TRS Standard pair #487072799

details

property	value
status	complete
benchmark	4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n187.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	2.71156 seconds
cpu usage	2.6684
user time	2.42633
system time	0.242072
max virtual memory	733492.0
max residence set size	27408.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
a(0,x:S) -> c(c(x:S))
c(c(b(c(x:S)))) -> b(a(0,c(x:S)))
c(c(x:S)) -> b(c(b(c(x:S))))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(0,x:S) -> C(c(x:S))
 A(0,x:S) -> C(x:S)
 C(c(b(c(x:S)))) -> A(0,c(x:S))
 C(c(x:S)) -> C(b(c(x:S)))
-> Rules:
 a(0,x:S) -> c(c(x:S))
 c(c(b(c(x:S)))) -> b(a(0,c(x:S)))
 c(c(x:S)) -> b(c(b(c(x:S))))

Problem 1: 

SCC Processor:
-> Pairs:
 A(0,x:S) -> C(c(x:S))
 A(0,x:S) -> C(x:S)
 C(c(b(c(x:S)))) -> A(0,c(x:S))
 C(c(x:S)) -> C(b(c(x:S)))
-> Rules:
 a(0,x:S) -> c(c(x:S))
 c(c(b(c(x:S)))) -> b(a(0,c(x:S)))
 c(c(x:S)) -> b(c(b(c(x:S))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(0,x:S) -> C(c(x:S))
 A(0,x:S) -> C(x:S)
 C(c(b(c(x:S)))) -> A(0,c(x:S))
->->-> Rules:
 a(0,x:S) -> c(c(x:S))
 c(c(b(c(x:S)))) -> b(a(0,c(x:S)))
 c(c(x:S)) -> b(c(b(c(x:S))))

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 A(0,x:S) -> C(c(x:S))
 C(c(b(c(x:S)))) -> A(0,c(x:S))
-> Rules:
 a(0,x:S) -> c(c(x:S))
 c(c(b(c(x:S)))) -> b(a(0,c(x:S)))
 c(c(x:S)) -> b(c(b(c(x:S))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(0,x:S) -> C(c(x:S))
 C(c(b(c(x:S)))) -> A(0,c(x:S))
->->-> Rules:
 a(0,x:S) -> c(c(x:S))
 c(c(b(c(x:S)))) -> b(a(0,c(x:S)))
 c(c(x:S)) -> b(c(b(c(x:S))))

Problem 1:

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job log

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