Problem Strategy outermost added 08 Ex3 3 25 Bor03 Z

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Strategy outermost added 08 Ex3 3 25 Bor03 Z

stdout:

MAYBE

Problem:
app(nil(),YS) -> YS
app(cons(X,XS),YS) -> cons(X,n__app(activate(XS),YS))
from(X) -> cons(X,n__from(s(X)))
zWadr(nil(),YS) -> nil()
zWadr(XS,nil()) -> nil()
zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,n__nil())),n__zWadr(activate(XS),activate(YS)))
prefix(L) -> cons(nil(),n__zWadr(L,prefix(L)))
app(X1,X2) -> n__app(X1,X2)
from(X) -> n__from(X)
nil() -> n__nil()
zWadr(X1,X2) -> n__zWadr(X1,X2)
activate(n__app(X1,X2)) -> app(X1,X2)
activate(n__from(X)) -> from(X)
activate(n__nil()) -> nil()
activate(n__zWadr(X1,X2)) -> zWadr(X1,X2)
activate(X) -> X

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Strategy outermost added 08 Ex3 3 25 Bor03 Z

stdout:

MAYBE
Warning when parsing problem:

Unsupported strategy 'OUTERMOST'

Tool IRC2

Execution Time	Unknown
Answer	MAYBE
Input	Strategy outermost added 08 Ex3 3 25 Bor03 Z

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  app(nil(), YS) -> YS
     , app(cons(X, XS), YS) -> cons(X, n__app(activate(XS), YS))
     , from(X) -> cons(X, n__from(s(X)))
     , zWadr(nil(), YS) -> nil()
     , zWadr(XS, nil()) -> nil()
     , zWadr(cons(X, XS), cons(Y, YS)) ->
       cons(app(Y, cons(X, n__nil())),
            n__zWadr(activate(XS), activate(YS)))
     , prefix(L) -> cons(nil(), n__zWadr(L, prefix(L)))
     , app(X1, X2) -> n__app(X1, X2)
     , from(X) -> n__from(X)
     , nil() -> n__nil()
     , zWadr(X1, X2) -> n__zWadr(X1, X2)
     , activate(n__app(X1, X2)) -> app(X1, X2)
     , activate(n__from(X)) -> from(X)
     , activate(n__nil()) -> nil()
     , activate(n__zWadr(X1, X2)) -> zWadr(X1, X2)
     , activate(X) -> X}

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: app^#(nil(), YS) -> c_0()
              , 2: app^#(cons(X, XS), YS) -> c_1(activate^#(XS))
              , 3: from^#(X) -> c_2()
              , 4: zWadr^#(nil(), YS) -> c_3(nil^#())
              , 5: zWadr^#(XS, nil()) -> c_4(nil^#())
              , 6: zWadr^#(cons(X, XS), cons(Y, YS)) ->
                   c_5(app^#(Y, cons(X, n__nil())), activate^#(XS), activate^#(YS))
              , 7: prefix^#(L) -> c_6(nil^#(), prefix^#(L))
              , 8: app^#(X1, X2) -> c_7()
              , 9: from^#(X) -> c_8()
              , 10: nil^#() -> c_9()
              , 11: zWadr^#(X1, X2) -> c_10()
              , 12: activate^#(n__app(X1, X2)) -> c_11(app^#(X1, X2))
              , 13: activate^#(n__from(X)) -> c_12(from^#(X))
              , 14: activate^#(n__nil()) -> c_13(nil^#())
              , 15: activate^#(n__zWadr(X1, X2)) -> c_14(zWadr^#(X1, X2))
              , 16: activate^#(X) -> c_15()}

           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)

             ->{7}                                                       [       MAYBE        ]
                |
                `->{10}                                                  [         NA         ]

             ->{2,12,6,15}                                               [         NA         ]
                |
                |->{1}                                                   [         NA         ]
                |
                |->{4}                                                   [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{5}                                                   [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{8}                                                   [         NA         ]
                |
                |->{11}                                                  [         NA         ]
                |
                |->{13}                                                  [         NA         ]
                |   |
                |   |->{3}                                               [         NA         ]
                |   |
                |   `->{9}                                               [         NA         ]
                |
                |->{14}                                                  [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                `->{16}                                                  [         NA         ]



