Problem Strategy outermost added 08 Ex6 15 AEL02

Tool CaT

Execution TimeUnknown
Answer
MAYBE
InputStrategy outermost added 08 Ex6 15 AEL02

stdout:

MAYBE

Problem:
 sel(s(X),cons(Y,Z)) -> sel(X,Z)
 sel(0(),cons(X,Z)) -> X
 first(0(),Z) -> nil()
 first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
 from(X) -> cons(X,from(s(X)))
 sel1(s(X),cons(Y,Z)) -> sel1(X,Z)
 sel1(0(),cons(X,Z)) -> quote(X)
 first1(0(),Z) -> nil1()
 first1(s(X),cons(Y,Z)) -> cons1(quote(Y),first1(X,Z))
 quote(0()) -> 01()
 quote1(cons(X,Z)) -> cons1(quote(X),quote1(Z))
 quote1(nil()) -> nil1()
 quote(s(X)) -> s1(quote(X))
 quote(sel(X,Z)) -> sel1(X,Z)
 quote1(first(X,Z)) -> first1(X,Z)
 unquote(01()) -> 0()
 unquote(s1(X)) -> s(unquote(X))
 unquote1(nil1()) -> nil()
 unquote1(cons1(X,Z)) -> fcons(unquote(X),unquote1(Z))
 fcons(X,Z) -> cons(X,Z)

Proof:
 Open

Tool IRC1

Execution TimeUnknown
Answer
MAYBE
InputStrategy outermost added 08 Ex6 15 AEL02

stdout:

MAYBE
 Warning when parsing problem:
                             
                               Unsupported strategy 'OUTERMOST'

Tool IRC2

Execution TimeUnknown
Answer
MAYBE
InputStrategy outermost added 08 Ex6 15 AEL02

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  sel(s(X), cons(Y, Z)) -> sel(X, Z)
     , sel(0(), cons(X, Z)) -> X
     , first(0(), Z) -> nil()
     , first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
     , from(X) -> cons(X, from(s(X)))
     , sel1(s(X), cons(Y, Z)) -> sel1(X, Z)
     , sel1(0(), cons(X, Z)) -> quote(X)
     , first1(0(), Z) -> nil1()
     , first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, Z))
     , quote(0()) -> 01()
     , quote1(cons(X, Z)) -> cons1(quote(X), quote1(Z))
     , quote1(nil()) -> nil1()
     , quote(s(X)) -> s1(quote(X))
     , quote(sel(X, Z)) -> sel1(X, Z)
     , quote1(first(X, Z)) -> first1(X, Z)
     , unquote(01()) -> 0()
     , unquote(s1(X)) -> s(unquote(X))
     , unquote1(nil1()) -> nil()
     , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
     , fcons(X, Z) -> cons(X, Z)}

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: sel^#(s(X), cons(Y, Z)) -> c_0(sel^#(X, Z))
              , 2: sel^#(0(), cons(X, Z)) -> c_1()
              , 3: first^#(0(), Z) -> c_2()
              , 4: first^#(s(X), cons(Y, Z)) -> c_3(first^#(X, Z))
              , 5: from^#(X) -> c_4(from^#(s(X)))
              , 6: sel1^#(s(X), cons(Y, Z)) -> c_5(sel1^#(X, Z))
              , 7: sel1^#(0(), cons(X, Z)) -> c_6(quote^#(X))
              , 8: first1^#(0(), Z) -> c_7()
              , 9: first1^#(s(X), cons(Y, Z)) -> c_8(quote^#(Y), first1^#(X, Z))
              , 10: quote^#(0()) -> c_9()
              , 11: quote1^#(cons(X, Z)) -> c_10(quote^#(X), quote1^#(Z))
              , 12: quote1^#(nil()) -> c_11()
              , 13: quote^#(s(X)) -> c_12(quote^#(X))
              , 14: quote^#(sel(X, Z)) -> c_13(sel1^#(X, Z))
              , 15: quote1^#(first(X, Z)) -> c_14(first1^#(X, Z))
              , 16: unquote^#(01()) -> c_15()
              , 17: unquote^#(s1(X)) -> c_16(unquote^#(X))
              , 18: unquote1^#(nil1()) -> c_17()
              , 19: unquote1^#(cons1(X, Z)) ->
                    c_18(fcons^#(unquote(X), unquote1(Z)))
              , 20: fcons^#(X, Z) -> c_19()}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{19}                                                      [         NA         ]
                |
                `->{20}                                                  [         NA         ]
             
             ->{18}                                                      [    YES(?,O(1))     ]
             
             ->{17}                                                      [   YES(?,O(n^2))    ]
                |
                `->{16}                                                  [   YES(?,O(n^2))    ]
             
             ->{11}                                                      [         NA         ]
                |
                |->{6,14,13,7}                                           [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{10}                                                  [         NA         ]
                |
                |->{12}                                                  [         NA         ]
                |
                `->{15}                                                  [         NA         ]
                    |
                    |->{8}                                               [         NA         ]
                    |
                    `->{9}                                               [         NA         ]
                        |
                        |->{6,14,13,7}                                   [         NA         ]
                        |   |
                        |   `->{10}                                      [         NA         ]
                        |
                        |->{8}                                           [         NA         ]
                        |
                        `->{10}                                          [         NA         ]
             
             ->{5}                                                       [       MAYBE        ]
             
             ->{4}                                                       [   YES(?,O(n^3))    ]
                |
                `->{3}                                                   [         NA         ]
             
             ->{1}                                                       [   YES(?,O(n^3))    ]
                |
                `->{2}                                                   [         NA         ]
             
           
         
         Sub-problems:
         -------------
           * Path {1}: YES(?,O(n^3))
             -----------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {1}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 3 0] x1 + [0]
                        [0 1 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [1 3 0] x1 + [0 0 0] x2 + [0]
                               [0 1 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(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(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_1() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 3'
             --------------------------------------
             Answer:           YES(?,O(n^3))
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {sel^#(s(X), cons(Y, Z)) -> c_0(sel^#(X, Z))}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s) = {}, Uargs(cons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s(x1) = [1 4 4] x1 + [2]
                        [0 1 2]      [2]
                        [0 0 0]      [2]
                cons(x1, x2) = [0 0 0] x1 + [1 4 4] x2 + [2]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 1]      [2]
                sel^#(x1, x2) = [0 2 0] x1 + [0 0 2] x2 + [0]
                                [2 0 2]      [2 0 0]      [0]
                                [0 2 2]      [1 0 0]      [0]
                c_0(x1) = [1 0 0] x1 + [5]
                          [2 0 2]      [3]
                          [0 0 0]      [7]
           
           * Path {1}->{2}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {1}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_1() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {4}: YES(?,O(n^3))
             -----------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {1},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 3 0] x1 + [0]
                        [0 1 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [1 3 0] x1 + [0 0 0] x2 + [0]
                               [0 1 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(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_2() = [0]
                        [0]
                        [0]
                c_3(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 3'
             --------------------------------------
             Answer:           YES(?,O(n^3))
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {first^#(s(X), cons(Y, Z)) -> c_3(first^#(X, Z))}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s) = {}, Uargs(cons) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s(x1) = [1 4 4] x1 + [2]
                        [0 1 2]      [2]
                        [0 0 0]      [2]
                cons(x1, x2) = [0 0 0] x1 + [1 4 4] x2 + [2]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 1]      [2]
                first^#(x1, x2) = [0 2 0] x1 + [0 0 2] x2 + [0]
                                  [2 0 2]      [2 0 0]      [0]
                                  [0 2 2]      [1 0 0]      [0]
                c_3(x1) = [1 0 0] x1 + [5]
                          [2 0 2]      [3]
                          [0 0 0]      [7]
           
