TRS Standard pair #487067104

details

property	value
status	complete
benchmark	linear1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n192.star.cs.uiowa.edu
space	Endrullis_06

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	3.4129 seconds
cpu usage	3.38868
user time	3.18443
system time	0.204252
max virtual memory	818332.0
max residence set size	53756.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

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