         Sub-problems:
         -------------
           * Path {2,12,6,15}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [0]
                        [0]
                        [0]
                cons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                n__app(x1, x2) = [1 3 3] x1 + [1 0 0] x2 + [0]
                                 [0 1 3]      [0 0 0]      [0]
                                 [0 0 1]      [0 0 0]      [0]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
                                   [0 0 0]      [0 0 0]      [0]
                                   [0 0 0]      [0 0 0]      [0]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [3 3 3]      [3 3 3]      [0]
                                [3 3 3]      [3 3 3]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [3 3 3]      [0]
                                 [3 3 3]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                  [3 3 3]      [3 3 3]      [0]
                                  [3 3 3]      [3 3 3]      [0]
                c_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15() = [0]
                         [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{1}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15() = [0]
                         [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{4}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15() = [0]
                         [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{4}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {1}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(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_3(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15() = [0]
                         [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{5}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15() = [0]
                         [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{5}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {1}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15() = [0]
                         [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{8}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15() = [0]
                         [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15() = [0]
                         [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{13}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(x1) = [1 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 1]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [3 0 0] x1 + [0]
                             [3 0 0]      [0]
                             [3 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15() = [0]
                         [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{13}->{3}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {1}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15() = [0]
                         [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{13}->{9}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {1}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15() = [0]
                         [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{14}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15() = [0]
                         [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{14}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {1}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15() = [0]
                         [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{16}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15() = [0]
                         [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {7}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {2}, Uargs(c_11) = {},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(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]
                prefix^#(x1) = [3 3 3] x1 + [0]
                               [3 3 3]      [0]
                               [3 3 3]      [0]
                c_6(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
                              [0 0 0]      [0 1 0]      [0]
                              [0 0 0]      [0 0 1]      [0]
                c_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_15() = [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: {prefix^#(L) -> c_6(nil^#(), prefix^#(L))}
               Weak Rules: {}

             Proof Output:
               The input cannot be shown compatible

           * Path {7}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {1, 2}, Uargs(c_11) = {},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0() = [0]
                        [0]
                        [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2() = [0]
                        [0]
                        [0]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(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]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
                              [0 1 0]      [0 1 0]      [0]
                              [0 0 1]      [0 0 1]      [0]
                c_7() = [0]
                        [0]
                        [0]
                c_8() = [0]
                        [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]

             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: app^#(nil(), YS) -> c_0()
              , 2: app^#(cons(X, XS), YS) -> c_1(activate^#(XS))
              , 3: from^#(X) -> c_2()
              , 4: zWadr^#(nil(), YS) -> c_3(nil^#())
              , 5: zWadr^#(XS, nil()) -> c_4(nil^#())
              , 6: zWadr^#(cons(X, XS), cons(Y, YS)) ->
                   c_5(app^#(Y, cons(X, n__nil())), activate^#(XS), activate^#(YS))
              , 7: prefix^#(L) -> c_6(nil^#(), prefix^#(L))
              , 8: app^#(X1, X2) -> c_7()
              , 9: from^#(X) -> c_8()
              , 10: nil^#() -> c_9()
              , 11: zWadr^#(X1, X2) -> c_10()
              , 12: activate^#(n__app(X1, X2)) -> c_11(app^#(X1, X2))
              , 13: activate^#(n__from(X)) -> c_12(from^#(X))
              , 14: activate^#(n__nil()) -> c_13(nil^#())
              , 15: activate^#(n__zWadr(X1, X2)) -> c_14(zWadr^#(X1, X2))
              , 16: activate^#(X) -> c_15()}

           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)

             ->{7}                                                       [       MAYBE        ]
                |
                `->{10}                                                  [         NA         ]

             ->{2,12,6,15}                                               [         NA         ]
                |
                |->{1}                                                   [         NA         ]
                |
                |->{4}                                                   [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{5}                                                   [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{8}                                                   [         NA         ]
                |
                |->{11}                                                  [         NA         ]
                |
                |->{13}                                                  [         NA         ]
                |   |
                |   |->{3}                                               [         NA         ]
                |   |
                |   `->{9}                                               [         NA         ]
                |
                |->{14}                                                  [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                `->{16}                                                  [         NA         ]



         Sub-problems:
         -------------
           * Path {2,12,6,15}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [1 3] x1 + [1 0] x2 + [0]
                                 [0 1]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [3 3]      [3 3]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [3 3]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [3 3]      [3 3]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15() = [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{1}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15() = [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{4}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15() = [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{4}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {1}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15() = [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{5}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15() = [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{5}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {1}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15() = [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{8}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15() = [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15() = [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{13}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [1 1] x1 + [0]
                              [0 1]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                activate^#(x1) = [1 3] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [3 0] x1 + [0]
                             [3 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15() = [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{13}->{3}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {1}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [0]
                        [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15() = [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{13}->{9}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {1}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [0]
                        [0]
                c_10() = [0]
                         [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15() = [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{14}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15() = [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{14}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {1}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15() = [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{16}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15() = [0]
                         [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {7}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {2}, Uargs(c_11) = {},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                prefix^#(x1) = [3 3] x1 + [0]
                               [3 3]      [0]
                c_6(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                              [0 0]      [0 1]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_15() = [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: {prefix^#(L) -> c_6(nil^#(), prefix^#(L))}
               Weak Rules: {}

