = [0]
                        [0]
                U21^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_2() = [0]
                        [0]
                U31^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_3() = [0]
                        [0]
                U41^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U42^#(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                c_5() = [0]
                        [0]
                U51^#(x1, x2) = [3 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_6(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                U52^#(x1) = [3 0] x1 + [0]
                            [0 0]      [0]
                c_7() = [0]
                        [0]
                U61^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                    [0 0]      [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                U62^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_9(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                length^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                isNat^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatIList^#(x1) = [0 0] x1 + [0]
                                   [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14() = [0]
                         [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                isNatList^#(x1) = [0 0] x1 + [0]
                                  [0 0]      [0]
                c_16() = [0]
                         [0]
                c_17(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_18() = [0]
                         [0]
                c_19(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
    
    3) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:
           
             {  1: zeros^#() -> c_0(zeros^#())
              , 2: U11^#(tt()) -> c_1()
              , 3: U21^#(tt()) -> c_2()
              , 4: U31^#(tt()) -> c_3()
              , 5: U41^#(tt(), V2) -> c_4(U42^#(isNatIList(V2)))
              , 6: U42^#(tt()) -> c_5()
              , 7: U51^#(tt(), V2) -> c_6(U52^#(isNatList(V2)))
              , 8: U52^#(tt()) -> c_7()
              , 9: U61^#(tt(), L, N) -> c_8(U62^#(isNat(N), L))
              , 10: U62^#(tt(), L) -> c_9(length^#(L))
              , 11: isNat^#(0()) -> c_10()
              , 12: isNat^#(length(V1)) -> c_11(U11^#(isNatList(V1)))
              , 13: isNat^#(s(V1)) -> c_12(U21^#(isNat(V1)))
              , 14: isNatIList^#(V) -> c_13(U31^#(isNatList(V)))
              , 15: isNatIList^#(zeros()) -> c_14()
              , 16: isNatIList^#(cons(V1, V2)) -> c_15(U41^#(isNat(V1), V2))
              , 17: isNatList^#(nil()) -> c_16()
              , 18: isNatList^#(cons(V1, V2)) -> c_17(U51^#(isNat(V1), V2))
              , 19: length^#(nil()) -> c_18()
              , 20: length^#(cons(N, L)) -> c_19(U61^#(isNatList(L), L, N))}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{18}                                                      [         NA         ]
                |
                `->{7}                                                   [         NA         ]
                    |
                    `->{8}                                               [         NA         ]
             
             ->{17}                                                      [         NA         ]
             
             ->{16}                                                      [         NA         ]
                |
                `->{5}                                                   [         NA         ]
                    |
                    `->{6}                                               [         NA         ]
             
             ->{15}                                                      [         NA         ]
             
             ->{14}                                                      [         NA         ]
                |
                `->{4}                                                   [         NA         ]
             
             ->{13}                                                      [         NA         ]
                |
                `->{3}                                                   [         NA         ]
             
             ->{12}                                                      [         NA         ]
                |
                `->{2}                                                   [         NA         ]
             
             ->{11}                                                      [         NA         ]
             
             ->{9,20,10}                                                 [         NA         ]
                |
                `->{19}                                                  [         NA         ]
             
