TRS Standard pair #516965496

details

property	value
status	complete
benchmark	jw36.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n060.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.202602863312 seconds
cpu usage	0.097186583
max memory	3723264.0

stage attributes

key	value
output-size	2112
starexec-result	YES

output

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


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


YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
f(f(x:S,a),a) -> f(f(f(a,a),f(x:S,a)),a)
)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(f(x:S,a),a) -> F(f(f(a,a),f(x:S,a)),a)
 F(f(x:S,a),a) -> F(f(a,a),f(x:S,a))
-> Rules:
 f(f(x:S,a),a) -> f(f(f(a,a),f(x:S,a)),a)
-> Usable rules:
 f(f(x:S,a),a) -> f(f(f(a,a),f(x:S,a)),a)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X1,X2) = 0
[a] = 2
[F](X1,X2) = 2.X2

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(f(x:S,a),a) -> F(f(f(a,a),f(x:S,a)),a)
-> Rules:
 f(f(x:S,a),a) -> f(f(f(a,a),f(x:S,a)),a)
-> Usable rules:
 f(f(x:S,a),a) -> f(f(f(a,a),f(x:S,a)),a)
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X1,X2) = 1/2.X2
[a] = 1
[F](X1,X2) = X1

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