             Proof Output:
               The input cannot be shown compatible

           * Path {7}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {1, 2}, Uargs(c_11) = {},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0() = [0]
                        [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2() = [0]
                        [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                              [0 1]      [0 1]      [0]
                c_7() = [0]
                        [0]
                c_8() = [0]
                        [0]
                c_9() = [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]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_15() = [0]
                         [0]

             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: app^#(nil(), YS) -> c_0()
              , 2: app^#(cons(X, XS), YS) -> c_1(activate^#(XS))
              , 3: from^#(X) -> c_2()
              , 4: zWadr^#(nil(), YS) -> c_3(nil^#())
              , 5: zWadr^#(XS, nil()) -> c_4(nil^#())
              , 6: zWadr^#(cons(X, XS), cons(Y, YS)) ->
                   c_5(app^#(Y, cons(X, n__nil())), activate^#(XS), activate^#(YS))
              , 7: prefix^#(L) -> c_6(nil^#(), prefix^#(L))
              , 8: app^#(X1, X2) -> c_7()
              , 9: from^#(X) -> c_8()
              , 10: nil^#() -> c_9()
              , 11: zWadr^#(X1, X2) -> c_10()
              , 12: activate^#(n__app(X1, X2)) -> c_11(app^#(X1, X2))
              , 13: activate^#(n__from(X)) -> c_12(from^#(X))
              , 14: activate^#(n__nil()) -> c_13(nil^#())
              , 15: activate^#(n__zWadr(X1, X2)) -> c_14(zWadr^#(X1, X2))
              , 16: activate^#(X) -> c_15()}

           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)

             ->{7}                                                       [       MAYBE        ]
                |
                `->{10}                                                  [         NA         ]

             ->{2,12,6,15}                                               [         NA         ]
                |
                |->{1}                                                   [         NA         ]
                |
                |->{4}                                                   [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{5}                                                   [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{8}                                                   [         NA         ]
                |
                |->{11}                                                  [         NA         ]
                |
                |->{13}                                                  [         NA         ]
                |   |
                |   |->{3}                                               [         NA         ]
                |   |
                |   `->{9}                                               [         NA         ]
                |
                |->{14}                                                  [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                `->{16}                                                  [         NA         ]



         Sub-problems:
         -------------
           * Path {2,12,6,15}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                n__app(x1, x2) = [1] x1 + [1] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [1] x1 + [1] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [1] x1 + [3] x2 + [0]
                c_0() = [0]
                c_1(x1) = [1] x1 + [0]
                activate^#(x1) = [3] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15() = [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{1}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0() = [0]
                c_1(x1) = [1] x1 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15() = [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{4}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0() = [0]
                c_1(x1) = [1] x1 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15() = [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{4}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {1}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0() = [0]
                c_1(x1) = [1] x1 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [1] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15() = [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{5}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0() = [0]
                c_1(x1) = [1] x1 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15() = [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{5}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {1}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0() = [0]
                c_1(x1) = [1] x1 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [1] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15() = [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{8}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0() = [0]
                c_1(x1) = [1] x1 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15() = [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0() = [0]
                c_1(x1) = [1] x1 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15() = [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{13}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [1] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0() = [0]
                c_1(x1) = [1] x1 + [0]
                activate^#(x1) = [3] x1 + [0]
                from^#(x1) = [1] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [3] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15() = [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{13}->{3}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {1}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0() = [0]
                c_1(x1) = [1] x1 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [1] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15() = [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{13}->{9}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {1}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0() = [0]
                c_1(x1) = [1] x1 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [1] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15() = [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{14}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0() = [0]
                c_1(x1) = [1] x1 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15() = [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{14}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {1}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0() = [0]
                c_1(x1) = [1] x1 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [1] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15() = [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{16}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {1},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {}, Uargs(c_11) = {1},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0() = [0]
                c_1(x1) = [1] x1 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15() = [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {7}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {2}, Uargs(c_11) = {},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0() = [0]
                c_1(x1) = [0] x1 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                prefix^#(x1) = [3] x1 + [0]
                c_6(x1, x2) = [0] x1 + [1] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                c_15() = [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: {prefix^#(L) -> c_6(nil^#(), prefix^#(L))}
               Weak Rules: {}

             Proof Output:
               The input cannot be shown compatible

           * Path {7}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_1) = {},
                 Uargs(activate^#) = {}, Uargs(from^#) = {}, Uargs(zWadr^#) = {},
                 Uargs(c_3) = {}, Uargs(c_4) = {}, Uargs(c_5) = {},
                 Uargs(prefix^#) = {}, Uargs(c_6) = {1, 2}, Uargs(c_11) = {},
                 Uargs(c_12) = {}, Uargs(c_13) = {}, Uargs(c_14) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0() = [0]
                c_1(x1) = [0] x1 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2() = [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2) = [1] x1 + [1] x2 + [0]
                c_7() = [0]
                c_8() = [0]
                c_9() = [0]
                c_10() = [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                c_15() = [0]