             ->{1}                                                       [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * Path {1}: MAYBE
             ---------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {1}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                U11(x1) = [0] x1 + [0]
                tt() = [0]
                U21(x1) = [0] x1 + [0]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [0] x1 + [0] x2 + [0]
                U52(x1) = [0] x1 + [0]
                isNatList(x1) = [0] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                length(x1) = [0] x1 + [0]
                nil() = [0]
                zeros^#() = [0]
                c_0(x1) = [1] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 1'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {zeros^#() -> c_0(zeros^#())}
               Weak Rules: {}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {9,20,10}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             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 {9,20,10}->{19}: NA
             ------------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {1}, Uargs(c_8) = {1},
                 Uargs(U62^#) = {1}, Uargs(c_9) = {1}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [1]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [2]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [2] x2 + [0]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [2] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [2] x1 + [0]
                s(x1) = [1] x1 + [1]
                length(x1) = [2] x1 + [2]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [3] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [1] x1 + [0]
                U62^#(x1, x2) = [3] x1 + [0] x2 + [0]
                c_9(x1) = [1] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [1] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                U11(x1) = [0] x1 + [0]
                tt() = [0]
                U21(x1) = [0] x1 + [0]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [0] x1 + [0] x2 + [0]
                U52(x1) = [0] x1 + [0]
                isNatList(x1) = [0] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                length(x1) = [0] x1 + [0]
                nil() = [0]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {12}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {1}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [2]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [2] x1 + [2] x2 + [0]
                U52(x1) = [1] x1 + [2]
                isNatList(x1) = [2] x1 + [1]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [1] x1 + [0]
                s(x1) = [1] x1 + [2]
                length(x1) = [2] x1 + [3]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [3] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [3] x1 + [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {12}->{2}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {1}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [2]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [2] x1 + [2] x2 + [0]
                U52(x1) = [1] x1 + [2]
                isNatList(x1) = [2] x1 + [1]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [1] x1 + [0]
                s(x1) = [1] x1 + [2]
                length(x1) = [2] x1 + [3]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [3] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {13}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {1},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {1},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [2]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [0]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [2] x2 + [2]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [2] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [2] x1 + [0]
                s(x1) = [1] x1 + [1]
                length(x1) = [2] x1 + [1]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [1] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [3] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [1] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {13}->{3}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {1},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {1},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [2]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [0]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [2] x2 + [2]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [2] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [2] x1 + [0]
                s(x1) = [1] x1 + [2]
                length(x1) = [2] x1 + [2]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [3] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [1] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {14}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {1}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {1}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [2]
                U11(x1) = [2] x1 + [3]
                tt() = [3]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [3] x2 + [0]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [3] x1 + [1]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [3] x1 + [0]
                s(x1) = [1] x1 + [3]
                length(x1) = [2] x1 + [3]
                nil() = [1]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [1] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [3] x1 + [0]
                c_13(x1) = [1] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {14}->{4}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {1}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {1}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [2]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [2] x1 + [2] x2 + [0]
                U52(x1) = [1] x1 + [2]
                isNatList(x1) = [2] x1 + [1]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [1] x1 + [0]
                s(x1) = [1] x1 + [2]
                length(x1) = [2] x1 + [3]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [3] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [1] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {15}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                U11(x1) = [0] x1 + [0]
                tt() = [0]
                U21(x1) = [0] x1 + [0]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [0] x1 + [0] x2 + [0]
                U52(x1) = [0] x1 + [0]
                isNatList(x1) = [0] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                length(x1) = [0] x1 + [0]
                nil() = [0]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [2]
                0() = [3]
                U11(x1) = [2] x1 + [1]
                tt() = [0]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [2] x2 + [2]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [2] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [2] x1 + [0]
                s(x1) = [1] x1 + [1]
                length(x1) = [2] x1 + [2]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [1] x1 + [3] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [3] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [1] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}->{5}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()
                , isNatIList(V) -> U31(isNatList(V))
                , isNatIList(zeros()) -> tt()
                , isNatIList(cons(V1, V2)) -> U41(isNat(V1), V2)
                , U31(tt()) -> tt()
                , U41(tt(), V2) -> U42(isNatIList(V2))
                , U42(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {1}, Uargs(U41) = {1}, Uargs(U42) = {1},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {1},
                 Uargs(U42^#) = {1}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [3]
                cons(x1, x2) = [1] x1 + [1] x2 + [3]
                0() = [1]
                U11(x1) = [1] x1 + [1]
                tt() = [2]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [2] x1 + [0]
                U41(x1, x2) = [2] x1 + [2] x2 + [1]
                U42(x1) = [1] x1 + [2]
                isNatIList(x1) = [2] x1 + [2]
                U51(x1, x2) = [1] x1 + [1] x2 + [0]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [1] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [1] x1 + [2]
                s(x1) = [1] x1 + [2]
                length(x1) = [1] x1 + [0]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_4(x1) = [1] x1 + [0]
                U42^#(x1) = [1] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [1] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {16}->{5}->{6}: NA
             -----------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()
                , isNatIList(V) -> U31(isNatList(V))
                , isNatIList(zeros()) -> tt()
                , isNatIList(cons(V1, V2)) -> U41(isNat(V1), V2)
                , U31(tt()) -> tt()
                , U41(tt(), V2) -> U42(isNatIList(V2))
                , U42(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {1}, Uargs(U41) = {1}, Uargs(U42) = {1},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {1}, Uargs(c_4) = {1},
                 Uargs(U42^#) = {1}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {1},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [3]
                cons(x1, x2) = [1] x1 + [1] x2 + [2]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [1]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [1] x1 + [1]
                U41(x1, x2) = [1] x1 + [2] x2 + [3]
                U42(x1) = [1] x1 + [1]
                isNatIList(x1) = [2] x1 + [2]
                U51(x1, x2) = [1] x1 + [2] x2 + [1]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [2] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [2] x1 + [0]
                s(x1) = [1] x1 + [1]
                length(x1) = [2] x1 + [2]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [3] x1 + [0] x2 + [0]
                c_4(x1) = [1] x1 + [0]
                U42^#(x1) = [3] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [1] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {17}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {}, Uargs(U21) = {},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {}, Uargs(U52) = {},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                U11(x1) = [0] x1 + [0]
                tt() = [0]
                U21(x1) = [0] x1 + [0]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [0] x1 + [0] x2 + [0]
                U52(x1) = [0] x1 + [0]
                isNatList(x1) = [0] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                length(x1) = [0] x1 + [0]
                nil() = [0]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [0] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}: NA
             -------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {},
                 Uargs(U52^#) = {}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [2]
                0() = [3]
                U11(x1) = [2] x1 + [1]
                tt() = [0]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [2] x2 + [2]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [2] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [2] x1 + [0]
                s(x1) = [1] x1 + [1]
                length(x1) = [2] x1 + [2]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [1] x1 + [3] x2 + [0]
                c_6(x1) = [0] x1 + [0]
                U52^#(x1) = [0] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [3] x1 + [0]
                c_16() = [0]
                c_17(x1) = [1] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}->{7}: NA
             ------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {1},
                 Uargs(U52^#) = {1}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [2]
                0() = [1]
                U11(x1) = [1] x1 + [1]
                tt() = [2]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [2] x2 + [0]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [2] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [1] x1 + [2]
                s(x1) = [1] x1 + [2]
                length(x1) = [2] x1 + [0]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_6(x1) = [1] x1 + [0]
                U52^#(x1) = [1] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [1] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}->{7}->{8}: NA
             -----------------------
             