           * Path {4}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {1},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {5}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {1}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 1 0] x1 + [0]
                        [0 0 1]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                from^#(x1) = [3 3 3] x1 + [0]
                             [3 3 3]      [0]
                             [3 3 3]      [0]
                c_4(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [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: {from^#(X) -> c_4(from^#(s(X)))}
               Weak Rules: {}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {11}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [1 0 0] x1 + [1 3 0] x2 + [0]
                               [0 1 0]      [0 1 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [3 0 0] x1 + [0]
                              [3 0 0]      [0]
                              [3 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 1 0] x1 + [0]
                               [3 3 3]      [0]
                               [3 3 3]      [0]
                c_10(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_11() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{6,14,13,7}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [1 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(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_5(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_6(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [3 3 3]      [0]
                              [3 3 3]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [0]
                         [0]
                         [0]
                c_12(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_13(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_14(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{6,14,13,7}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_6(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [0]
                         [0]
                         [0]
                c_12(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_13(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_14(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{12}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [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) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {2}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 3 0] x1 + [0]
                        [0 1 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [1 0 0] x1 + [1 3 0] x2 + [0]
                               [0 1 0]      [0 1 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [3 0 0] x1 + [0]
                              [3 0 0]      [0]
                              [3 0 0]      [0]
                first1^#(x1, x2) = [0 0 0] x1 + [0 1 0] x2 + [0]
                                   [3 3 3]      [3 3 3]      [0]
                                   [3 3 3]      [3 3 3]      [0]
                c_7() = [0]
                        [0]
                        [0]
                c_8(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_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [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) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{6,14,13,7}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [1 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(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_5(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_6(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [3 3 3]      [0]
                              [3 3 3]      [0]
                first1^#(x1, 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(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_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [0]
                         [0]
                         [0]
                c_12(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{6,14,13,7}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_6(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(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_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [0]
                         [0]
                         [0]
                c_12(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {2}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(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_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [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) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(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_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [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) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {17}: YES(?,O(n^2))
             ------------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [1 3 0] x1 + [0]
                         [0 1 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [3 3 3]      [0]
                                [3 3 3]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 3'
             --------------------------------------
             Answer:           YES(?,O(n^2))
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s1(x1) = [1 2 2] x1 + [2]
                         [0 1 2]      [2]
                         [0 0 0]      [0]
                unquote^#(x1) = [0 1 0] x1 + [2]
                                [6 0 0]      [0]
                                [2 3 0]      [2]
                c_16(x1) = [1 0 0] x1 + [1]
                           [2 0 2]      [0]
                           [0 0 0]      [0]
           
           * Path {17}->{16}: YES(?,O(n^2))
             ------------------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 3'
             --------------------------------------
             Answer:           YES(?,O(n^2))
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {unquote^#(01()) -> c_15()}
               Weak Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                01() = [2]
                       [2]
                       [2]
                s1(x1) = [1 1 0] x1 + [0]
                         [0 1 1]      [1]
                         [0 0 0]      [0]
                unquote^#(x1) = [2 2 2] x1 + [0]
                                [0 6 0]      [0]
                                [0 0 2]      [0]
                c_15() = [1]
                         [0]
                         [0]
                c_16(x1) = [1 0 0] x1 + [2]
                           [0 0 0]      [3]
                           [0 0 0]      [0]
           
           * Path {18}: YES(?,O(1))
             ----------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19() = [0]
                         [0]
                         [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 3'
             --------------------------------------
             Answer:           YES(?,O(1))
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {unquote1^#(nil1()) -> c_17()}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(unquote1^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                nil1() = [2]
                         [2]
                         [2]
                unquote1^#(x1) = [0 2 0] x1 + [7]
                                 [2 2 0]      [3]
                                 [2 2 2]      [3]
                c_17() = [0]
                         [1]
                         [1]
           
           * Path {19}: NA
             -------------
             
             The usable rules for this path are:
             
               {  unquote(01()) -> 0()
                , unquote(s1(X)) -> s(unquote(X))
                , unquote1(nil1()) -> nil()
                , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
                , fcons(X, Z) -> cons(X, Z)}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {1}, Uargs(fcons^#) = {1, 2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 0 0]      [3]
                        [0 0 1]      [0]
                cons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [1]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [1]
                0() = [0]
                      [1]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [3]
                         [0]
                cons1(x1, x2) = [1 2 3] x1 + [1 3 3] x2 + [3]
                                [0 1 0]      [0 0 0]      [3]
                                [0 0 1]      [0 0 1]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [1 0 0] x1 + [2]
                         [0 0 0]      [2]
                         [0 0 0]      [1]
                unquote(x1) = [2 0 0] x1 + [1]
                              [0 2 1]      [3]
                              [0 0 0]      [0]
                unquote1(x1) = [3 3 0] x1 + [0]
                               [3 0 0]      [0]
                               [2 0 2]      [0]
                fcons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [2]
                                [0 0 0]      [0 0 0]      [2]
                                [0 0 0]      [0 0 0]      [1]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [3 1 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                fcons^#(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
                                  [3 3 3]      [3 3 3]      [0]
                                  [3 3 3]      [3 3 3]      [0]
                c_19() = [0]
                         [0]
                         [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {19}->{20}: NA
             -------------------
             
             The usable rules for this path are:
             
               {  unquote(01()) -> 0()
                , unquote(s1(X)) -> s(unquote(X))
                , unquote1(nil1()) -> nil()
                , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
                , fcons(X, Z) -> cons(X, Z)}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {1}, Uargs(fcons^#) = {1, 2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 0 0] x1 + [1]
                        [0 0 1]      [3]
                        [0 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]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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() = [1]
                        [0]
                        [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [1]
                         [0]
                         [0]
                cons1(x1, x2) = [1 0 1] x1 + [1 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 1]      [3]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [1 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 1]      [3]
                unquote(x1) = [0 0 1] x1 + [1]
                              [0 0 1]      [0]
                              [0 0 1]      [0]
                unquote1(x1) = [2 0 3] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [1]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, 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() = [0]
                        [0]
                        [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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_4(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                fcons^#(x1, x2) = [3 0 0] x1 + [3 0 0] x2 + [0]
                                  [0 0 0]      [0 0 0]      [0]
                                  [0 0 0]      [0 0 0]      [0]
                c_19() = [0]
                         [0]
                         [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             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: sel^#(s(X), cons(Y, Z)) -> c_0(sel^#(X, Z))
              , 2: sel^#(0(), cons(X, Z)) -> c_1()
              , 3: first^#(0(), Z) -> c_2()
              , 4: first^#(s(X), cons(Y, Z)) -> c_3(first^#(X, Z))
              , 5: from^#(X) -> c_4(from^#(s(X)))
              , 6: sel1^#(s(X), cons(Y, Z)) -> c_5(sel1^#(X, Z))
              , 7: sel1^#(0(), cons(X, Z)) -> c_6(quote^#(X))
              , 8: first1^#(0(), Z) -> c_7()
              , 9: first1^#(s(X), cons(Y, Z)) -> c_8(quote^#(Y), first1^#(X, Z))
              , 10: quote^#(0()) -> c_9()
              , 11: quote1^#(cons(X, Z)) -> c_10(quote^#(X), quote1^#(Z))
              , 12: quote1^#(nil()) -> c_11()
              , 13: quote^#(s(X)) -> c_12(quote^#(X))
              , 14: quote^#(sel(X, Z)) -> c_13(sel1^#(X, Z))
              , 15: quote1^#(first(X, Z)) -> c_14(first1^#(X, Z))
              , 16: unquote^#(01()) -> c_15()
              , 17: unquote^#(s1(X)) -> c_16(unquote^#(X))
              , 18: unquote1^#(nil1()) -> c_17()
              , 19: unquote1^#(cons1(X, Z)) ->
                    c_18(fcons^#(unquote(X), unquote1(Z)))
              , 20: fcons^#(X, Z) -> c_19()}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{19}                                                      [         NA         ]
                |
                `->{20}                                                  [         NA         ]
             
             ->{18}                                                      [    YES(?,O(1))     ]
             
             ->{17}                                                      [   YES(?,O(n^1))    ]
                |
                `->{16}                                                  [   YES(?,O(n^1))    ]
             
             ->{11}                                                      [         NA         ]
                |
                |->{6,14,13,7}                                           [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{10}                                                  [         NA         ]
                |
                |->{12}                                                  [         NA         ]
                |
                `->{15}                                                  [         NA         ]
                    |
                    |->{8}                                               [         NA         ]
                    |
                    `->{9}                                               [         NA         ]
                        |
                        |->{6,14,13,7}                                   [         NA         ]
                        |   |
                        |   `->{10}                                      [         NA         ]
                        |
                        |->{8}                                           [         NA         ]
                        |
                        `->{10}                                          [         NA         ]
             
             ->{5}                                                       [       MAYBE        ]
             
             ->{4}                                                       [         NA         ]
                |
                `->{3}                                                   [         NA         ]
             
             ->{1}                                                       [         NA         ]
                |
                `->{2}                                                   [         NA         ]
             
           
         
