/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...
## 4 initial DP problems to solve.
## First, we try to decompose these problems into smaller problems.
## Round 1 [4 DP problems]:
  ## DP problem:
  Dependency pairs = [bsort^#(.(_0,_1)) -> bsort^#(butlast(bubble(.(_0,_1))))]
  TRS = {bsort(nil) -> nil, bsort(.(_0,_1)) -> last(.(bubble(.(_0,_1)),bsort(butlast(bubble(.(_0,_1)))))), bubble(nil) -> nil, bubble(.(_0,nil)) -> .(_0,nil), bubble(.(_0,.(_1,_2))) -> if(<=(_0,_1),.(_1,bubble(.(_0,_2))),.(_0,bubble(.(_1,_2)))), last(nil) -> 0, last(.(_0,nil)) -> _0, last(.(_0,.(_1,_2))) -> last(.(_1,_2)), butlast(nil) -> nil, butlast(.(_0,nil)) -> nil, butlast(.(_0,.(_1,_2))) -> .(_0,butlast(.(_1,_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.
  ## DP problem:
  Dependency pairs = [butlast^#(.(_0,.(_1,_2))) -> butlast^#(.(_1,_2))]
  TRS = {bsort(nil) -> nil, bsort(.(_0,_1)) -> last(.(bubble(.(_0,_1)),bsort(butlast(bubble(.(_0,_1)))))), bubble(nil) -> nil, bubble(.(_0,nil)) -> .(_0,nil), bubble(.(_0,.(_1,_2))) -> if(<=(_0,_1),.(_1,bubble(.(_0,_2))),.(_0,bubble(.(_1,_2)))), last(nil) -> 0, last(.(_0,nil)) -> _0, last(.(_0,.(_1,_2))) -> last(.(_1,_2)), butlast(nil) -> nil, butlast(.(_0,nil)) -> nil, butlast(.(_0,.(_1,_2))) -> .(_0,butlast(.(_1,_2)))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [bubble^#(.(_0,.(_1,_2))) -> bubble^#(.(_0,_2)), bubble^#(.(_0,.(_1,_2))) -> bubble^#(.(_1,_2))]
  TRS = {bsort(nil) -> nil, bsort(.(_0,_1)) -> last(.(bubble(.(_0,_1)),bsort(butlast(bubble(.(_0,_1)))))), bubble(nil) -> nil, bubble(.(_0,nil)) -> .(_0,nil), bubble(.(_0,.(_1,_2))) -> if(<=(_0,_1),.(_1,bubble(.(_0,_2))),.(_0,bubble(.(_1,_2)))), last(nil) -> 0, last(.(_0,nil)) -> _0, last(.(_0,.(_1,_2))) -> last(.(_1,_2)), butlast(nil) -> nil, butlast(.(_0,nil)) -> nil, butlast(.(_0,.(_1,_2))) -> .(_0,butlast(.(_1,_2)))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [last^#(.(_0,.(_1,_2))) -> last^#(.(_1,_2))]
  TRS = {bsort(nil) -> nil, bsort(.(_0,_1)) -> last(.(bubble(.(_0,_1)),bsort(butlast(bubble(.(_0,_1)))))), bubble(nil) -> nil, bubble(.(_0,nil)) -> .(_0,nil), bubble(.(_0,.(_1,_2))) -> if(<=(_0,_1),.(_1,bubble(.(_0,_2))),.(_0,bubble(.(_1,_2)))), last(nil) -> 0, last(.(_0,nil)) -> _0, last(.(_0,.(_1,_2))) -> last(.(_1,_2)), butlast(nil) -> nil, butlast(.(_0,nil)) -> nil, butlast(.(_0,.(_1,_2))) -> .(_0,butlast(.(_1,_2)))}
    ## Trying with homeomorphic embeddings... Success!
  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 = [bsort^#(.(_0,_1)) -> bsort^#(butlast(bubble(.(_0,_1))))]
TRS = {bsort(nil) -> nil, bsort(.(_0,_1)) -> last(.(bubble(.(_0,_1)),bsort(butlast(bubble(.(_0,_1)))))), bubble(nil) -> nil, bubble(.(_0,nil)) -> .(_0,nil), bubble(.(_0,.(_1,_2))) -> if(<=(_0,_1),.(_1,bubble(.(_0,_2))),.(_0,bubble(.(_1,_2)))), last(nil) -> 0, last(.(_0,nil)) -> _0, last(.(_0,.(_1,_2))) -> last(.(_1,_2)), butlast(nil) -> nil, butlast(.(_0,nil)) -> nil, butlast(.(_0,.(_1,_2))) -> .(_0,butlast(.(_1,_2)))}
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 = 239