TRS Standard pair #615304647

details

property	value
status	complete
benchmark	#3.41.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n046.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0718679428101 seconds
cpu usage	0.053556127
max memory	3002368.0

stage attributes

key	value
output-size	1875
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
fac(0) -> s(0)
fac(s(x:S)) -> times(s(x:S),fac(p(s(x:S))))
p(s(x:S)) -> x:S
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 fac(0) -> s(0)
 fac(s(x:S)) -> times(s(x:S),fac(p(s(x:S))))
 p(s(x:S)) -> x:S
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 FAC(s(x:S)) -> FAC(p(s(x:S)))
 FAC(s(x:S)) -> P(s(x:S))
-> Rules:
 fac(0) -> s(0)
 fac(s(x:S)) -> times(s(x:S),fac(p(s(x:S))))
 p(s(x:S)) -> x:S

Problem 1: 

SCC Processor:
-> Pairs:
 FAC(s(x:S)) -> FAC(p(s(x:S)))
 FAC(s(x:S)) -> P(s(x:S))
-> Rules:
 fac(0) -> s(0)
 fac(s(x:S)) -> times(s(x:S),fac(p(s(x:S))))
 p(s(x:S)) -> x:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 FAC(s(x:S)) -> FAC(p(s(x:S)))
->->-> Rules:
 fac(0) -> s(0)
 fac(s(x:S)) -> times(s(x:S),fac(p(s(x:S))))
 p(s(x:S)) -> x:S

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 FAC(s(x:S)) -> FAC(p(s(x:S)))
-> Rules:
 fac(0) -> s(0)
 fac(s(x:S)) -> times(s(x:S),fac(p(s(x:S))))
 p(s(x:S)) -> x:S
-> Usable rules:
 p(s(x:S)) -> x:S
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[fac](X) = 0
[p](X) = 1/2.X
[0] = 0
[fSNonEmpty] = 0
[s](X) = 2.X + 1/2
[times](X1,X2) = 0
[FAC](X) = 2.X
[P](X) = 0

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 fac(0) -> s(0)
 fac(s(x:S)) -> times(s(x:S),fac(p(s(x:S))))
 p(s(x:S)) -> x:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

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