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


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NO

** BEGIN proof argument **
The following rule was generated while unfolding the analyzed TRS:
[iteration = 5] ifappend(cons(_0,_1),_2,false) -> ifappend(cons(_0,_1),_2,false)
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 = ifappend(cons(_0,_1),_2,false) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = ifappend(cons(_0,_1),_2,false) 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...
## 1 initial DP problem to solve.
## First, we try to decompose this problem into smaller problems.
## Round 1 [1 DP problem]:
  ## DP problem:
  Dependency pairs = [append^#(_0,_1) -> ifappend^#(_0,_1,is_empty(_0)), ifappend^#(_0,_1,false) -> append^#(tl(_0),_1)]
  TRS = {is_empty(nil) -> true, is_empty(cons(_0,_1)) -> false, hd(cons(_0,_1)) -> _0, tl(cons(_0,_1)) -> cons(_0,_1), append(_0,_1) -> ifappend(_0,_1,is_empty(_0)), ifappend(_0,_1,true) -> _1, ifappend(_0,_1,false) -> cons(hd(_0),append(tl(_0),_1))}
    ## 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... Failed!
  Don't know whether this DP problem is finite.
## A DP problem could not be proved finite.
## Now, we try to prove that this problem is infinite.
    ## Trying to find a loop (forward=true, backward=false, max=-1)
      # max_depth=3, unfold_variables=false:
        # Iteration 0: no loop found, 2 unfolded rules generated.
        # Iteration 1: no loop found, 3 unfolded rules generated.
        # Iteration 2: no loop found, 7 unfolded rules generated.
        # Iteration 3: no loop found, 1 unfolded rule generated.
        # Iteration 4: no loop found, 2 unfolded rules generated.
        # Iteration 5: success, found a loop, 1 unfolded rule generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = ifappend^#(_0,_1,false) -> append^#(tl(_0),_1) [trans] is in U_IR^0.
        D = append^#(_0,_1) -> ifappend^#(_0,_1,is_empty(_0)) is a dependency pair of IR.
        We build a composed triple from L0 and D.
        ==> L1 = ifappend^#(_0,_1,false) -> ifappend^#(tl(_0),_1,is_empty(tl(_0))) [trans] is in U_IR^1.
        We build a unit triple from L1.
        ==> L2 = ifappend^#(_0,_1,false) -> ifappend^#(tl(_0),_1,is_empty(tl(_0))) [unit] is in U_IR^2.
        Let p2 = [2, 0].
        We unfold the rule of L2 forwards at position p2
        with the rule tl(cons(_0,_1)) -> cons(_0,_1).
        ==> L3 = ifappend^#(cons(_0,_1),_2,false) -> ifappend^#(tl(cons(_0,_1)),_2,is_empty(cons(_0,_1))) [unit] is in U_IR^3.
        Let p3 = [0].
        We unfold the rule of L3 forwards at position p3
        with the rule tl(cons(_0,_1)) -> cons(_0,_1).
        ==> L4 = ifappend^#(cons(_0,_1),_2,false) -> ifappend^#(cons(_0,_1),_2,is_empty(cons(_0,_1))) [unit] is in U_IR^4.
        Let p4 = [2].
        We unfold the rule of L4 forwards at position p4
        with the rule is_empty(cons(_0,_1)) -> false.
        ==> L5 = ifappend^#(cons(_0,_1),_2,false) -> ifappend^#(cons(_0,_1),_2,false) [unit] is in U_IR^5.
  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 = 53