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


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MAYBE

** 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 = [mark^#(f(_0)) -> mark^#(_0), mark^#(p(_0)) -> mark^#(_0), mark^#(cons(_0,_1)) -> mark^#(_0), mark^#(s(_0)) -> mark^#(_0)]
  TRS = {a__f(0) -> cons(0,f(s(0))), a__f(s(0)) -> a__f(a__p(s(0))), a__p(s(0)) -> 0, mark(f(_0)) -> a__f(mark(_0)), mark(p(_0)) -> a__p(mark(_0)), mark(0) -> 0, mark(cons(_0,_1)) -> cons(mark(_0),_1), mark(s(_0)) -> s(mark(_0)), a__f(_0) -> f(_0), a__p(_0) -> p(_0)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [a__f^#(s(0)) -> a__f^#(a__p(s(0)))]
  TRS = {a__f(0) -> cons(0,f(s(0))), a__f(s(0)) -> a__f(a__p(s(0))), a__p(s(0)) -> 0, mark(f(_0)) -> a__f(mark(_0)), mark(p(_0)) -> a__p(mark(_0)), mark(0) -> 0, mark(cons(_0,_1)) -> cons(mark(_0),_1), mark(s(_0)) -> s(mark(_0)), a__f(_0) -> f(_0), a__p(_0) -> p(_0)}
    ## 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.
## Could not solve the following DP problems:
1: Dependency pairs = [a__f^#(s(0)) -> a__f^#(a__p(s(0)))]
TRS = {a__f(0) -> cons(0,f(s(0))), a__f(s(0)) -> a__f(a__p(s(0))), a__p(s(0)) -> 0, mark(f(_0)) -> a__f(mark(_0)), mark(p(_0)) -> a__p(mark(_0)), mark(0) -> 0, mark(cons(_0,_1)) -> cons(mark(_0),_1), mark(s(_0)) -> s(mark(_0)), a__f(_0) -> f(_0), a__p(_0) -> p(_0)}
Hence, could not prove (non)termination of the TRS under analysis.
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 = 28