             The usable rules for this path are:
             
               {  isNat(0()) -> tt()
                , isNat(length(V1)) -> U11(isNatList(V1))
                , isNat(s(V1)) -> U21(isNat(V1))
                , U11(tt()) -> tt()
                , U21(tt()) -> tt()
                , isNatList(nil()) -> tt()
                , isNatList(cons(V1, V2)) -> U51(isNat(V1), V2)
                , U51(tt(), V2) -> U52(isNatList(V2))
                , U52(tt()) -> tt()}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(U11) = {1}, Uargs(U21) = {1},
                 Uargs(U31) = {}, Uargs(U41) = {}, Uargs(U42) = {},
                 Uargs(isNatIList) = {}, Uargs(U51) = {1}, Uargs(U52) = {1},
                 Uargs(isNatList) = {}, Uargs(U61) = {}, Uargs(U62) = {},
                 Uargs(isNat) = {}, Uargs(s) = {}, Uargs(length) = {},
                 Uargs(c_0) = {}, Uargs(U11^#) = {}, Uargs(U21^#) = {},
                 Uargs(U31^#) = {}, Uargs(U41^#) = {}, Uargs(c_4) = {},
                 Uargs(U42^#) = {}, Uargs(U51^#) = {1}, Uargs(c_6) = {1},
                 Uargs(U52^#) = {1}, Uargs(U61^#) = {}, Uargs(c_8) = {},
                 Uargs(U62^#) = {}, Uargs(c_9) = {}, Uargs(length^#) = {},
                 Uargs(isNat^#) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(isNatIList^#) = {}, Uargs(c_13) = {}, Uargs(c_15) = {},
                 Uargs(isNatList^#) = {}, Uargs(c_17) = {1}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                zeros() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [3]
                0() = [3]
                U11(x1) = [1] x1 + [1]
                tt() = [0]
                U21(x1) = [1] x1 + [1]
                U31(x1) = [0] x1 + [0]
                U41(x1, x2) = [0] x1 + [0] x2 + [0]
                U42(x1) = [0] x1 + [0]
                isNatIList(x1) = [0] x1 + [0]
                U51(x1, x2) = [1] x1 + [1] x2 + [2]
                U52(x1) = [1] x1 + [1]
                isNatList(x1) = [1] x1 + [0]
                U61(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                U62(x1, x2) = [0] x1 + [0] x2 + [0]
                isNat(x1) = [1] x1 + [0]
                s(x1) = [1] x1 + [2]
                length(x1) = [2] x1 + [2]
                nil() = [3]
                zeros^#() = [0]
                c_0(x1) = [0] x1 + [0]
                U11^#(x1) = [0] x1 + [0]
                c_1() = [0]
                U21^#(x1) = [0] x1 + [0]
                c_2() = [0]
                U31^#(x1) = [0] x1 + [0]
                c_3() = [0]
                U41^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_4(x1) = [0] x1 + [0]
                U42^#(x1) = [0] x1 + [0]
                c_5() = [0]
                U51^#(x1, x2) = [3] x1 + [0] x2 + [0]
                c_6(x1) = [1] x1 + [0]
                U52^#(x1) = [3] x1 + [0]
                c_7() = [0]
                U61^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_8(x1) = [0] x1 + [0]
                U62^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9(x1) = [0] x1 + [0]
                length^#(x1) = [0] x1 + [0]
                isNat^#(x1) = [0] x1 + [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                isNatIList^#(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14() = [0]
                c_15(x1) = [0] x1 + [0]
                isNatList^#(x1) = [0] x1 + [0]
                c_16() = [0]
                c_17(x1) = [1] x1 + [0]
                c_18() = [0]
                c_19(x1) = [0] x1 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
    
    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.