         Sub-problems:
         -------------
           * Path {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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {1}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [1 2] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [1 3] x1 + [0 0] x2 + [0]
                               [0 1]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [3 3] x1 + [1 3] x2 + [0]
                                [3 3]      [3 3]      [0]
                c_0(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_1() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {1}->{2}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {1}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_1() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {1},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [1 2] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [1 3] x1 + [0 0] x2 + [0]
                               [0 1]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [3 3] x1 + [1 3] x2 + [0]
                                  [3 3]      [3 3]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {4}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {1},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {5}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {1}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [1 0] x1 + [0]
                        [0 1]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [3 3] x1 + [0]
                             [3 3]      [0]
                c_4(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [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: {from^#(X) -> c_4(from^#(s(X)))}
               Weak Rules: {}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {11}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
                               [0 1]      [0 1]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [3 0] x1 + [0]
                              [3 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [1 3] x1 + [0]
                               [3 3]      [0]
                c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 1]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{6,14,13,7}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [3 3] x1 + [0 0] x2 + [0]
                              [3 3]      [0 0]      [0]
                s(x1) = [1 3] x1 + [0]
                        [0 1]      [0]
                cons(x1, x2) = [1 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [3 3]      [3 3]      [0]
                c_5(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_6(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [3 3]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [0]
                c_11() = [0]
                         [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_13(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_14(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{6,14,13,7}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_6(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [0]
                c_11() = [0]
                         [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_13(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_14(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{12}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 1]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 1]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 1]      [0]
                c_11() = [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) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {2}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [1 2] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
                               [0 1]      [0 1]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [3 0] x1 + [0]
                              [0 1]      [0]
                first1^#(x1, x2) = [3 3] x1 + [1 2] x2 + [0]
                                   [3 3]      [3 3]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 3] x1 + [1 0] x2 + [0]
                              [0 0]      [0 1]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 1]      [0]
                c_11() = [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) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{6,14,13,7}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [3 3] x1 + [0 0] x2 + [0]
                              [3 3]      [0 0]      [0]
                s(x1) = [1 3] x1 + [0]
                        [0 1]      [0]
                cons(x1, x2) = [1 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [3 3]      [3 3]      [0]
                c_5(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_6(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [3 3]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                              [0 1]      [0 1]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [0]
                c_11() = [0]
                         [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_13(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{6,14,13,7}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_6(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                              [0 1]      [0 1]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [0]
                c_11() = [0]
                         [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_13(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {2}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                              [0 0]      [0 1]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 1]      [0]
                c_11() = [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) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                              [0 1]      [0 1]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [0]
                c_11() = [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) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {17}: YES(?,O(n^1))
             ------------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [1 2] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [3 3] x1 + [0]
                                [3 3]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           YES(?,O(n^1))
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s1(x1) = [1 0] x1 + [0]
                         [0 1]      [1]
                unquote^#(x1) = [0 1] x1 + [1]
                                [0 0]      [0]
                c_16(x1) = [1 0] x1 + [0]
                           [0 0]      [0]
           
           * Path {17}->{16}: YES(?,O(n^1))
             ------------------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           YES(?,O(n^1))
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {unquote^#(01()) -> c_15()}
               Weak Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                01() = [2]
                       [2]
                s1(x1) = [1 2] x1 + [1]
                         [0 0]      [3]
                unquote^#(x1) = [1 2] x1 + [2]
                                [6 1]      [0]
                c_15() = [1]
                         [0]
                c_16(x1) = [1 0] x1 + [5]
                           [2 0]      [3]
           
           * Path {18}: YES(?,O(1))
             ----------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           YES(?,O(1))
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {unquote1^#(nil1()) -> c_17()}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(unquote1^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                nil1() = [2]
                         [2]
                unquote1^#(x1) = [2 0] x1 + [7]
                                 [2 2]      [7]
                c_17() = [0]
                         [1]
           
           * Path {19}: NA
             -------------
             
             The usable rules for this path are:
             
               {  unquote(01()) -> 0()
                , unquote(s1(X)) -> s(unquote(X))
                , unquote1(nil1()) -> nil()
                , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
                , fcons(X, Z) -> cons(X, Z)}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {1}, Uargs(fcons^#) = {1, 2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [1 0] x1 + [0]
                        [0 1]      [0]
                cons(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 0]      [1]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [1]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [1 3] x1 + [1 0] x2 + [3]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [1 0] x1 + [2]
                         [0 0]      [0]
                unquote(x1) = [1 0] x1 + [1]
                              [0 0]      [0]
                unquote1(x1) = [2 0] x1 + [2]
                               [2 0]      [2]
                fcons(x1, x2) = [2 0] x1 + [1 0] x2 + [1]
                                [0 0]      [0 0]      [3]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [3 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                fcons^#(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                                  [3 3]      [3 3]      [0]
                c_19() = [0]
                         [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {19}->{20}: NA
             -------------------
             
             The usable rules for this path are:
             
               {  unquote(01()) -> 0()
                , unquote(s1(X)) -> s(unquote(X))
                , unquote1(nil1()) -> nil()
                , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
                , fcons(X, Z) -> cons(X, Z)}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {1}, Uargs(fcons^#) = {1, 2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [1 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 0]      [1]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [1]
                        [1]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [3]
                         [0]
                cons1(x1, x2) = [1 0] x1 + [1 0] x2 + [3]
                                [0 0]      [0 1]      [3]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [1 0] x1 + [2]
                         [0 0]      [0]
                unquote(x1) = [1 0] x1 + [1]
                              [0 0]      [0]
                unquote1(x1) = [2 1] x1 + [0]
                               [3 3]      [0]
                fcons(x1, x2) = [2 0] x1 + [1 0] x2 + [1]
                                [0 0]      [0 0]      [3]
                sel^#(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() = [0]
                        [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                fcons^#(x1, x2) = [3 0] x1 + [3 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19() = [0]
                         [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
    
    3) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:
           
             {  1: sel^#(s(X), cons(Y, Z)) -> c_0(sel^#(X, Z))
              , 2: sel^#(0(), cons(X, Z)) -> c_1()
              , 3: first^#(0(), Z) -> c_2()
              , 4: first^#(s(X), cons(Y, Z)) -> c_3(first^#(X, Z))
              , 5: from^#(X) -> c_4(from^#(s(X)))
              , 6: sel1^#(s(X), cons(Y, Z)) -> c_5(sel1^#(X, Z))
              , 7: sel1^#(0(), cons(X, Z)) -> c_6(quote^#(X))
              , 8: first1^#(0(), Z) -> c_7()
              , 9: first1^#(s(X), cons(Y, Z)) -> c_8(quote^#(Y), first1^#(X, Z))
              , 10: quote^#(0()) -> c_9()
              , 11: quote1^#(cons(X, Z)) -> c_10(quote^#(X), quote1^#(Z))
              , 12: quote1^#(nil()) -> c_11()
              , 13: quote^#(s(X)) -> c_12(quote^#(X))
              , 14: quote^#(sel(X, Z)) -> c_13(sel1^#(X, Z))
              , 15: quote1^#(first(X, Z)) -> c_14(first1^#(X, Z))
              , 16: unquote^#(01()) -> c_15()
              , 17: unquote^#(s1(X)) -> c_16(unquote^#(X))
              , 18: unquote1^#(nil1()) -> c_17()
              , 19: unquote1^#(cons1(X, Z)) ->
                    c_18(fcons^#(unquote(X), unquote1(Z)))
              , 20: fcons^#(X, Z) -> c_19()}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{19}                                                      [         NA         ]
                |
                `->{20}                                                  [         NA         ]
             
             ->{18}                                                      [    YES(?,O(1))     ]
             
             ->{17}                                                      [         NA         ]
                |
                `->{16}                                                  [         NA         ]
             
             ->{11}                                                      [         NA         ]
                |
                |->{6,14,13,7}                                           [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{10}                                                  [         NA         ]
                |
                |->{12}                                                  [         NA         ]
                |
                `->{15}                                                  [         NA         ]
                    |
                    |->{8}                                               [         NA         ]
                    |
                    `->{9}                                               [         NA         ]
                        |
                        |->{6,14,13,7}                                   [         NA         ]
                        |   |
                        |   `->{10}                                      [         NA         ]
                        |
                        |->{8}                                           [         NA         ]
                        |
                        `->{10}                                          [         NA         ]
             
             ->{5}                                                       [       MAYBE        ]
             
             ->{4}                                                       [         NA         ]
                |
                `->{3}                                                   [         NA         ]
             
