/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 double path program (DPP) was generated while unfolding the analyzed TRS:
[iteration = 1] [f^#(0,_0,g(_1),_2) -> f^#(s(_0),s(_0),g(1),_2), f^#(s(_3),_4,_5,s(_6)) -> f^#(_3,_4,_5,s(2))] [comp]
This DPP admits the recurrent pair:
< C1 = f^#(0,□,g(1),s(2)), C2 = f^#(s(□),◯,g(1),s(2)), Δ = s(□), u = 0 >
Hence, the term f(0,0,g(1),s(2)) is nonterminating 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 = [f^#(0,_0,g(_1),_2) -> f^#(s(_0),s(_0),g(1),_2), f^#(s(_0),_1,_2,s(_3)) -> f^#(_0,_1,_2,s(2))]
  TRS = {f(0,_0,g(_1),_2) -> f(s(_0),s(_0),g(1),_2), f(s(_0),_1,_2,s(_3)) -> f(_0,_1,_2,s(2))}
    ## 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=2, unfold_variables=false:
        # Iteration 0: no loop found, 2 unfolded rules generated.
        # Iteration 1: success, found a loop, 1 unfolded rule generated.
  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 = 8