             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 Time	Unknown
Answer	MAYBE
Input	Strategy outermost added 08 Ex3 3 25 Bor03 Z

stdout:

MAYBE
Warning when parsing problem:

Unsupported strategy 'OUTERMOST'

Tool RC2

Execution Time	Unknown
Answer	MAYBE
Input	Strategy outermost added 08 Ex3 3 25 Bor03 Z

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    runtime-complexity with respect to
  Rules:
    {  app(nil(), YS) -> YS
     , app(cons(X, XS), YS) -> cons(X, n__app(activate(XS), YS))
     , from(X) -> cons(X, n__from(s(X)))
     , zWadr(nil(), YS) -> nil()
     , zWadr(XS, nil()) -> nil()
     , zWadr(cons(X, XS), cons(Y, YS)) ->
       cons(app(Y, cons(X, n__nil())),
            n__zWadr(activate(XS), activate(YS)))
     , prefix(L) -> cons(nil(), n__zWadr(L, prefix(L)))
     , app(X1, X2) -> n__app(X1, X2)
     , from(X) -> n__from(X)
     , nil() -> n__nil()
     , zWadr(X1, X2) -> n__zWadr(X1, X2)
     , activate(n__app(X1, X2)) -> app(X1, X2)
     , activate(n__from(X)) -> from(X)
     , activate(n__nil()) -> nil()
     , activate(n__zWadr(X1, X2)) -> zWadr(X1, X2)
     , activate(X) -> X}

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: app^#(nil(), YS) -> c_0(YS)
              , 2: app^#(cons(X, XS), YS) -> c_1(X, activate^#(XS), YS)
              , 3: from^#(X) -> c_2(X, X)
              , 4: zWadr^#(nil(), YS) -> c_3(nil^#())
              , 5: zWadr^#(XS, nil()) -> c_4(nil^#())
              , 6: zWadr^#(cons(X, XS), cons(Y, YS)) ->
                   c_5(app^#(Y, cons(X, n__nil())), activate^#(XS), activate^#(YS))
              , 7: prefix^#(L) -> c_6(nil^#(), L, prefix^#(L))
              , 8: app^#(X1, X2) -> c_7(X1, X2)
              , 9: from^#(X) -> c_8(X)
              , 10: nil^#() -> c_9()
              , 11: zWadr^#(X1, X2) -> c_10(X1, X2)
              , 12: activate^#(n__app(X1, X2)) -> c_11(app^#(X1, X2))
              , 13: activate^#(n__from(X)) -> c_12(from^#(X))
              , 14: activate^#(n__nil()) -> c_13(nil^#())
              , 15: activate^#(n__zWadr(X1, X2)) -> c_14(zWadr^#(X1, X2))
              , 16: activate^#(X) -> c_15(X)}

           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)

             ->{7}                                                       [       MAYBE        ]
                |
                `->{10}                                                  [         NA         ]

             ->{2,12,6,15}                                               [         NA         ]
                |
                |->{1}                                                   [         NA         ]
                |
                |->{4}                                                   [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{5}                                                   [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{8}                                                   [         NA         ]
                |
                |->{11}                                                  [         NA         ]
                |
                |->{13}                                                  [         NA         ]
                |   |
                |   |->{3}                                               [         NA         ]
                |   |
                |   `->{9}                                               [         NA         ]
                |
                |->{14}                                                  [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                `->{16}                                                  [         NA         ]



