TRS Inner 89993 pair #381733606

details

property	value
status	complete
benchmark	#4.28.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n075.star.cs.uiowa.edu
space	AG01_innermost

run statistics

property	value
solver	muterm 5.18
configuration	default
runtime (wallclock)	1.19959497452 seconds
cpu usage	0.044951317
max memory	3665920.0

stage attributes

key	value
output-size	2531
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 x)
(RULES
bits(0) -> 0
bits(s(x)) -> s(bits(half(s(x))))
half(0) -> 0
half(s(0)) -> 0
half(s(s(x))) -> s(half(x))
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 BITS(s(x)) -> BITS(half(s(x)))
 BITS(s(x)) -> HALF(s(x))
 HALF(s(s(x))) -> HALF(x)
-> Rules:
 bits(0) -> 0
 bits(s(x)) -> s(bits(half(s(x))))
 half(0) -> 0
 half(s(0)) -> 0
 half(s(s(x))) -> s(half(x))

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

The problem is finite.

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