Runti Compl Full Rewri 10127 pair #381903052

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	n041.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	0.429863929749 seconds
cpu usage	1.650838066
max memory	4.8410624E7

stage attributes

key	value
output-size	22516
starexec-result	WORST_CASE(Omega(n^1),O(n^1))

output

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


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


WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            half(0()) -> 0()
            half(s(s(x))) -> s(half(x))
            log(s(0())) -> 0()
            log(s(s(x))) -> s(log(s(half(x))))
        - Signature:
            {half/1,log/1} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {half,log} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            half(0()) -> 0()
            half(s(s(x))) -> s(half(x))
            log(s(0())) -> 0()
            log(s(s(x))) -> s(log(s(half(x))))
        - Signature:
            {half/1,log/1} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {half,log} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          half(x){x -> s(s(x))} =
            half(s(s(x))) ->^+ s(half(x))
              = C[half(x) = half(x){}]

** Step 1.b:1: ToInnermost WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            half(0()) -> 0()
            half(s(s(x))) -> s(half(x))
            log(s(0())) -> 0()
            log(s(s(x))) -> s(log(s(half(x))))
        - Signature:
            {half/1,log/1} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {half,log} and constructors {0,s}
    + Applied Processor:
        ToInnermost
    + Details:
        switch to innermost, as the system is overlay and right linear and does not contain weak rules
** Step 1.b:2: DependencyPairs WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            half(0()) -> 0()
            half(s(s(x))) -> s(half(x))
            log(s(0())) -> 0()
            log(s(s(x))) -> s(log(s(half(x))))
        - Signature:
            {half/1,log/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {half,log} and constructors {0,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = WIDP}
    + Details:
        We add the following weak innermost dependency pairs:
        
        Strict DPs
          half#(0()) -> c_1()
          half#(s(s(x))) -> c_2(half#(x))
          log#(s(0())) -> c_3()
          log#(s(s(x))) -> c_4(log#(s(half(x))))
        Weak DPs
          
        
        and mark the set of starting terms.
** Step 1.b:3: UsableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            half#(0()) -> c_1()
            half#(s(s(x))) -> c_2(half#(x))
            log#(s(0())) -> c_3()
            log#(s(s(x))) -> c_4(log#(s(half(x))))
        - Strict TRS:
            half(0()) -> 0()
            half(s(s(x))) -> s(half(x))
            log(s(0())) -> 0()
            log(s(s(x))) -> s(log(s(half(x))))
        - Signature:
            {half/1,log/1,half#/1,log#/1} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {half#,log#} and constructors {0,s}
    + Applied Processor:
        UsableRules
    + Details:

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to Runti Compl Full Rewri 10127