             ->{1}                                                       [         NA         ]
                |
                `->{2}                                                   [         NA         ]
             
           
         
         Sub-problems:
         -------------
           * Path {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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {1}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [1] x1 + [0]
                cons(x1, x2) = [1] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_0(x1) = [1] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {1}->{2}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {1}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [1] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {1},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [1] x1 + [0]
                cons(x1, x2) = [1] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_2() = [0]
                c_3(x1) = [1] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {4}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {1},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [1] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {5}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {1}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [3] x1 + [0]
                c_4(x1) = [1] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [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: {from^#(X) -> c_4(from^#(s(X)))}
               Weak Rules: {}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {11}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [1] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [3] x1 + [0]
                c_10(x1, x2) = [3] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{6,14,13,7}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [3] x1 + [3] x2 + [0]
                s(x1) = [1] x1 + [0]
                cons(x1, x2) = [1] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [2] x2 + [0]
                c_5(x1) = [1] x1 + [0]
                c_6(x1) = [1] x1 + [0]
                quote^#(x1) = [2] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [1] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [1] x1 + [0]
                c_13(x1) = [1] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{6,14,13,7}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [1] x1 + [0]
                c_6(x1) = [1] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [1] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [1] x1 + [0]
                c_13(x1) = [1] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [1] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{12}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [3] x1 + [3] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [1] x1 + [1] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [1] x1 + [0]
                c_10(x1, x2) = [0] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [3] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {2}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [1] x1 + [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [1] x1 + [0]
                first1^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [3] x1 + [1] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{6,14,13,7}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [2] x1 + [2] x2 + [0]
                s(x1) = [1] x1 + [0]
                cons(x1, x2) = [1] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [3] x2 + [0]
                c_5(x1) = [1] x1 + [0]
                c_6(x1) = [1] x1 + [0]
                quote^#(x1) = [3] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [1] x1 + [1] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [1] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [1] x1 + [0]
                c_13(x1) = [1] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{6,14,13,7}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [1] x1 + [0]
                c_6(x1) = [1] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [1] x1 + [1] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [1] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [1] x1 + [0]
                c_13(x1) = [1] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {2}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [1] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {1, 2}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [1] x1 + [1] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [1] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {17}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [1] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [3] x1 + [0]
                c_15() = [0]
                c_16(x1) = [1] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {17}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [1] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}: YES(?,O(1))
             ----------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19() = [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 1'
             --------------------------------------
             Answer:           YES(?,O(1))
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules: {unquote1^#(nil1()) -> c_17()}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(unquote1^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                nil1() = [7]
                unquote1^#(x1) = [1] x1 + [7]
                c_17() = [1]
           
           * Path {19}: NA
             -------------
             
             The usable rules for this path are:
             
               {  unquote(01()) -> 0()
                , unquote(s1(X)) -> s(unquote(X))
                , unquote1(nil1()) -> nil()
                , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
                , fcons(X, Z) -> cons(X, Z)}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {1}, Uargs(fcons^#) = {1, 2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [1] x1 + [3]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [1]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [1]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [3]
                cons1(x1, x2) = [1] x1 + [1] x2 + [2]
                01() = [3]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [1] x1 + [2]
                unquote(x1) = [2] x1 + [0]
                unquote1(x1) = [2] x1 + [0]
                fcons(x1, x2) = [1] x1 + [1] x2 + [1]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [3] x1 + [0]
                c_17() = [0]
                c_18(x1) = [1] x1 + [0]
                fcons^#(x1, x2) = [1] x1 + [1] x2 + [0]
                c_19() = [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {19}->{20}: NA
             -------------------
             
             The usable rules for this path are:
             
               {  unquote(01()) -> 0()
                , unquote(s1(X)) -> s(unquote(X))
                , unquote1(nil1()) -> nil()
                , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
                , fcons(X, Z) -> cons(X, Z)}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
                 Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
                 Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
                 Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
                 Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
                 Uargs(unquote1^#) = {}, Uargs(c_18) = {1}, Uargs(fcons^#) = {1, 2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [1] x1 + [3]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [1]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [1]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [3]
                cons1(x1, x2) = [1] x1 + [1] x2 + [2]
                01() = [3]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [1] x1 + [2]
                unquote(x1) = [2] x1 + [0]
                unquote1(x1) = [2] x1 + [0]
                fcons(x1, x2) = [1] x1 + [1] x2 + [1]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1() = [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1) = [0] x1 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1) = [0] x1 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [1] x1 + [0]
                fcons^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_19() = [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
    
    4) 'matrix-interpretation of dimension 1' failed due to the following reason:
         The input cannot be shown compatible
    
    5) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
         match-boundness of the problem could not be verified.
    
    6) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
         match-boundness of the problem could not be verified.
    

Tool RC1

Execution TimeUnknown
Answer
MAYBE
InputStrategy outermost added 08 Ex6 15 AEL02

stdout:

MAYBE
 Warning when parsing problem:
                             
                               Unsupported strategy 'OUTERMOST'

Tool RC2

Execution TimeUnknown
Answer
MAYBE
InputStrategy outermost added 08 Ex6 15 AEL02

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    runtime-complexity with respect to
  Rules:
    {  sel(s(X), cons(Y, Z)) -> sel(X, Z)
     , sel(0(), cons(X, Z)) -> X
     , first(0(), Z) -> nil()
     , first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
     , from(X) -> cons(X, from(s(X)))
     , sel1(s(X), cons(Y, Z)) -> sel1(X, Z)
     , sel1(0(), cons(X, Z)) -> quote(X)
     , first1(0(), Z) -> nil1()
     , first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, Z))
     , quote(0()) -> 01()
     , quote1(cons(X, Z)) -> cons1(quote(X), quote1(Z))
     , quote1(nil()) -> nil1()
     , quote(s(X)) -> s1(quote(X))
     , quote(sel(X, Z)) -> sel1(X, Z)
     , quote1(first(X, Z)) -> first1(X, Z)
     , unquote(01()) -> 0()
     , unquote(s1(X)) -> s(unquote(X))
     , unquote1(nil1()) -> nil()
     , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
     , fcons(X, Z) -> cons(X, Z)}

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: sel^#(s(X), cons(Y, Z)) -> c_0(sel^#(X, Z))
              , 2: sel^#(0(), cons(X, Z)) -> c_1(X)
              , 3: first^#(0(), Z) -> c_2()
              , 4: first^#(s(X), cons(Y, Z)) -> c_3(Y, first^#(X, Z))
              , 5: from^#(X) -> c_4(X, from^#(s(X)))
              , 6: sel1^#(s(X), cons(Y, Z)) -> c_5(sel1^#(X, Z))
              , 7: sel1^#(0(), cons(X, Z)) -> c_6(quote^#(X))
              , 8: first1^#(0(), Z) -> c_7()
              , 9: first1^#(s(X), cons(Y, Z)) -> c_8(quote^#(Y), first1^#(X, Z))
              , 10: quote^#(0()) -> c_9()
              , 11: quote1^#(cons(X, Z)) -> c_10(quote^#(X), quote1^#(Z))
              , 12: quote1^#(nil()) -> c_11()
              , 13: quote^#(s(X)) -> c_12(quote^#(X))
              , 14: quote^#(sel(X, Z)) -> c_13(sel1^#(X, Z))
              , 15: quote1^#(first(X, Z)) -> c_14(first1^#(X, Z))
              , 16: unquote^#(01()) -> c_15()
              , 17: unquote^#(s1(X)) -> c_16(unquote^#(X))
              , 18: unquote1^#(nil1()) -> c_17()
              , 19: unquote1^#(cons1(X, Z)) ->
                    c_18(fcons^#(unquote(X), unquote1(Z)))
              , 20: fcons^#(X, Z) -> c_19(X, Z)}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{19}                                                      [         NA         ]
                |
                `->{20}                                                  [         NA         ]
             
             ->{18}                                                      [    YES(?,O(1))     ]
             
             ->{17}                                                      [   YES(?,O(n^2))    ]
                |
                `->{16}                                                  [   YES(?,O(n^2))    ]
             
             ->{11}                                                      [   YES(?,O(n^3))    ]
                |
                |->{6,14,13,7}                                           [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{10}                                                  [         NA         ]
                |
                |->{12}                                                  [         NA         ]
                |
                `->{15}                                                  [         NA         ]
                    |
                    |->{8}                                               [         NA         ]
                    |
                    `->{9}                                               [         NA         ]
                        |
                        |->{6,14,13,7}                                   [         NA         ]
                        |   |
                        |   `->{10}                                      [         NA         ]
                        |
                        |->{8}                                           [         NA         ]
                        |
                        `->{10}                                          [         NA         ]
             
