/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 = 2] +(+(_0,*(_1,_2)),*(_1,_3)) -> +(+(_0,*(_1,_2)),*(_1,_3))
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 = +(+(_0,*(_1,_2)),*(_1,_3)) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = +(+(_0,*(_1,_2)),*(_1,_3)) 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 = [+^#(_0,+(_1,_2)) -> +^#(+(_0,_1),_2), +^#(_0,+(_1,_2)) -> +^#(_0,_1), *^#(_0,+(_1,_2)) -> +^#(*(_0,_1),*(_0,_2)), *^#(_0,+(_1,_2)) -> *^#(_0,_1), *^#(_0,+(_1,_2)) -> *^#(_0,_2), +^#(+(_0,*(_1,_2)),*(_1,_3)) -> *^#(_1,+(_2,_3)), +^#(+(_0,*(_1,_2)),*(_1,_3)) -> +^#(_0,*(_1,+(_2,_3))), +^#(+(_0,*(_1,_2)),*(_1,_3)) -> +^#(_2,_3)]
  TRS = {+(_0,+(_1,_2)) -> +(+(_0,_1),_2), *(_0,+(_1,_2)) -> +(*(_0,_1),*(_0,_2)), +(+(_0,*(_1,_2)),*(_1,_3)) -> +(_0,*(_1,+(_2,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
    Successfully decomposed the DP problem into 1 smaller problem to solve!
## Round 2 [1 DP problem]:
  ## DP problem:
  Dependency pairs = [+^#(+(_0,*(_1,_2)),*(_1,_3)) -> +^#(_0,*(_1,+(_2,_3))), +^#(_0,+(_1,_2)) -> +^#(+(_0,_1),_2)]
  TRS = {+(_0,+(_1,_2)) -> +(+(_0,_1),_2), *(_0,+(_1,_2)) -> +(*(_0,_1),*(_0,_2)), +(+(_0,*(_1,_2)),*(_1,_3)) -> +(_0,*(_1,+(_2,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## 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, 5 unfolded rules generated.
        # Iteration 2: success, found a loop, 3 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = +^#(+(_0,*(_1,_2)),*(_1,_3)) -> +^#(_0,*(_1,+(_2,_3))) [trans] is in U_IR^0.
        D = +^#(_0,+(_1,_2)) -> +^#(+(_0,_1),_2) is a dependency pair of IR.
        We build a composed triple from L0 and D.
        ==> L1 = [+^#(+(_0,*(_1,_2)),*(_1,_3)) -> +^#(_0,*(_1,+(_2,_3))), +^#(_4,+(_5,_6)) -> +^#(+(_4,_5),_6)] [comp] is in U_IR^1.
        Let p1 = [1].
        We unfold the first rule of L1 forwards at position p1
        with the rule *(_0,+(_1,_2)) -> +(*(_0,_1),*(_0,_2)).
        ==> L2 = +^#(+(_0,*(_1,_2)),*(_1,_3)) -> +^#(+(_0,*(_1,_2)),*(_1,_3)) [trans] is in U_IR^2.
  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 = 20