Runti Compl Inner Rewri 22807 pair #381904960

details

property	value
status	complete
benchmark	4.05.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	SK90

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci
runtime (wallclock)	0.81939291954 seconds
cpu usage	4.183641832
max memory	5.494784E7

stage attributes

key	value
output-size	3863
starexec-result	WORST_CASE(Omega(n^1),O(n^2))

output

/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(Omega(n^1),O(n^2))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(x,+(y,z)) -> +(*(x,y),*(x,z))
            *(x,1()) -> x
            *(+(x,y),z) -> +(*(x,z),*(y,z))
            *(1(),y) -> y
        - Signature:
            {*/2} / {+/2,1/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*} and constructors {+,1}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            *(x,+(y,z)) -> +(*(x,y),*(x,z))
            *(x,1()) -> x
            *(+(x,y),z) -> +(*(x,z),*(y,z))
            *(1(),y) -> y
        - Signature:
            {*/2} / {+/2,1/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*} and constructors {+,1}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          *(x,y){y -> +(y,z)} =
            *(x,+(y,z)) ->^+ +(*(x,y),*(x,z))
              = C[*(x,y) = *(x,y){}]

** Step 1.b:1: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(x,+(y,z)) -> +(*(x,y),*(x,z))
            *(x,1()) -> x
            *(+(x,y),z) -> +(*(x,z),*(y,z))
            *(1(),y) -> y
        - Signature:
            {*/2} / {+/2,1/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*} and constructors {+,1}
    + Applied Processor:
        NaturalPI {shape = Mixed 2, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(mixed(2)):
        The following argument positions are considered usable:
          uargs(+) = {1,2}
        
        Following symbols are considered usable:
          {*}
        TcT has computed the following interpretation:
          p(*) = 1 + 2*x1 + 3*x1*x2 + 5*x2
          p(+) = 2 + x1 + x2              
          p(1) = 1                        
        
        Following rules are strictly oriented:
        *(x,+(y,z)) = 11 + 8*x + 3*x*y + 3*x*z + 5*y + 5*z
                    > 4 + 4*x + 3*x*y + 3*x*z + 5*y + 5*z 
                    = +(*(x,y),*(x,z))                    
        
           *(x,1()) = 6 + 5*x                             
                    > x                                   
                    = x                                   
        
        *(+(x,y),z) = 5 + 2*x + 3*x*z + 2*y + 3*y*z + 11*z
                    > 4 + 2*x + 3*x*z + 2*y + 3*y*z + 10*z
                    = +(*(x,z),*(y,z))                    
        
           *(1(),y) = 3 + 8*y                             
                    > y                                   
                    = y                                   
        
        
        Following rules are (at-least) weakly oriented:
        
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            *(x,+(y,z)) -> +(*(x,y),*(x,z))
            *(x,1()) -> x
            *(+(x,y),z) -> +(*(x,z),*(y,z))
            *(1(),y) -> y
        - Signature:
            {*/2} / {+/2,1/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*} and constructors {+,1}
    + Applied Processor:
        EmptyProcessor
    + Details:

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