             ->{5}                                                       [       MAYBE        ]
             
             ->{4}                                                       [         NA         ]
                |
                `->{3}                                                   [         NA         ]
             
             ->{1}                                                       [   YES(?,O(n^3))    ]
                |
                `->{2}                                                   [         NA         ]
             
           
         
         Sub-problems:
         -------------
           * Path {1}: YES(?,O(n^3))
             -----------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {1}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 3 0] x1 + [0]
                        [0 1 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [1 3 0] x1 + [0 0 0] x2 + [0]
                               [0 1 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(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(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 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:           YES(?,O(n^3))
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {sel^#(s(X), cons(Y, Z)) -> c_0(sel^#(X, Z))}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s) = {}, Uargs(cons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s(x1) = [1 4 4] x1 + [2]
                        [0 1 2]      [2]
                        [0 0 0]      [2]
                cons(x1, x2) = [0 0 0] x1 + [1 4 4] x2 + [2]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 1]      [2]
                sel^#(x1, x2) = [0 2 0] x1 + [0 0 2] x2 + [0]
                                [2 0 2]      [2 0 0]      [0]
                                [0 2 2]      [1 0 0]      [0]
                c_0(x1) = [1 0 0] x1 + [5]
                          [2 0 2]      [3]
                          [0 0 0]      [7]
           
           * Path {1}->{2}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {1}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [1 1 1] x1 + [0 0 0] x2 + [0]
                               [0 1 3]      [0 0 0]      [0]
                               [0 0 1]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [3 1 3] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_1(x1) = [1 0 1] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {2}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 3 0] x1 + [0]
                        [0 1 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [1 3 3] x1 + [1 3 0] x2 + [0]
                               [0 1 3]      [0 1 0]      [0]
                               [0 0 1]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(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_2() = [0]
                        [0]
                        [0]
                c_3(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]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {4}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {2}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(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]
                from^#(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {5}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {2},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 1 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 1]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                from^#(x1) = [1 3 3] x1 + [0]
                             [3 3 3]      [0]
                             [3 3 3]      [0]
                c_4(x1, x2) = [0 1 0] x1 + [1 0 0] x2 + [0]
                              [0 0 0]      [0 1 0]      [0]
                              [0 0 0]      [0 0 1]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 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: {from^#(X) -> c_4(X, from^#(s(X)))}
               Weak Rules: {}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {11}: YES(?,O(n^3))
             ------------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [1 0 0] x1 + [1 3 0] x2 + [0]
                               [0 1 0]      [0 1 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [3 0 0] x1 + [0]
                              [3 0 0]      [0]
                              [3 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 1 0] x1 + [0]
                               [3 3 3]      [0]
                               [3 3 3]      [0]
                c_10(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_11() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 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:           YES(?,O(n^3))
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules:
                 {quote1^#(cons(X, Z)) -> c_10(quote^#(X), quote1^#(Z))}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(cons) = {}, Uargs(quote^#) = {}, Uargs(quote1^#) = {},
                 Uargs(c_10) = {2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                cons(x1, x2) = [1 2 3] x1 + [1 4 3] x2 + [2]
                               [0 1 0]      [0 0 1]      [0]
                               [0 0 1]      [0 0 1]      [2]
                quote^#(x1) = [0 0 2] x1 + [0]
                              [0 0 0]      [2]
                              [0 0 2]      [2]
                quote1^#(x1) = [2 4 0] x1 + [0]
                               [2 0 2]      [0]
                               [0 0 4]      [2]
                c_10(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [1]
                               [0 0 2]      [0 0 2]      [0]
                               [2 2 0]      [0 0 0]      [3]
           
           * Path {11}->{6,14,13,7}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
                 Uargs(c_13) = {1}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [1 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(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_5(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_6(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [3 3 3]      [0]
                              [3 3 3]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [0]
                         [0]
                         [0]
                c_12(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_13(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_14(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{6,14,13,7}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
                 Uargs(c_13) = {1}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_6(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [0]
                         [0]
                         [0]
                c_12(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_13(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                c_14(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{12}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [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) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {2},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 3 0] x1 + [0]
                        [0 1 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [1 0 0] x1 + [1 3 0] x2 + [0]
                               [0 1 0]      [0 1 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [3 0 0] x1 + [0]
                              [3 0 0]      [0]
                              [3 0 0]      [0]
                first1^#(x1, x2) = [0 0 0] x1 + [0 1 0] x2 + [0]
                                   [3 3 3]      [3 3 3]      [0]
                                   [3 3 3]      [3 3 3]      [0]
                c_7() = [0]
                        [0]
                        [0]
                c_8(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_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [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) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{6,14,13,7}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
                 Uargs(c_13) = {1}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [1 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(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_5(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_6(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [3 3 3]      [0]
                              [3 3 3]      [0]
                first1^#(x1, 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(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_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [0]
                         [0]
                         [0]
                c_12(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{6,14,13,7}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
                 Uargs(c_13) = {1}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_6(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(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_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [0]
                         [0]
                         [0]
                c_12(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {2},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(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_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [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) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(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_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                c_10(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_11() = [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) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {17}: YES(?,O(n^2))
             ------------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {1}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [1 3 0] x1 + [0]
                         [0 1 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [3 3 3]      [0]
                                [3 3 3]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 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:           YES(?,O(n^2))
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s1(x1) = [1 2 2] x1 + [2]
                         [0 1 2]      [2]
                         [0 0 0]      [0]
                unquote^#(x1) = [0 1 0] x1 + [2]
                                [6 0 0]      [0]
                                [2 3 0]      [2]
                c_16(x1) = [1 0 0] x1 + [1]
                           [2 0 2]      [0]
                           [0 0 0]      [0]
           
           * Path {17}->{16}: YES(?,O(n^2))
             ------------------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {1}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 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:           YES(?,O(n^2))
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {unquote^#(01()) -> c_15()}
               Weak Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                01() = [2]
                       [2]
                       [2]
                s1(x1) = [1 1 0] x1 + [0]
                         [0 1 1]      [1]
                         [0 0 0]      [0]
                unquote^#(x1) = [2 2 2] x1 + [0]
                                [0 6 0]      [0]
                                [0 0 2]      [0]
                c_15() = [1]
                         [0]
                         [0]
                c_16(x1) = [1 0 0] x1 + [2]
                           [0 0 0]      [3]
                           [0 0 0]      [0]
           
           * Path {18}: YES(?,O(1))
             ----------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [0 0 0] x1 + [0]
                        [0 0 0]      [0]
                        [0 0 0]      [0]
                cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [0 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 0]      [0]
                unquote(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                fcons^#(x1, 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_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 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:           YES(?,O(1))
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {unquote1^#(nil1()) -> c_17()}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(unquote1^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                nil1() = [2]
                         [2]
                         [2]
                unquote1^#(x1) = [0 2 0] x1 + [7]
                                 [2 2 0]      [3]
                                 [2 2 2]      [3]
                c_17() = [0]
                         [1]
                         [1]
           
           * Path {19}: NA
             -------------
             
             The usable rules for this path are:
             
               {  unquote(01()) -> 0()
                , unquote(s1(X)) -> s(unquote(X))
                , unquote1(nil1()) -> nil()
                , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
                , fcons(X, Z) -> cons(X, Z)}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {1, 2},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {1},
                 Uargs(fcons^#) = {1, 2}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 0 1]      [2]
                        [0 0 0]      [1]
                cons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [1]
                               [0 0 0]      [0 0 0]      [1]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [0]
                cons1(x1, x2) = [1 0 0] x1 + [1 0 3] x2 + [3]
                                [0 1 2]      [0 0 3]      [3]
                                [0 0 1]      [0 0 1]      [3]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [1 0 0] x1 + [0]
                         [0 0 0]      [0]
                         [0 0 1]      [2]
                unquote(x1) = [0 0 1] x1 + [1]
                              [0 0 1]      [0]
                              [0 0 1]      [0]
                unquote1(x1) = [0 0 1] x1 + [1]
                               [3 0 0]      [0]
                               [0 3 0]      [0]
                fcons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [1]
                                [0 0 0]      [0 0 0]      [3]
                                [0 0 0]      [0 0 0]      [3]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 1 2] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                fcons^#(x1, x2) = [2 0 0] x1 + [2 0 0] x2 + [0]
                                  [3 3 3]      [3 3 3]      [0]
                                  [3 3 3]      [3 3 3]      [0]
                c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {19}->{20}: NA
             -------------------
             
