TRS Stand 20472 pair #381713778

details

property	value
status	complete
benchmark	#3.7.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n101.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	muterm 5.18
configuration	default
runtime (wallclock)	0.0391471385956 seconds
cpu usage	0.02879392
max memory	3186688.0

stage attributes

key	value
output-size	2659
starexec-result	YES

output

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


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YES

Problem 1: 

(VAR x)
(RULES
half(0) -> 0
half(s(s(x))) -> s(half(x))
log(s(0)) -> 0
log(s(s(x))) -> s(log(s(half(x))))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 half(0) -> 0
 half(s(s(x))) -> s(half(x))
 log(s(0)) -> 0
 log(s(s(x))) -> s(log(s(half(x))))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

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