         Sub-problems:
         -------------
           * Path {2,12,6,15}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [0]
                        [0]
                        [0]
                cons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
                               [0 1 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                n__app(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(x1, x2) = [1 2 0] x1 + [1 0 0] x2 + [0]
                                   [0 0 0]      [0 0 0]      [0]
                                   [0 0 0]      [0 0 0]      [0]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [2 0 0] x1 + [0 0 0] x2 + [0]
                                [3 3 3]      [3 3 3]      [0]
                                [3 3 3]      [3 3 3]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, x2, x3) = [0 0 0] x1 + [1 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 1 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 1]      [0 0 0]      [0]
                activate^#(x1) = [2 0 0] x1 + [0]
                                 [3 3 3]      [0]
                                 [3 3 3]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2(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]
                zWadr^#(x1, x2) = [2 1 0] x1 + [2 0 0] x2 + [0]
                                  [3 3 3]      [3 3 3]      [0]
                                  [3 3 3]      [3 3 3]      [0]
                c_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                c_10(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_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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15(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 {2,12,6,15}->{1}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [3 3 3] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [1 1 1] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, x2, x3) = [0 0 0] x1 + [1 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 1 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 1]      [0 0 0]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2(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]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                c_10(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_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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15(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 {2,12,6,15}->{4}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, x2, x3) = [0 0 0] x1 + [1 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 1 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 1]      [0 0 0]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2(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]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                c_10(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_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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15(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 {2,12,6,15}->{4}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {1},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, x2, x3) = [0 0 0] x1 + [1 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 1 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 1]      [0 0 0]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2(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]
                zWadr^#(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_3(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                c_10(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_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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15(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 {2,12,6,15}->{5}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, x2, x3) = [0 0 0] x1 + [1 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 1 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 1]      [0 0 0]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2(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]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                c_10(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_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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15(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 {2,12,6,15}->{5}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {1}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, x2, x3) = [0 0 0] x1 + [1 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 1 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 1]      [0 0 0]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2(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]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                c_10(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_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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15(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 {2,12,6,15}->{8}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [3 3 3] x1 + [3 3 3] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, x2, x3) = [0 0 0] x1 + [1 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 1 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 1]      [0 0 0]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2(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]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7(x1, x2) = [1 1 1] x1 + [1 1 1] x2 + [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]
                c_9() = [0]
                        [0]
                        [0]
                c_10(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_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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15(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 {2,12,6,15}->{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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, x2, x3) = [0 0 0] x1 + [1 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 1 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 1]      [0 0 0]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2(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]
                zWadr^#(x1, x2) = [3 3 3] x1 + [3 3 3] x2 + [0]
                                  [0 0 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 0]      [0]
                c_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                c_10(x1, x2) = [1 1 1] x1 + [1 1 1] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15(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 {2,12,6,15}->{13}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(x1) = [1 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 1]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, x2, x3) = [0 0 0] x1 + [1 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 1 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 1]      [0 0 0]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [3 0 0] x1 + [0]
                             [3 0 0]      [0]
                             [3 0 0]      [0]
                c_2(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]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                c_10(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_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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15(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 {2,12,6,15}->{13}->{3}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {1},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, x2, x3) = [0 0 0] x1 + [1 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 1 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 1]      [0 0 0]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [3 3 3] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2(x1, x2) = [2 0 1] x1 + [1 3 1] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                c_10(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_11(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_12(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15(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 {2,12,6,15}->{13}->{9}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {1},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, x2, x3) = [0 0 0] x1 + [1 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 1 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 1]      [0 0 0]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [3 3 3] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2(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]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7(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_8(x1) = [1 1 1] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                c_10(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_11(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_12(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15(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 {2,12,6,15}->{14}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, x2, x3) = [0 0 0] x1 + [1 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 1 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 1]      [0 0 0]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2(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]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                c_10(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_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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15(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 {2,12,6,15}->{14}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {1}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, x2, x3) = [0 0 0] x1 + [1 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 1 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 1]      [0 0 0]      [0]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2(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]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                c_10(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_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]
                c_13(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15(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 {2,12,6,15}->{16}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, x2, x3) = [0 0 0] x1 + [1 0 0] x2 + [0 0 0] x3 + [0]
                                  [0 0 0]      [0 1 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 1]      [0 0 0]      [0]
                activate^#(x1) = [3 3 3] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2(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]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(x1, x2, x3) = [1 0 0] x1 + [1 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 1 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 1]      [0 0 1]      [0]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(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_7(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                c_10(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_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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_15(x1) = [1 1 1] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {7}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {3}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, 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]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2(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]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(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]
                prefix^#(x1) = [2 3 2] x1 + [0]
                               [3 3 3]      [0]
                               [3 3 3]      [0]
                c_6(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 0 0]      [0 0 0]      [0 1 0]      [0]
                                  [0 0 0]      [0 0 0]      [0 0 1]      [0]
                c_7(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                c_10(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_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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_15(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: {prefix^#(L) -> c_6(nil^#(), L, prefix^#(L))}
               Weak Rules: {}

             Proof Output:
               The input cannot be shown compatible

           * Path {7}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {1, 3}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(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]
                nil() = [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]
                n__app(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]
                activate(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                n__from(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]
                zWadr(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]
                n__nil() = [0]
                           [0]
                           [0]
                n__zWadr(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]
                prefix(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                app^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1, 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]
                activate^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_2(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]
                zWadr^#(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_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                nil^#() = [0]
                          [0]
                          [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_5(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]
                prefix^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_6(x1, x2, x3) = [1 0 0] x1 + [0 0 0] x2 + [1 0 0] x3 + [0]
                                  [0 1 0]      [0 0 0]      [0 1 0]      [0]
                                  [0 0 1]      [0 0 0]      [0 0 1]      [0]
                c_7(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_8(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                c_10(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_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]
                c_13(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_14(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                c_15(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.

