TRS Standard pair #516967186

details

property	value
status	complete
benchmark	#3.26.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n119.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.105626106262 seconds
cpu usage	0.037106916
max memory	3158016.0

stage attributes

key	value
output-size	1817
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
f(s(s(x:S))) -> s(f(f(x:S)))
f(x:S) -> s(x:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(s(s(x:S))) -> F(f(x:S))
 F(s(s(x:S))) -> F(x:S)
-> Rules:
 f(s(s(x:S))) -> s(f(f(x:S)))
 f(x:S) -> s(x:S)

Problem 1: 

SCC Processor:
-> Pairs:
 F(s(s(x:S))) -> F(f(x:S))
 F(s(s(x:S))) -> F(x:S)
-> Rules:
 f(s(s(x:S))) -> s(f(f(x:S)))
 f(x:S) -> s(x:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(s(s(x:S))) -> F(f(x:S))
 F(s(s(x:S))) -> F(x:S)
->->-> Rules:
 f(s(s(x:S))) -> s(f(f(x:S)))
 f(x:S) -> s(x:S)

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(s(s(x:S))) -> F(f(x:S))
 F(s(s(x:S))) -> F(x:S)
-> Rules:
 f(s(s(x:S))) -> s(f(f(x:S)))
 f(x:S) -> s(x:S)
-> Usable rules:
 f(s(s(x:S))) -> s(f(f(x:S)))
 f(x:S) -> s(x:S)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X) = 2.X + 1
[s](X) = 2.X + 1
[F](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 F(s(s(x:S))) -> F(x:S)
-> Rules:
 f(s(s(x:S))) -> s(f(f(x:S)))
 f(x:S) -> s(x:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(s(s(x:S))) -> F(x:S)
->->-> Rules:
 f(s(s(x:S))) -> s(f(f(x:S)))
 f(x:S) -> s(x:S)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(s(s(x:S))) -> F(x:S)
-> Rules:
 f(s(s(x:S))) -> s(f(f(x:S)))
 f(x:S) -> s(x:S)
->Projection:
 pi(F) = 1

Problem 1: 

SCC Processor:

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Standard