/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 double path program (DPP) was generated while unfolding the analyzed TRS:
[iteration = 1] [f^#(_0,s(_1)) -> f^#(s(_0),_1), f^#(_2,0) -> f^#(_2,s(_2))] [comp]
This DPP admits the recurrent pair:
< C1 = f^#(s(□),0), C2 = f^#(◯,s(□)), Δ = s(□), u = 0 >
Hence, the term f(s(0),0) 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,s(_1)) -> f^#(s(_0),_1), f^#(_0,0) -> f^#(_0,s(_0))]
  TRS = {f(_0,s(_1)) -> f(s(_0),_1), f(_0,0) -> f(_0,s(_0))}
    ## 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=true, max=20)
      # max_depth=20, 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