TRS Standard pair #615299316

details
property	value
status	complete
benchmark	PALINDROME_nokinds-noand_L.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n178.star.cs.uiowa.edu
space	Transformed_CSR_04
run statistics
property	value
solver	NTI_23
configuration	default
runtime (wallclock)	0.297034978867 seconds
cpu usage	0.548562754
max memory	6.6609152E7
stage attributes
key	value
output-size	6626
starexec-result	"NO"
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


NO

** BEGIN proof argument **
* Certificate: isList is non-terminating
* Description:
The following rule R was generated while unfolding
the dependency pairs of the analyzed TRS:
[iteration = 0] isList^# -> isList^#
Let l be the left-hand side and r be the right-hand side of R.
Let p = epsilon, theta1 = {} and theta2 = {}.
We have r|p = isList^#
and theta2(theta1(l)) = theta1(r|p), i.e., l semi-unifies with r|p.
So, the term theta1(l) = isList
starts an infinite rewrite sequence 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}
    ## DP Processor: homeomorphic embeddings. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      Failed!
    ## DP Processor: lexicographic path orders. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      This DP problem is too complex (23 symbols to deal with)! Aborting!
      Failed!
    ## DP Processor: polynomial interpretations. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      This DP problem is too complex (35 coefficients to instantiate)! Aborting!
      Failed!
    ## DP Processor: Knuth-Bendix orders. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      This DP problem is too complex (20 weights to instantiate)! Aborting!
      Failed!
  All the DP processors have failed!
  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}
    ## DP Processor: homeomorphic embeddings. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      Failed!
    ## DP Processor: lexicographic path orders. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      This DP problem is too complex (25 symbols to deal with)! Aborting!
      Failed!
    ## DP Processor: polynomial interpretations. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      Failed!
    ## DP Processor: Knuth-Bendix orders. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      This DP problem is too complex (20 weights to instantiate)! Aborting!
      Failed!
  All the DP processors have failed!
  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}
    ## DP Processor: homeomorphic embeddings. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      Failed!
    ## DP Processor: lexicographic path orders. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      This DP problem is too complex (21 symbols to deal with)! Aborting!
      Failed!
    ## DP Processor: polynomial interpretations. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      This DP problem is too complex (35 coefficients to instantiate)! Aborting!
      Failed!
    ## DP Processor: Knuth-Bendix orders. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      This DP problem is too complex (20 weights to instantiate)! Aborting!
      Failed!
  All the DP processors have failed!
  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.
    ## DP Processor: [Payet, LOPSTR'18] + [Payet, Non-termination in TRS and LP] (forward=true, backward=true, max=20). 
      # max_depth=20, unfold_variables=false:
        # Iteration 0: success, loop found, 8 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = isList^# -> isList^# [trans] is in U_IR^0.
  This DP problem is infinite.
Proof run on Linux version 3.10.0-1160.62.1.el7.x86_64 for amd64
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