             The usable rules for this path are:
             
               {  unquote(01()) -> 0()
                , unquote(s1(X)) -> s(unquote(X))
                , unquote1(nil1()) -> nil()
                , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
                , fcons(X, Z) -> cons(X, Z)}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {1, 2},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {1},
                 Uargs(fcons^#) = {1, 2}, Uargs(c_19) = {1, 2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 0 0] x1 + [0]
                        [0 1 0]      [1]
                        [0 0 0]      [0]
                cons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [1]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                0() = [0]
                      [0]
                      [0]
                first(x1, 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() = [1]
                        [0]
                        [0]
                from(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                               [0 0 0]      [0 0 0]      [0]
                               [0 0 0]      [0 0 0]      [0]
                quote(x1) = [0 0 0] x1 + [0]
                            [0 0 0]      [0]
                            [0 0 0]      [0]
                first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                 [0 0 0]      [0 0 0]      [0]
                                 [0 0 0]      [0 0 0]      [0]
                nil1() = [0]
                         [0]
                         [1]
                cons1(x1, x2) = [1 0 0] x1 + [1 3 3] x2 + [0]
                                [0 0 0]      [0 1 0]      [2]
                                [0 0 1]      [0 0 0]      [2]
                01() = [0]
                       [0]
                       [0]
                quote1(x1) = [0 0 0] x1 + [0]
                             [0 0 0]      [0]
                             [0 0 0]      [0]
                s1(x1) = [1 0 1] x1 + [0]
                         [0 1 2]      [0]
                         [0 0 0]      [2]
                unquote(x1) = [1 0 1] x1 + [1]
                              [2 1 1]      [0]
                              [0 0 0]      [0]
                unquote1(x1) = [1 2 2] x1 + [0]
                               [3 0 0]      [0]
                               [0 0 0]      [0]
                fcons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [2]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                                [0 0 0]      [0 0 0]      [0]
                                [0 0 0]      [0 0 0]      [0]
                c_0(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_1(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                first^#(x1, 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_2() = [0]
                        [0]
                        [0]
                c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 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_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                sel1^#(x1, 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_5(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                c_6(x1) = [0 0 0] x1 + [0]
                          [0 0 0]      [0]
                          [0 0 0]      [0]
                quote^#(x1) = [0 0 0] x1 + [0]
                              [0 0 0]      [0]
                              [0 0 0]      [0]
                first1^#(x1, 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(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [0 0 0]      [0 0 0]      [0]
                              [0 0 0]      [0 0 0]      [0]
                c_9() = [0]
                        [0]
                        [0]
                quote1^#(x1) = [0 0 0] x1 + [0]
                               [0 0 0]      [0]
                               [0 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() = [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]
                unquote^#(x1) = [0 0 0] x1 + [0]
                                [0 0 0]      [0]
                                [0 0 0]      [0]
                c_15() = [0]
                         [0]
                         [0]
                c_16(x1) = [0 0 0] x1 + [0]
                           [0 0 0]      [0]
                           [0 0 0]      [0]
                unquote1^#(x1) = [0 0 0] x1 + [0]
                                 [0 0 0]      [0]
                                 [0 0 0]      [0]
                c_17() = [0]
                         [0]
                         [0]
                c_18(x1) = [1 0 0] x1 + [0]
                           [0 1 0]      [0]
                           [0 0 1]      [0]
                fcons^#(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_19(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]
             Complexity induced by the adequate RMI: YES(?,O(n^3))
             
             We have not generated a proof for the resulting sub-problem.
    
    2) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:
           
             {  1: sel^#(s(X), cons(Y, Z)) -> c_0(sel^#(X, Z))
              , 2: sel^#(0(), cons(X, Z)) -> c_1(X)
              , 3: first^#(0(), Z) -> c_2()
              , 4: first^#(s(X), cons(Y, Z)) -> c_3(Y, first^#(X, Z))
              , 5: from^#(X) -> c_4(X, from^#(s(X)))
              , 6: sel1^#(s(X), cons(Y, Z)) -> c_5(sel1^#(X, Z))
              , 7: sel1^#(0(), cons(X, Z)) -> c_6(quote^#(X))
              , 8: first1^#(0(), Z) -> c_7()
              , 9: first1^#(s(X), cons(Y, Z)) -> c_8(quote^#(Y), first1^#(X, Z))
              , 10: quote^#(0()) -> c_9()
              , 11: quote1^#(cons(X, Z)) -> c_10(quote^#(X), quote1^#(Z))
              , 12: quote1^#(nil()) -> c_11()
              , 13: quote^#(s(X)) -> c_12(quote^#(X))
              , 14: quote^#(sel(X, Z)) -> c_13(sel1^#(X, Z))
              , 15: quote1^#(first(X, Z)) -> c_14(first1^#(X, Z))
              , 16: unquote^#(01()) -> c_15()
              , 17: unquote^#(s1(X)) -> c_16(unquote^#(X))
              , 18: unquote1^#(nil1()) -> c_17()
              , 19: unquote1^#(cons1(X, Z)) ->
                    c_18(fcons^#(unquote(X), unquote1(Z)))
              , 20: fcons^#(X, Z) -> c_19(X, Z)}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{19}                                                      [         NA         ]
                |
                `->{20}                                                  [         NA         ]
             
             ->{18}                                                      [    YES(?,O(1))     ]
             
             ->{17}                                                      [   YES(?,O(n^1))    ]
                |
                `->{16}                                                  [   YES(?,O(n^1))    ]
             
             ->{11}                                                      [         NA         ]
                |
                |->{6,14,13,7}                                           [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{10}                                                  [         NA         ]
                |
                |->{12}                                                  [         NA         ]
                |
                `->{15}                                                  [         NA         ]
                    |
                    |->{8}                                               [         NA         ]
                    |
                    `->{9}                                               [         NA         ]
                        |
                        |->{6,14,13,7}                                   [         NA         ]
                        |   |
                        |   `->{10}                                      [         NA         ]
                        |
                        |->{8}                                           [         NA         ]
                        |
                        `->{10}                                          [         NA         ]
             
             ->{5}                                                       [       MAYBE        ]
             
             ->{4}                                                       [         NA         ]
                |
                `->{3}                                                   [         NA         ]
             
             ->{1}                                                       [         NA         ]
                |
                `->{2}                                                   [         NA         ]
             
           
         
         Sub-problems:
         -------------
           * Path {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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {1}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [1 2] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [1 3] x1 + [0 0] x2 + [0]
                               [0 1]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [3 3] x1 + [1 3] x2 + [0]
                                [3 3]      [3 3]      [0]
                c_0(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {1}->{2}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {1}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [1 3] x1 + [0 0] x2 + [0]
                               [0 1]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [1 3] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {2}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [1 2] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [1 3] x1 + [1 3] x2 + [0]
                               [0 1]      [0 1]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [3 3] x1 + [1 3] x2 + [0]
                                  [3 3]      [3 3]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                              [0 0]      [0 1]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {4}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {2}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                              [0 0]      [0 1]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {5}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {2},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [1 1] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [1 3] x1 + [0]
                             [3 3]      [0]
                c_4(x1, x2) = [0 1] x1 + [1 0] x2 + [0]
                              [0 0]      [0 1]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 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: {from^#(X) -> c_4(X, from^#(s(X)))}
               Weak Rules: {}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {11}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
                               [0 1]      [0 1]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [3 0] x1 + [0]
                              [3 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [1 3] x1 + [0]
                               [3 3]      [0]
                c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 1]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{6,14,13,7}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
                 Uargs(c_13) = {1}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [3 3] x1 + [0 0] x2 + [0]
                              [3 3]      [0 0]      [0]
                s(x1) = [1 3] x1 + [0]
                        [0 1]      [0]
                cons(x1, x2) = [1 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [3 3]      [3 3]      [0]
                c_5(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_6(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [3 3]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [0]
                c_11() = [0]
                         [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_13(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_14(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{6,14,13,7}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
                 Uargs(c_13) = {1}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_6(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [0]
                c_11() = [0]
                         [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_13(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_14(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{12}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 1]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 1]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 1]      [0]
                c_11() = [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) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {2},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [1 2] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
                               [0 1]      [0 1]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [3 0] x1 + [0]
                              [0 1]      [0]
                first1^#(x1, x2) = [3 3] x1 + [1 2] x2 + [0]
                                   [3 3]      [3 3]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 3] x1 + [1 0] x2 + [0]
                              [0 0]      [0 1]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 1]      [0]
                c_11() = [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) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{6,14,13,7}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
                 Uargs(c_13) = {1}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [3 3] x1 + [0 0] x2 + [0]
                              [3 3]      [0 0]      [0]
                s(x1) = [1 3] x1 + [0]
                        [0 1]      [0]
                cons(x1, x2) = [1 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [3 3]      [3 3]      [0]
                c_5(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_6(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [3 3]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                              [0 1]      [0 1]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [0]
                c_11() = [0]
                         [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_13(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{6,14,13,7}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
                 Uargs(c_13) = {1}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_6(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                              [0 1]      [0 1]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [0]
                c_11() = [0]
                         [0]
                c_12(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_13(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                c_14(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {2},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                              [0 0]      [0 1]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 1]      [0]
                c_11() = [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) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                              [0 1]      [0 1]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [0]
                c_11() = [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) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {17}: YES(?,O(n^1))
             ------------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {1}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [1 2] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [3 3] x1 + [0]
                                [3 3]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           YES(?,O(n^1))
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                s1(x1) = [1 0] x1 + [0]
                         [0 1]      [1]
                unquote^#(x1) = [0 1] x1 + [1]
                                [0 0]      [0]
                c_16(x1) = [1 0] x1 + [0]
                           [0 0]      [0]
           