    2) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:

             {  1: app^#(nil(), YS) -> c_0(YS)
              , 2: app^#(cons(X, XS), YS) -> c_1(X, activate^#(XS), YS)
              , 3: from^#(X) -> c_2(X, X)
              , 4: zWadr^#(nil(), YS) -> c_3(nil^#())
              , 5: zWadr^#(XS, nil()) -> c_4(nil^#())
              , 6: zWadr^#(cons(X, XS), cons(Y, YS)) ->
                   c_5(app^#(Y, cons(X, n__nil())), activate^#(XS), activate^#(YS))
              , 7: prefix^#(L) -> c_6(nil^#(), L, prefix^#(L))
              , 8: app^#(X1, X2) -> c_7(X1, X2)
              , 9: from^#(X) -> c_8(X)
              , 10: nil^#() -> c_9()
              , 11: zWadr^#(X1, X2) -> c_10(X1, X2)
              , 12: activate^#(n__app(X1, X2)) -> c_11(app^#(X1, X2))
              , 13: activate^#(n__from(X)) -> c_12(from^#(X))
              , 14: activate^#(n__nil()) -> c_13(nil^#())
              , 15: activate^#(n__zWadr(X1, X2)) -> c_14(zWadr^#(X1, X2))
              , 16: activate^#(X) -> c_15(X)}

           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)

             ->{7}                                                       [       MAYBE        ]
                |
                `->{10}                                                  [         NA         ]

             ->{2,12,6,15}                                               [         NA         ]
                |
                |->{1}                                                   [         NA         ]
                |
                |->{4}                                                   [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{5}                                                   [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{8}                                                   [         NA         ]
                |
                |->{11}                                                  [         NA         ]
                |
                |->{13}                                                  [         NA         ]
                |   |
                |   |->{3}                                               [         NA         ]
                |   |
                |   `->{9}                                               [         NA         ]
                |
                |->{14}                                                  [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                `->{16}                                                  [         NA         ]



         Sub-problems:
         -------------
           * Path {2,12,6,15}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 0]      [0]
                n__app(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [2 0] x1 + [0 0] x2 + [0]
                                [3 3]      [3 3]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [1 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 1]      [0 0]      [0]
                activate^#(x1) = [2 0] x1 + [0]
                                 [3 3]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [2 1] x1 + [2 0] x2 + [0]
                                  [3 3]      [3 3]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{1}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [3 3] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [1 1] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [1 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 1]      [0 0]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{4}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [1 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 1]      [0 0]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{4}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {1},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [1 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 1]      [0 0]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{5}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [1 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 1]      [0 0]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{5}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {1}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [1 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 1]      [0 0]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{8}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [3 3] x1 + [3 3] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [1 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 1]      [0 0]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_7(x1, x2) = [1 1] x1 + [1 1] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [1 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 1]      [0 0]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [3 3] x1 + [3 3] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [1 1] x1 + [1 1] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{13}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [1 1] x1 + [0]
                              [0 1]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [1 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 1]      [0 0]      [0]
                activate^#(x1) = [1 3] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [3 0] x1 + [0]
                             [3 0]      [0]
                c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{13}->{3}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {1},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [1 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 1]      [0 0]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [3 3] x1 + [0]
                             [0 0]      [0]
                c_2(x1, x2) = [1 0] x1 + [1 3] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{13}->{9}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {1},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [1 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 1]      [0 0]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [3 3] x1 + [0]
                             [0 0]      [0]
                c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [1 1] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{14}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [1 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 1]      [0 0]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{14}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {1}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [1 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 1]      [0 0]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_13(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{16}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [1 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 1]      [0 0]      [0]
                activate^#(x1) = [3 3] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 1]      [0 1]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_15(x1) = [1 1] x1 + [0]
                           [0 0]      [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {7}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {3}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                prefix^#(x1) = [2 3] x1 + [0]
                               [3 3]      [0]
                c_6(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [1 0] x3 + [0]
                                  [0 0]      [0 0]      [0 1]      [0]
                c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_15(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: {prefix^#(L) -> c_6(nil^#(), L, prefix^#(L))}
               Weak Rules: {}

             Proof Output:
               The input cannot be shown compatible

           * Path {7}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {1, 3}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                n__app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                activate(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                n__from(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                n__nil() = [0]
                           [0]
                n__zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                prefix(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                app^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                activate^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                nil^#() = [0]
                          [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_5(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
                                  [0 0]      [0 0]      [0 0]      [0]
                prefix^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_6(x1, x2, x3) = [1 0] x1 + [0 0] x2 + [1 0] x3 + [0]
                                  [0 1]      [0 0]      [0 1]      [0]
                c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_8(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_9() = [0]
                        [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_12(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_13(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_14(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                c_15(x1) = [0 0] x1 + [0]
                           [0 0]      [0]

