TRS Standard pair #615297185

details

property	value
status	complete
benchmark	jw05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n002.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.111449956894 seconds
cpu usage	0.094509869
max memory	4059136.0

stage attributes

key	value
output-size	1533
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(f(a,x:S),a) -> f(f(x:S,f(a,a)),a)
)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(f(a,x:S),a) -> F(f(x:S,f(a,a)),a)
-> Rules:
 f(f(a,x:S),a) -> f(f(x:S,f(a,a)),a)
-> Usable rules:
 f(f(a,x:S),a) -> f(f(x:S,f(a,a)),a)
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[f](X1,X2) = 1/4.X1 + 1/4.X2
[a] = 1/4
[fSNonEmpty] = 0
[F](X1,X2) = 3/4.X1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(f(a,x:S),a) -> f(f(x:S,f(a,a)),a)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

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