           * Path {17}->{16}: YES(?,O(n^1))
             ------------------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {1}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           YES(?,O(n^1))
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {unquote^#(01()) -> c_15()}
               Weak Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                01() = [2]
                       [2]
                s1(x1) = [1 2] x1 + [1]
                         [0 0]      [3]
                unquote^#(x1) = [1 2] x1 + [2]
                                [6 1]      [0]
                c_15() = [1]
                         [0]
                c_16(x1) = [1 0] x1 + [5]
                           [2 0]      [3]
           
           * Path {18}: YES(?,O(1))
             ----------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [0 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [0 0] x1 + [0]
                         [0 0]      [0]
                unquote(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                unquote1(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           YES(?,O(1))
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {unquote1^#(nil1()) -> c_17()}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(unquote1^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                nil1() = [2]
                         [2]
                unquote1^#(x1) = [2 0] x1 + [7]
                                 [2 2]      [7]
                c_17() = [0]
                         [1]
           
           * Path {19}: NA
             -------------
             
             The usable rules for this path are:
             
               {  unquote(01()) -> 0()
                , unquote(s1(X)) -> s(unquote(X))
                , unquote1(nil1()) -> nil()
                , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
                , fcons(X, Z) -> cons(X, Z)}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {1, 2},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {1},
                 Uargs(fcons^#) = {1, 2}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [1 0] x1 + [0]
                        [0 0]      [0]
                cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [1]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [2]
                         [0]
                cons1(x1, x2) = [1 1] x1 + [1 0] x2 + [2]
                                [0 1]      [0 0]      [0]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [1 0] x1 + [2]
                         [0 0]      [0]
                unquote(x1) = [1 0] x1 + [1]
                              [0 0]      [0]
                unquote1(x1) = [2 0] x1 + [0]
                               [0 0]      [0]
                fcons(x1, x2) = [2 0] x1 + [1 0] x2 + [1]
                                [0 0]      [0 0]      [0]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [2 2] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                fcons^#(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                                  [3 3]      [3 3]      [0]
                c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {19}->{20}: NA
             -------------------
             
             The usable rules for this path are:
             
               {  unquote(01()) -> 0()
                , unquote(s1(X)) -> s(unquote(X))
                , unquote1(nil1()) -> nil()
                , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
                , fcons(X, Z) -> cons(X, Z)}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {1, 2},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {1},
                 Uargs(fcons^#) = {1, 2}, Uargs(c_19) = {1, 2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                s(x1) = [1 0] x1 + [0]
                        [0 1]      [0]
                cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                0() = [0]
                      [0]
                first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                nil() = [0]
                        [0]
                from(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                quote(x1) = [0 0] x1 + [0]
                            [0 0]      [0]
                first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                nil1() = [0]
                         [0]
                cons1(x1, x2) = [1 2] x1 + [1 2] x2 + [2]
                                [0 1]      [0 0]      [3]
                01() = [0]
                       [0]
                quote1(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                s1(x1) = [1 0] x1 + [2]
                         [0 0]      [0]
                unquote(x1) = [1 0] x1 + [1]
                              [0 0]      [0]
                unquote1(x1) = [2 1] x1 + [1]
                               [2 0]      [0]
                fcons(x1, x2) = [2 0] x1 + [1 0] x2 + [1]
                                [0 0]      [0 0]      [2]
                sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                [0 0]      [0 0]      [0]
                c_0(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_1(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_2() = [0]
                        [0]
                c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                from^#(x1) = [0 0] x1 + [0]
                             [0 0]      [0]
                c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                c_5(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                c_6(x1) = [0 0] x1 + [0]
                          [0 0]      [0]
                quote^#(x1) = [0 0] x1 + [0]
                              [0 0]      [0]
                first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                                   [0 0]      [0 0]      [0]
                c_7() = [0]
                        [0]
                c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                c_9() = [0]
                        [0]
                quote1^#(x1) = [0 0] x1 + [0]
                               [0 0]      [0]
                c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                c_11() = [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]
                unquote^#(x1) = [0 0] x1 + [0]
                                [0 0]      [0]
                c_15() = [0]
                         [0]
                c_16(x1) = [0 0] x1 + [0]
                           [0 0]      [0]
                unquote1^#(x1) = [0 0] x1 + [0]
                                 [0 0]      [0]
                c_17() = [0]
                         [0]
                c_18(x1) = [1 0] x1 + [0]
                           [0 1]      [0]
                fcons^#(x1, x2) = [3 3] x1 + [3 3] x2 + [0]
                                  [0 0]      [0 0]      [0]
                c_19(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 1]      [0 1]      [0]
             Complexity induced by the adequate RMI: YES(?,O(n^2))
             
             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: sel^#(s(X), cons(Y, Z)) -> c_0(sel^#(X, Z))
              , 2: sel^#(0(), cons(X, Z)) -> c_1(X)
              , 3: first^#(0(), Z) -> c_2()
              , 4: first^#(s(X), cons(Y, Z)) -> c_3(Y, first^#(X, Z))
              , 5: from^#(X) -> c_4(X, from^#(s(X)))
              , 6: sel1^#(s(X), cons(Y, Z)) -> c_5(sel1^#(X, Z))
              , 7: sel1^#(0(), cons(X, Z)) -> c_6(quote^#(X))
              , 8: first1^#(0(), Z) -> c_7()
              , 9: first1^#(s(X), cons(Y, Z)) -> c_8(quote^#(Y), first1^#(X, Z))
              , 10: quote^#(0()) -> c_9()
              , 11: quote1^#(cons(X, Z)) -> c_10(quote^#(X), quote1^#(Z))
              , 12: quote1^#(nil()) -> c_11()
              , 13: quote^#(s(X)) -> c_12(quote^#(X))
              , 14: quote^#(sel(X, Z)) -> c_13(sel1^#(X, Z))
              , 15: quote1^#(first(X, Z)) -> c_14(first1^#(X, Z))
              , 16: unquote^#(01()) -> c_15()
              , 17: unquote^#(s1(X)) -> c_16(unquote^#(X))
              , 18: unquote1^#(nil1()) -> c_17()
              , 19: unquote1^#(cons1(X, Z)) ->
                    c_18(fcons^#(unquote(X), unquote1(Z)))
              , 20: fcons^#(X, Z) -> c_19(X, Z)}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{19}                                                      [         NA         ]
                |
                `->{20}                                                  [         NA         ]
             
             ->{18}                                                      [    YES(?,O(1))     ]
             
             ->{17}                                                      [         NA         ]
                |
                `->{16}                                                  [         NA         ]
             
