SRS Standard pair #487091448

details

property	value
status	complete
benchmark	z094.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n054.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	1.24097 seconds
cpu usage	1.2236
user time	1.0048
system time	0.218794
max virtual memory	711732.0
max residence set size	8012.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

(VAR v_NonEmpty:S x1:S)
(RULES
c(c(x1:S)) -> c(x1:S)
c(f(x1:S)) -> f(c(c(x1:S)))
f(x1:S) -> n(c(c(x1:S)))
n(f(x1:S)) -> f(n(x1:S))
n(s(x1:S)) -> f(s(s(x1:S)))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 C(f(x1:S)) -> C(c(x1:S))
 C(f(x1:S)) -> C(x1:S)
 C(f(x1:S)) -> F(c(c(x1:S)))
 F(x1:S) -> C(c(x1:S))
 F(x1:S) -> C(x1:S)
 F(x1:S) -> N(c(c(x1:S)))
 N(f(x1:S)) -> F(n(x1:S))
 N(f(x1:S)) -> N(x1:S)
 N(s(x1:S)) -> F(s(s(x1:S)))
-> Rules:
 c(c(x1:S)) -> c(x1:S)
 c(f(x1:S)) -> f(c(c(x1:S)))
 f(x1:S) -> n(c(c(x1:S)))
 n(f(x1:S)) -> f(n(x1:S))
 n(s(x1:S)) -> f(s(s(x1:S)))

Problem 1: 

SCC Processor:
-> Pairs:
 C(f(x1:S)) -> C(c(x1:S))
 C(f(x1:S)) -> C(x1:S)
 C(f(x1:S)) -> F(c(c(x1:S)))
 F(x1:S) -> C(c(x1:S))
 F(x1:S) -> C(x1:S)
 F(x1:S) -> N(c(c(x1:S)))
 N(f(x1:S)) -> F(n(x1:S))
 N(f(x1:S)) -> N(x1:S)
 N(s(x1:S)) -> F(s(s(x1:S)))
-> Rules:
 c(c(x1:S)) -> c(x1:S)
 c(f(x1:S)) -> f(c(c(x1:S)))
 f(x1:S) -> n(c(c(x1:S)))
 n(f(x1:S)) -> f(n(x1:S))
 n(s(x1:S)) -> f(s(s(x1:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 C(f(x1:S)) -> C(c(x1:S))
 C(f(x1:S)) -> C(x1:S)
 C(f(x1:S)) -> F(c(c(x1:S)))
 F(x1:S) -> C(c(x1:S))
 F(x1:S) -> C(x1:S)
 F(x1:S) -> N(c(c(x1:S)))
 N(f(x1:S)) -> F(n(x1:S))
 N(f(x1:S)) -> N(x1:S)
 N(s(x1:S)) -> F(s(s(x1:S)))
->->-> Rules:
 c(c(x1:S)) -> c(x1:S)
 c(f(x1:S)) -> f(c(c(x1:S)))
 f(x1:S) -> n(c(c(x1:S)))
 n(f(x1:S)) -> f(n(x1:S))
 n(s(x1:S)) -> f(s(s(x1:S)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 C(f(x1:S)) -> C(c(x1:S))
 C(f(x1:S)) -> C(x1:S)
 C(f(x1:S)) -> F(c(c(x1:S)))
 F(x1:S) -> C(c(x1:S))
 F(x1:S) -> C(x1:S)
 F(x1:S) -> N(c(c(x1:S)))
 N(f(x1:S)) -> F(n(x1:S))
 N(f(x1:S)) -> N(x1:S)
 N(s(x1:S)) -> F(s(s(x1:S)))
-> Rules:
 c(c(x1:S)) -> c(x1:S)
 c(f(x1:S)) -> f(c(c(x1:S)))
 f(x1:S) -> n(c(c(x1:S)))
 n(f(x1:S)) -> f(n(x1:S))
 n(s(x1:S)) -> f(s(s(x1:S)))
-> Usable rules:
 c(c(x1:S)) -> c(x1:S)
 c(f(x1:S)) -> f(c(c(x1:S)))
 f(x1:S) -> n(c(c(x1:S)))
 n(f(x1:S)) -> f(n(x1:S))
 n(s(x1:S)) -> f(s(s(x1:S)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers

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