/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 pattern rule was generated by the strategy
presented in Sect. 3 of [Emmes, Enger, Giesl, IJCAR'12]:
[iteration = 0] isList{}^n{} -> U21(isList){}^n{}
We apply Theorem 8 of [Emmes, Enger, Giesl, IJCAR'12]
on this rule with m = 1, b = 0, pi = [0],
sigma' = {} and mu' = {}.
Hence the term isList, obtained from
instantiating n with 0 in the left-hand side of
the rule, starts an infinite derivation 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...
## 3 initial DP problems to solve.
## First, we try to decompose these problems into smaller problems.
## Round 1 [3 DP problems]:
  ## DP problem:
  Dependency pairs = [U71^#(tt) -> isPal^#, isNePal^# -> U71^#(isQid), isPal^# -> isNePal^#]
  TRS = {__(__(_0,_1),_2) -> __(_0,__(_1,_2)), __(_0,nil) -> _0, __(nil,_0) -> _0, U11(tt) -> tt, U21(tt) -> U22(isList), U22(tt) -> tt, U31(tt) -> tt, U41(tt) -> U42(isNeList), U42(tt) -> tt, U51(tt) -> U52(isList), U52(tt) -> tt, U61(tt) -> tt, U71(tt) -> U72(isPal), U72(tt) -> tt, U81(tt) -> tt, isList -> U11(isNeList), isList -> tt, isList -> U21(isList), isNeList -> U31(isQid), isNeList -> U41(isList), isNeList -> U51(isNeList), isNePal -> U61(isQid), isNePal -> U71(isQid), isPal -> U81(isNePal), isPal -> tt, isQid -> tt}
    ## 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... This DP problem is too complex! Aborting!
  Don't know whether this DP problem is finite.
  ## DP problem:
  Dependency pairs = [U21^#(tt) -> isList^#, isList^# -> U21^#(isList), U51^#(tt) -> isList^#, isNeList^# -> U51^#(isNeList), U41^#(tt) -> isNeList^#, isNeList^# -> U41^#(isList), isList^# -> isNeList^#, isList^# -> isList^#, isNeList^# -> isList^#, isNeList^# -> isNeList^#]
  TRS = {__(__(_0,_1),_2) -> __(_0,__(_1,_2)), __(_0,nil) -> _0, __(nil,_0) -> _0, U11(tt) -> tt, U21(tt) -> U22(isList), U22(tt) -> tt, U31(tt) -> tt, U41(tt) -> U42(isNeList), U42(tt) -> tt, U51(tt) -> U52(isList), U52(tt) -> tt, U61(tt) -> tt, U71(tt) -> U72(isPal), U72(tt) -> tt, U81(tt) -> tt, isList -> U11(isNeList), isList -> tt, isList -> U21(isList), isNeList -> U31(isQid), isNeList -> U41(isList), isNeList -> U51(isNeList), isNePal -> U61(isQid), isNePal -> U71(isQid), isPal -> U81(isNePal), isPal -> tt, isQid -> tt}
    ## 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... This DP problem is too complex! Aborting!
  Don't know whether this DP problem is finite.
  ## DP problem:
  Dependency pairs = [__^#(__(_0,_1),_2) -> __^#(_0,__(_1,_2)), __^#(__(_0,_1),_2) -> __^#(_1,_2)]
  TRS = {__(__(_0,_1),_2) -> __(_0,__(_1,_2)), __(_0,nil) -> _0, __(nil,_0) -> _0, U11(tt) -> tt, U21(tt) -> U22(isList), U22(tt) -> tt, U31(tt) -> tt, U41(tt) -> U42(isNeList), U42(tt) -> tt, U51(tt) -> U52(isList), U52(tt) -> tt, U61(tt) -> tt, U71(tt) -> U72(isPal), U72(tt) -> tt, U81(tt) -> tt, isList -> U11(isNeList), isList -> tt, isList -> U21(isList), isNeList -> U31(isQid), isNeList -> U41(isList), isNeList -> U51(isNeList), isNePal -> U61(isQid), isNePal -> U71(isQid), isPal -> U81(isNePal), isPal -> tt, isQid -> tt}
    ## 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... This DP problem is too complex! Aborting!
  Don't know whether this DP problem is finite.
## Some DP problems could not be proved finite.
## Now, we try to prove that one of these problems is infinite.
    ## Trying to prove non-looping nontermination
      # Iteration 0: success, non-looping nontermination proved, 2 unfolded rules generated.
      Here is the successful unfolding. Let IR be the TRS under analysis.
      IR contains the dependency pair isList^# -> U21^#(isList).
      We apply (I) of [Emmes, Enger, Giesl, IJCAR'12] to this dependency pair.
      ==> P0 = isList^#{}^n{} -> U21^#(isList){}^n{} is in U_IR^0.
  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 = 23