             ->{11}                                                      [         NA         ]
                |
                |->{6,14,13,7}                                           [         NA         ]
                |   |
                |   `->{10}                                              [         NA         ]
                |
                |->{10}                                                  [         NA         ]
                |
                |->{12}                                                  [         NA         ]
                |
                `->{15}                                                  [         NA         ]
                    |
                    |->{8}                                               [         NA         ]
                    |
                    `->{9}                                               [         NA         ]
                        |
                        |->{6,14,13,7}                                   [         NA         ]
                        |   |
                        |   `->{10}                                      [         NA         ]
                        |
                        |->{8}                                           [         NA         ]
                        |
                        `->{10}                                          [         NA         ]
             
             ->{5}                                                       [       MAYBE        ]
             
             ->{4}                                                       [         NA         ]
                |
                `->{3}                                                   [         NA         ]
             
             ->{1}                                                       [         NA         ]
                |
                `->{2}                                                   [         NA         ]
             
           
         
         Sub-problems:
         -------------
           * Path {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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {1}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [1] x1 + [0]
                cons(x1, x2) = [1] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_0(x1) = [1] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {1}->{2}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {1}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [1] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [3] x2 + [0]
                c_0(x1) = [1] x1 + [0]
                c_1(x1) = [1] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {2}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [1] x1 + [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [1] x1 + [1] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {4}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {2}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [1] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {5}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {2},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [3] x1 + [0]
                c_4(x1, x2) = [2] x1 + [1] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [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: {from^#(X) -> c_4(X, from^#(s(X)))}
               Weak Rules: {}
             
             Proof Output:    
               The input cannot be shown compatible
           
           * Path {11}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [1] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [3] x1 + [0]
                c_10(x1, x2) = [3] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{6,14,13,7}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
                 Uargs(c_13) = {1}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [3] x1 + [3] x2 + [0]
                s(x1) = [1] x1 + [0]
                cons(x1, x2) = [1] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [2] x2 + [0]
                c_5(x1) = [1] x1 + [0]
                c_6(x1) = [1] x1 + [0]
                quote^#(x1) = [2] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [1] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [1] x1 + [0]
                c_13(x1) = [1] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{6,14,13,7}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
                 Uargs(c_13) = {1}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [1] x1 + [0]
                c_6(x1) = [1] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [1] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [1] x1 + [0]
                c_13(x1) = [1] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [1] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{12}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [3] x1 + [3] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [1] x1 + [1] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [1] x1 + [0]
                c_10(x1, x2) = [0] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [3] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {2},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [1] x1 + [0]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [1] x1 + [0]
                first1^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [3] x1 + [1] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{6,14,13,7}: 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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
                 Uargs(c_13) = {1}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [2] x1 + [2] x2 + [0]
                s(x1) = [1] x1 + [0]
                cons(x1, x2) = [1] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [3] x2 + [0]
                c_5(x1) = [1] x1 + [0]
                c_6(x1) = [1] x1 + [0]
                quote^#(x1) = [3] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [1] x1 + [1] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [1] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [1] x1 + [0]
                c_13(x1) = [1] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{6,14,13,7}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
                 Uargs(c_13) = {1}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [1] x1 + [0]
                c_6(x1) = [1] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [1] x1 + [1] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [1] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [1] x1 + [0]
                c_13(x1) = [1] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {2},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [1] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {11}->{15}->{9}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [1] x1 + [1] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [1] x1 + [1] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [1] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {17}: NA
             -------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {1}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [1] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [3] x1 + [0]
                c_15() = [0]
                c_16(x1) = [1] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {17}->{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(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {1}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [1] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {18}: YES(?,O(1))
             ----------------------
             
             The usable rules of this path are empty.
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
                 Uargs(fcons^#) = {}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [0] x1 + [0]
                cons(x1, x2) = [0] x1 + [0] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [0]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [0]
                cons1(x1, x2) = [0] x1 + [0] x2 + [0]
                01() = [0]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [0] x1 + [0]
                unquote(x1) = [0] x1 + [0]
                unquote1(x1) = [0] x1 + [0]
                fcons(x1, x2) = [0] x1 + [0] x2 + [0]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [0] x1 + [0]
                fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             
             We apply the sub-processor on the resulting sub-problem:
             
             'matrix-interpretation of dimension 1'
             --------------------------------------
             Answer:           YES(?,O(1))
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules: {unquote1^#(nil1()) -> c_17()}
               Weak Rules: {}
             
             Proof Output:    
               The following argument positions are usable:
                 Uargs(unquote1^#) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                nil1() = [7]
                unquote1^#(x1) = [1] x1 + [7]
                c_17() = [1]
           
           * Path {19}: NA
             -------------
             
             The usable rules for this path are:
             
               {  unquote(01()) -> 0()
                , unquote(s1(X)) -> s(unquote(X))
                , unquote1(nil1()) -> nil()
                , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
                , fcons(X, Z) -> cons(X, Z)}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {1, 2},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {1},
                 Uargs(fcons^#) = {1, 2}, Uargs(c_19) = {}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [1] x1 + [2]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [1]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [3]
                cons1(x1, x2) = [1] x1 + [1] x2 + [2]
                01() = [3]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [1] x1 + [3]
                unquote(x1) = [1] x1 + [0]
                unquote1(x1) = [2] x1 + [0]
                fcons(x1, x2) = [1] x1 + [1] x2 + [1]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [3] x1 + [0]
                c_17() = [0]
                c_18(x1) = [1] x1 + [0]
                fcons^#(x1, x2) = [3] x1 + [1] x2 + [0]
                c_19(x1, x2) = [0] x1 + [0] x2 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
           
           * Path {19}->{20}: NA
             -------------------
             
             The usable rules for this path are:
             
               {  unquote(01()) -> 0()
                , unquote(s1(X)) -> s(unquote(X))
                , unquote1(nil1()) -> nil()
                , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
                , fcons(X, Z) -> cons(X, Z)}
             
             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {1, 2},
                 Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
                 Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
                 Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
                 Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
                 Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
                 Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
                 Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
                 Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
                 Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
                 Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
                 Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {1},
                 Uargs(fcons^#) = {1, 2}, Uargs(c_19) = {1, 2}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                sel(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [1] x1 + [2]
                cons(x1, x2) = [1] x1 + [1] x2 + [0]
                0() = [0]
                first(x1, x2) = [0] x1 + [0] x2 + [0]
                nil() = [1]
                from(x1) = [0] x1 + [0]
                sel1(x1, x2) = [0] x1 + [0] x2 + [0]
                quote(x1) = [0] x1 + [0]
                first1(x1, x2) = [0] x1 + [0] x2 + [0]
                nil1() = [3]
                cons1(x1, x2) = [1] x1 + [1] x2 + [2]
                01() = [3]
                quote1(x1) = [0] x1 + [0]
                s1(x1) = [1] x1 + [3]
                unquote(x1) = [1] x1 + [0]
                unquote1(x1) = [2] x1 + [0]
                fcons(x1, x2) = [1] x1 + [1] x2 + [1]
                sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [0] x1 + [0]
                c_1(x1) = [0] x1 + [0]
                first^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_2() = [0]
                c_3(x1, x2) = [0] x1 + [0] x2 + [0]
                from^#(x1) = [0] x1 + [0]
                c_4(x1, x2) = [0] x1 + [0] x2 + [0]
                sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_5(x1) = [0] x1 + [0]
                c_6(x1) = [0] x1 + [0]
                quote^#(x1) = [0] x1 + [0]
                first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_7() = [0]
                c_8(x1, x2) = [0] x1 + [0] x2 + [0]
                c_9() = [0]
                quote1^#(x1) = [0] x1 + [0]
                c_10(x1, x2) = [0] x1 + [0] x2 + [0]
                c_11() = [0]
                c_12(x1) = [0] x1 + [0]
                c_13(x1) = [0] x1 + [0]
                c_14(x1) = [0] x1 + [0]
                unquote^#(x1) = [0] x1 + [0]
                c_15() = [0]
                c_16(x1) = [0] x1 + [0]
                unquote1^#(x1) = [0] x1 + [0]
                c_17() = [0]
                c_18(x1) = [1] x1 + [0]
                fcons^#(x1, x2) = [3] x1 + [3] x2 + [0]
                c_19(x1, x2) = [1] x1 + [1] x2 + [0]
             Complexity induced by the adequate RMI: YES(?,O(n^1))
             
             We have not generated a proof for the resulting sub-problem.
    
    4) 'matrix-interpretation of dimension 1' failed due to the following reason:
         The input cannot be shown compatible
    
    5) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
         match-boundness of the problem could not be verified.
    
    6) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
         match-boundness of the problem could not be verified.