TRS Standard pair #615302851

details

property	value
status	complete
benchmark	BTreeMember.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n029.star.cs.uiowa.edu
space	Applicative_05

run statistics

property	value
solver	NTI_23
configuration	default
runtime (wallclock)	0.271069049835 seconds
cpu usage	0.521492753
max memory	5.4677504E7

stage attributes

key	value
output-size	3725
starexec-result	"YES"

output

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


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YES

** BEGIN proof argument **
All the DP problems were proved finite.
As all the involved DP processors are sound,
the TRS under analysis terminates.
** 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 = [app^#(app(lt,app(s,_0)),app(s,_1)) -> app^#(app(lt,_0),_1), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(app(if,app(app(lt,_0),_2)),app(app(member,_0),_1)),app(app(app(if,app(app(eq,_0),_2)),true),app(app(member,_0),_3))), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(if,app(app(lt,_0),_2)),app(app(member,_0),_1)), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(lt,_0),_2), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(member,_0),_1), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(app(if,app(app(eq,_0),_2)),true),app(app(member,_0),_3)), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(eq,_0),_2), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(member,_0),_3)]
  TRS = {app(app(lt,app(s,_0)),app(s,_1)) -> app(app(lt,_0),_1), app(app(lt,0),app(s,_0)) -> true, app(app(lt,_0),0) -> false, app(app(eq,_0),_0) -> true, app(app(eq,app(s,_0)),0) -> false, app(app(eq,0),app(s,_0)) -> false, app(app(member,_0),null) -> false, app(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app(app(app(if,app(app(lt,_0),_2)),app(app(member,_0),_1)),app(app(app(if,app(app(eq,_0),_2)),true),app(app(member,_0),_3)))}
    ## 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 argument filtering: {app^#:[0], app:[0]}.
      Lexicographic path order induced by the precedence: member > [if, false, app^#, true, lt, eq, app], lt > [false, true], eq > [false, true]
      Decomposed the DP problem into 1 smaller problem to solve!
## Round 2 [1 DP problem]:
  ## DP problem:
  Dependency pairs = [app^#(app(lt,app(s,_0)),app(s,_1)) -> app^#(app(lt,_0),_1), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(member,_0),_1), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(member,_0),_3)]
  TRS = {app(app(lt,app(s,_0)),app(s,_1)) -> app(app(lt,_0),_1), app(app(lt,0),app(s,_0)) -> true, app(app(lt,_0),0) -> false, app(app(eq,_0),_0) -> true, app(app(eq,app(s,_0)),0) -> false, app(app(eq,0),app(s,_0)) -> false, app(app(member,_0),null) -> false, app(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app(app(app(if,app(app(lt,_0),_2)),app(app(member,_0),_1)),app(app(app(if,app(app(eq,_0),_2)),true),app(app(member,_0),_3)))}
    ## DP Processor: homeomorphic embeddings. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      Success, finiteness proved!
  This DP problem is finite.
## All the DP problems were proved finite.
As all the involved DP processors are sound,
the TRS under analysis terminates.
Proof run on Linux version 3.10.0-1160.62.1.el7.x86_64 for amd64
using Java version 1.8.0_322
** END proof description **
Total number of generated unfolded rules = 0

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