SRS Standard pair #487520095

details

property	value
status	complete
benchmark	z109.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n035.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	1.04323601723 seconds
cpu usage	0.750960477
max memory	5963776.0

stage attributes

key	value
output-size	3687
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 x1:S)
(RULES
a(a(a(x1:S))) -> b(b(x1:S))
b(b(b(x1:S))) -> c(x1:S)
c(x1:S) -> d(d(x1:S))
d(x1:S) -> a(a(x1:S))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(a(a(x1:S))) -> B(b(x1:S))
 A(a(a(x1:S))) -> B(x1:S)
 B(b(b(x1:S))) -> C(x1:S)
 C(x1:S) -> D(d(x1:S))
 C(x1:S) -> D(x1:S)
 D(x1:S) -> A(a(x1:S))
 D(x1:S) -> A(x1:S)
-> Rules:
 a(a(a(x1:S))) -> b(b(x1:S))
 b(b(b(x1:S))) -> c(x1:S)
 c(x1:S) -> d(d(x1:S))
 d(x1:S) -> a(a(x1:S))

Problem 1: 

SCC Processor:
-> Pairs:
 A(a(a(x1:S))) -> B(b(x1:S))
 A(a(a(x1:S))) -> B(x1:S)
 B(b(b(x1:S))) -> C(x1:S)
 C(x1:S) -> D(d(x1:S))
 C(x1:S) -> D(x1:S)
 D(x1:S) -> A(a(x1:S))
 D(x1:S) -> A(x1:S)
-> Rules:
 a(a(a(x1:S))) -> b(b(x1:S))
 b(b(b(x1:S))) -> c(x1:S)
 c(x1:S) -> d(d(x1:S))
 d(x1:S) -> a(a(x1:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(a(a(x1:S))) -> B(b(x1:S))
 A(a(a(x1:S))) -> B(x1:S)
 B(b(b(x1:S))) -> C(x1:S)
 C(x1:S) -> D(d(x1:S))
 C(x1:S) -> D(x1:S)
 D(x1:S) -> A(a(x1:S))
 D(x1:S) -> A(x1:S)
->->-> Rules:
 a(a(a(x1:S))) -> b(b(x1:S))
 b(b(b(x1:S))) -> c(x1:S)
 c(x1:S) -> d(d(x1:S))
 d(x1:S) -> a(a(x1:S))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(a(a(x1:S))) -> B(b(x1:S))
 A(a(a(x1:S))) -> B(x1:S)
 B(b(b(x1:S))) -> C(x1:S)
 C(x1:S) -> D(d(x1:S))
 C(x1:S) -> D(x1:S)
 D(x1:S) -> A(a(x1:S))
 D(x1:S) -> A(x1:S)
-> Rules:
 a(a(a(x1:S))) -> b(b(x1:S))
 b(b(b(x1:S))) -> c(x1:S)
 c(x1:S) -> d(d(x1:S))
 d(x1:S) -> a(a(x1:S))
-> Usable rules:
 a(a(a(x1:S))) -> b(b(x1:S))
 b(b(b(x1:S))) -> c(x1:S)
 c(x1:S) -> d(d(x1:S))
 d(x1:S) -> a(a(x1:S))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[a](X) = X + 1
[b](X) = X + 3/2

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