             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: app^#(nil(), YS) -> c_0(YS)
              , 2: app^#(cons(X, XS), YS) -> c_1(X, activate^#(XS), YS)
              , 3: from^#(X) -> c_2(X, X)
              , 4: zWadr^#(nil(), YS) -> c_3(nil^#())
              , 5: zWadr^#(XS, nil()) -> c_4(nil^#())
              , 6: zWadr^#(cons(X, XS), cons(Y, YS)) ->
                   c_5(app^#(Y, cons(X, n__nil())), activate^#(XS), activate^#(YS))
              , 7: prefix^#(L) -> c_6(nil^#(), L, prefix^#(L))
              , 8: app^#(X1, X2) -> c_7(X1, X2)
              , 9: from^#(X) -> c_8(X)
              , 10: nil^#() -> c_9()
              , 11: zWadr^#(X1, X2) -> c_10(X1, X2)
              , 12: activate^#(n__app(X1, X2)) -> c_11(app^#(X1, X2))
              , 13: activate^#(n__from(X)) -> c_12(from^#(X))
              , 14: activate^#(n__nil()) -> c_13(nil^#())
              , 15: activate^#(n__zWadr(X1, X2)) -> c_14(zWadr^#(X1, X2))
              , 16: activate^#(X) -> c_15(X)}

           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)

             ->{7}                                                       [         NA         ]
                |
                `->{10}                                                  [       MAYBE        ]

             ->{2,12,6,15}                                               [         NA         ]
                |
                |->{1}                                                   [         NA         ]
                |
                |->{4}                                                   [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{5}                                                   [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{8}                                                   [         NA         ]
                |
                |->{11}                                                  [         NA         ]
                |
                |->{13}                                                  [         NA         ]
                |   |
                |   |->{3}                                               [         NA         ]
                |   |
                |   `->{9}                                               [         NA         ]
                |
                |->{14}                                                  [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                `->{16}                                                  [         NA         ]



