/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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NO

** BEGIN proof argument **
The following rule was generated while unfolding the analyzed TRS:
[iteration = 1] list1 -> list1
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {}.
We have r|p = list1 and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = list1 loops w.r.t. the analyzed TRS.
** END proof argument **

** BEGIN proof description **
## Searching for a generalized rewrite rule
(a rule whose right-hand side contains a variable
that does not occur in the left-hand side)...
No generalized rewrite rule found!

## Applying the DP framework...
## 2 initial DP problems to solve.
## First, we try to decompose these problems into smaller problems.
## Round 1 [2 DP problems]:
  ## DP problem:
  Dependency pairs = [list1^# -> hamming^#, hamming^# -> list1^#, list2^# -> hamming^#, hamming^# -> list2^#, list3^# -> hamming^#, hamming^# -> list3^#]
  TRS = {app(app(app(if,true),_0),_1) -> _0, app(app(app(if,false),_0),_1) -> _1, app(app(lt,app(s,_0)),app(s,_1)) -> app(app(lt,_0),_1), app(app(lt,0),app(s,_0)) -> true, app(app(lt,_0),0) -> false, app(app(eq,_0),_0) -> true, app(app(eq,app(s,_0)),0) -> false, app(app(eq,0),app(s,_0)) -> false, app(app(merge,_0),nil) -> _0, app(app(merge,nil),_0) -> _0, app(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app(app(app(if,app(app(lt,_0),_2)),app(app(cons,_0),app(app(merge,_1),app(app(cons,_2),_3)))),app(app(app(if,app(app(eq,_0),_2)),app(app(cons,_0),app(app(merge,_1),_3))),app(app(cons,_2),app(app(merge,app(app(cons,_0),_1)),_3)))), app(app(map,_0),nil) -> nil, app(app(map,_0),app(app(cons,_1),_2)) -> app(app(cons,app(_0,_1)),app(app(map,_0),_2)), app(app(mult,0),_0) -> 0, app(app(mult,app(s,_0)),_1) -> app(app(plus,_1),app(app(mult,_0),_1)), app(app(plus,0),_0) -> 0, app(app(plus,app(s,_0)),_1) -> app(s,app(app(plus,_0),_1)), list1 -> app(app(map,app(mult,app(s,app(s,0)))),hamming), list2 -> app(app(map,app(mult,app(s,app(s,app(s,0))))),hamming), list3 -> app(app(map,app(mult,app(s,app(s,app(s,app(s,app(s,0))))))),hamming), hamming -> app(app(cons,app(s,0)),app(app(merge,list1),app(app(merge,list2),list3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... This DP problem is too complex! Aborting!
    ## Trying with lexicographic path orders... Failed!
    ## Trying with Knuth-Bendix orders... This DP problem is too complex! Aborting!
  Don't know whether this DP problem is finite.
  ## DP problem:
  Dependency pairs = [app^#(app(lt,app(s,_0)),app(s,_1)) -> app^#(app(lt,_0),_1), app^#(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app^#(app(app(if,app(app(lt,_0),_2)),app(app(cons,_0),app(app(merge,_1),app(app(cons,_2),_3)))),app(app(app(if,app(app(eq,_0),_2)),app(app(cons,_0),app(app(merge,_1),_3))),app(app(cons,_2),app(app(merge,app(app(cons,_0),_1)),_3)))), app^#(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app^#(app(if,app(app(lt,_0),_2)),app(app(cons,_0),app(app(merge,_1),app(app(cons,_2),_3)))), app^#(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app^#(app(lt,_0),_2), app^#(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app^#(app(cons,_0),app(app(merge,_1),app(app(cons,_2),_3))), app^#(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app^#(app(merge,_1),app(app(cons,_2),_3)), app^#(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app^#(app(cons,_2),_3), app^#(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app^#(app(app(if,app(app(eq,_0),_2)),app(app(cons