TRS Standard pair #615298347

details

property	value
status	complete
benchmark	t008.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n025.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.094929933548 seconds
cpu usage	0.0618846
max memory	3833856.0

stage attributes

key	value
output-size	2837
starexec-result	"YES"

output

/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
half(s(s(x:S))) -> s(half(x:S))
half(s(0)) -> 0
half(0) -> 0
log(s(x:S)) -> s(log(half(s(x:S))))
s(log(0)) -> s(0)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 HALF(s(s(x:S))) -> HALF(x:S)
 HALF(s(s(x:S))) -> S(half(x:S))
 LOG(s(x:S)) -> HALF(s(x:S))
 LOG(s(x:S)) -> LOG(half(s(x:S)))
 LOG(s(x:S)) -> S(log(half(s(x:S))))
-> Rules:
 half(s(s(x:S))) -> s(half(x:S))
 half(s(0)) -> 0
 half(0) -> 0
 log(s(x:S)) -> s(log(half(s(x:S))))
 s(log(0)) -> s(0)

Problem 1: 

SCC Processor:
-> Pairs:
 HALF(s(s(x:S))) -> HALF(x:S)
 HALF(s(s(x:S))) -> S(half(x:S))
 LOG(s(x:S)) -> HALF(s(x:S))
 LOG(s(x:S)) -> LOG(half(s(x:S)))
 LOG(s(x:S)) -> S(log(half(s(x:S))))
-> Rules:
 half(s(s(x:S))) -> s(half(x:S))
 half(s(0)) -> 0
 half(0) -> 0
 log(s(x:S)) -> s(log(half(s(x:S))))
 s(log(0)) -> s(0)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 HALF(s(s(x:S))) -> HALF(x:S)
->->-> Rules:
 half(s(s(x:S))) -> s(half(x:S))
 half(s(0)) -> 0
 half(0) -> 0
 log(s(x:S)) -> s(log(half(s(x:S))))
 s(log(0)) -> s(0)
->->Cycle:
->->-> Pairs:
 LOG(s(x:S)) -> LOG(half(s(x:S)))
->->-> Rules:
 half(s(s(x:S))) -> s(half(x:S))
 half(s(0)) -> 0
 half(0) -> 0
 log(s(x:S)) -> s(log(half(s(x:S))))
 s(log(0)) -> s(0)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 HALF(s(s(x:S))) -> HALF(x:S)
-> Rules:
 half(s(s(x:S))) -> s(half(x:S))
 half(s(0)) -> 0
 half(0) -> 0
 log(s(x:S)) -> s(log(half(s(x:S))))
 s(log(0)) -> s(0)
->Projection:
 pi(HALF) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 half(s(s(x:S))) -> s(half(x:S))
 half(s(0)) -> 0
 half(0) -> 0
 log(s(x:S)) -> s(log(half(s(x:S))))
 s(log(0)) -> s(0)
->Strongly Connected Components:
 There is no strongly connected component

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