         Sub-problems:
         -------------
           * Path {2,12,6,15}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                n__app(x1, x2) = [1] x1 + [1] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [1] x1 + [1] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [3] x1 + [1] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                activate^#(x1) = [3] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2(x1, x2) = [0] x1 + [0] x2 + [0]
                zWadr^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_7(x1, x2) = [0] x1 + [0] x2 + [0]
                c_8(x1) = [0] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15(x1) = [0] x1 + [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{1}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [3] x2 + [0]
                c_0(x1) = [1] x1 + [0]
                c_1(x1, x2, x3) = [0] x1 + [1] x2 + [0] x3 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2(x1, x2) = [0] x1 + [0] x2 + [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_7(x1, x2) = [0] x1 + [0] x2 + [0]
                c_8(x1) = [0] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15(x1) = [0] x1 + [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{4}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1, x2, x3) = [0] x1 + [1] x2 + [0] x3 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2(x1, x2) = [0] x1 + [0] x2 + [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_7(x1, x2) = [0] x1 + [0] x2 + [0]
                c_8(x1) = [0] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15(x1) = [0] x1 + [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{4}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {1},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1, x2, x3) = [0] x1 + [1] x2 + [0] x3 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2(x1, x2) = [0] x1 + [0] x2 + [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [1] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_7(x1, x2) = [0] x1 + [0] x2 + [0]
                c_8(x1) = [0] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15(x1) = [0] x1 + [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{5}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1, x2, x3) = [0] x1 + [1] x2 + [0] x3 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2(x1, x2) = [0] x1 + [0] x2 + [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_7(x1, x2) = [0] x1 + [0] x2 + [0]
                c_8(x1) = [0] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15(x1) = [0] x1 + [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{5}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {1}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1, x2, x3) = [0] x1 + [1] x2 + [0] x3 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2(x1, x2) = [0] x1 + [0] x2 + [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [1] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_7(x1, x2) = [0] x1 + [0] x2 + [0]
                c_8(x1) = [0] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15(x1) = [0] x1 + [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{8}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1, x2, x3) = [0] x1 + [1] x2 + [0] x3 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2(x1, x2) = [0] x1 + [0] x2 + [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_7(x1, x2) = [1] x1 + [1] x2 + [0]
                c_8(x1) = [0] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15(x1) = [0] x1 + [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1, x2, x3) = [0] x1 + [1] x2 + [0] x3 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2(x1, x2) = [0] x1 + [0] x2 + [0]
                zWadr^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_7(x1, x2) = [0] x1 + [0] x2 + [0]
                c_8(x1) = [0] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [1] x1 + [1] x2 + [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15(x1) = [0] x1 + [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{13}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [1] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1, x2, x3) = [0] x1 + [1] x2 + [0] x3 + [0]
                activate^#(x1) = [3] x1 + [0]
                from^#(x1) = [1] x1 + [0]
                c_2(x1, x2) = [0] x1 + [0] x2 + [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_7(x1, x2) = [0] x1 + [0] x2 + [0]
                c_8(x1) = [0] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [3] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15(x1) = [0] x1 + [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{13}->{3}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {1},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1, x2, x3) = [0] x1 + [1] x2 + [0] x3 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [3] x1 + [0]
                c_2(x1, x2) = [2] x1 + [1] x2 + [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_7(x1, x2) = [0] x1 + [0] x2 + [0]
                c_8(x1) = [0] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [1] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15(x1) = [0] x1 + [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{13}->{9}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {1},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1, x2, x3) = [0] x1 + [1] x2 + [0] x3 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [3] x1 + [0]
                c_2(x1, x2) = [0] x1 + [0] x2 + [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_7(x1, x2) = [0] x1 + [0] x2 + [0]
                c_8(x1) = [1] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [1] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15(x1) = [0] x1 + [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{14}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1, x2, x3) = [0] x1 + [1] x2 + [0] x3 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2(x1, x2) = [0] x1 + [0] x2 + [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_7(x1, x2) = [0] x1 + [0] x2 + [0]
                c_8(x1) = [0] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15(x1) = [0] x1 + [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{14}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {1}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1, x2, x3) = [0] x1 + [1] x2 + [0] x3 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2(x1, x2) = [0] x1 + [0] x2 + [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_7(x1, x2) = [0] x1 + [0] x2 + [0]
                c_8(x1) = [0] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [1] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15(x1) = [0] x1 + [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {2,12,6,15}->{16}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {2}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {1, 2, 3}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {1}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1, x2, x3) = [0] x1 + [1] x2 + [0] x3 + [0]
                activate^#(x1) = [3] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2(x1, x2) = [0] x1 + [0] x2 + [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                c_7(x1, x2) = [0] x1 + [0] x2 + [0]
                c_8(x1) = [0] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11(x1) = [1] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                c_15(x1) = [1] x1 + [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {7}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {3}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2(x1, x2) = [0] x1 + [0] x2 + [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                prefix^#(x1) = [3] x1 + [0]
                c_6(x1, x2, x3) = [0] x1 + [0] x2 + [1] x3 + [0]
                c_7(x1, x2) = [0] x1 + [0] x2 + [0]
                c_8(x1) = [0] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                c_15(x1) = [0] x1 + [0]

             We have not generated a proof for the resulting sub-problem.

           * Path {7}->{10}: 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(app) = {}, Uargs(cons) = {}, Uargs(n__app) = {},
                 Uargs(activate) = {}, Uargs(from) = {}, Uargs(n__from) = {},
                 Uargs(s) = {}, Uargs(zWadr) = {}, Uargs(n__zWadr) = {},
                 Uargs(prefix) = {}, Uargs(app^#) = {}, Uargs(c_0) = {},
                 Uargs(c_1) = {}, Uargs(activate^#) = {}, Uargs(from^#) = {},
                 Uargs(c_2) = {}, Uargs(zWadr^#) = {}, Uargs(c_3) = {},
                 Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(prefix^#) = {},
                 Uargs(c_6) = {1, 3}, Uargs(c_7) = {}, Uargs(c_8) = {},
                 Uargs(c_10) = {}, Uargs(c_11) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(c_15) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                app(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                n__app(x1, x2) = [0] x1 + [0] x2 + [0]
                activate(x1) = [0] x1 + [0]
                from(x1) = [0] x1 + [0]
                n__from(x1) = [0] x1 + [0]
                s(x1) = [0] x1 + [0]
                zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                n__nil() = [0]
                n__zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
                prefix(x1) = [0] x1 + [0]
                app^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                activate^#(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_2(x1, x2) = [0] x1 + [0] x2 + [0]
                zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_3(x1) = [0] x1 + [0]
                nil^#() = [0]
                c_4(x1) = [0] x1 + [0]
                c_5(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
                prefix^#(x1) = [0] x1 + [0]
                c_6(x1, x2, x3) = [1] x1 + [0] x2 + [1] x3 + [0]
                c_7(x1, x2) = [0] x1 + [0] x2 + [0]
                c_8(x1) = [0] x1 + [0]
                c_9() = [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11(x1) = [0] x1 + [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                c_15(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: {nil^#() -> c_9()}
               Weak Rules: {prefix^#(L) -> c_6(nil^#(), L, prefix^#(L))}

             Proof Output:
               The input cannot be shown compatible

    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.