,_0),app(app(merge,_1),_3))),app(app(cons,_2),app(app(merge,app(app(cons,_0),_1)),_3))), app^#(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app^#(app(if,app(app(eq,_0),_2)),app(app(cons,_0),app(app(merge,_1),_3))), app^#(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app^#(app(eq,_0),_2), app^#(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app^#(app(cons,_0),app(app(merge,_1),_3)), app^#(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app^#(app(merge,_1),_3), app^#(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app^#(app(cons,_2),app(app(merge,app(app(cons,_0),_1)),_3)), app^#(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app^#(app(merge,app(app(cons,_0),_1)),_3), app^#(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app^#(app(cons,_0),_1), app^#(app(map,_0),app(app(cons,_1),_2)) -> app^#(app(cons,app(_0,_1)),app(app(map,_0),_2)), app^#(app(map,_0),app(app(cons,_1),_2)) -> app^#(_0,_1), app^#(app(map,_0),app(app(cons,_1),_2)) -> app^#(app(map,_0),_2), app^#(app(mult,app(s,_0)),_1) -> app^#(app(plus,_1),app(app(mult,_0),_1)), app^#(app(mult,app(s,_0)),_1) -> app^#(app(mult,_0),_1), app^#(app(plus,app(s,_0)),_1) -> app^#(app(plus,_0),_1)]
  TRS = {app(app(app(if,true),_0),_1) -> _0, app(app(app(if,false),_0),_1) -> _1, app(app(lt,app(s,_0)),app(s,_1)) -> app(app(lt,_0),_1), app(app(lt,0),app(s,_0)) -> true, app(app(lt,_0),0) -> false, app(app(eq,_0),_0) -> true, app(app(eq,app(s,_0)),0) -> false, app(app(eq,0),app(s,_0)) -> false, app(app(merge,_0),nil) -> _0, app(app(merge,nil),_0) -> _0, app(app(merge,app(app(cons,_0),_1)),app(app(cons,_2),_3)) -> app(app(app(if,app(app(lt,_0),_2)),app(app(cons,_0),app(app(merge,_1),app(app(cons,_2),_3)))),app(app(app(if,app(app(eq,_0),_2)),app(app(cons,_0),app(app(merge,_1),_3))),app(app(cons,_2),app(app(merge,app(app(cons,_0),_1)),_3)))), app(app(map,_0),nil) -> nil, app(app(map,_0),app(app(cons,_1),_2)) -> app(app(cons,app(_0,_1)),app(app(map,_0),_2)), app(app(mult,0),_0) -> 0, app(app(mult,app(s,_0)),_1) -> app(app(plus,_1),app(app(mult,_0),_1)), app(app(plus,0),_0) -> 0, app(app(plus,app(s,_0)),_1) -> app(s,app(app(plus,_0),_1)), list1 -> app(app(map,app(mult,app(s,app(s,0)))),hamming), list2 -> app(app(map,app(mult,app(s,app(s,app(s,0))))),hamming), list3 -> app(app(map,app(mult,app(s,app(s,app(s,app(s,app(s,0))))))),hamming), hamming -> app(app(cons,app(s,0)),app(app(merge,list1),app(app(merge,list2),list3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... This DP problem is too complex! Aborting!
    ## Trying with lexicographic path orders... Failed!
    ## Trying with Knuth-Bendix orders... This DP problem is too complex! Aborting!
  Don't know whether this DP problem is finite.
## Some DP problems could not be proved finite.
## Now, we try to prove that one of these problems is infinite.
    ## Trying to find a loop (forward=true, backward=true, max=20)
      # max_depth=20, unfold_variables=false:
        # Iteration 0: no loop found, 6 unfolded rules generated.
        # Iteration 1: success, found a loop, 2 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = list1^# -> hamming^# [trans] is in U_IR^0.
        D = hamming^# -> list1^# is a dependency pair of IR.
        We build a composed triple from L0 and D.
        ==> L1 = list1^# -> list1^# [trans] is in U_IR^1.
  This DP problem is infinite.
Proof run on Linux version 3.10.0-1160.25.1.el7.x86_64 for amd64
using Java version 1.8.0_292
** END proof description **
Total number of generated unfolded rules = 89