Runti Compl Full Rewri 10127 pair #381902446

details

property	value
status	complete
benchmark	4.10.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n077.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	1.41592693329 seconds
cpu usage	5.287763587
max memory	8.1760256E7

stage attributes

key	value
output-size	8250
starexec-result	WORST_CASE(Omega(n^1),O(n^2))

output

/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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)) -> *(otimes(x,y),z)
            *(x,oplus(y,z)) -> oplus(*(x,y),*(x,z))
            *(+(x,y),z) -> oplus(*(x,z),*(y,z))
            *(1(),y) -> y
        - Signature:
            {*/2} / {+/2,1/0,oplus/2,otimes/2}
        - Obligation:
             runtime complexity wrt. defined symbols {*} and constructors {+,1,oplus,otimes}
    + 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)) -> *(otimes(x,y),z)
            *(x,oplus(y,z)) -> oplus(*(x,y),*(x,z))
            *(+(x,y),z) -> oplus(*(x,z),*(y,z))
            *(1(),y) -> y
        - Signature:
            {*/2} / {+/2,1/0,oplus/2,otimes/2}
        - Obligation:
             runtime complexity wrt. defined symbols {*} and constructors {+,1,oplus,otimes}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          *(x,y){y -> oplus(y,z)} =
            *(x,oplus(y,z)) ->^+ oplus(*(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)) -> *(otimes(x,y),z)
            *(x,oplus(y,z)) -> oplus(*(x,y),*(x,z))
            *(+(x,y),z) -> oplus(*(x,z),*(y,z))
            *(1(),y) -> y
        - Signature:
            {*/2} / {+/2,1/0,oplus/2,otimes/2}
        - Obligation:
             runtime complexity wrt. defined symbols {*} and constructors {+,1,oplus,otimes}
    + 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(oplus) = {1,2}
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
               p(*) = x1 + x1*x2 + x2
               p(+) = 1 + x1 + x2    
               p(1) = 1              
           p(oplus) = 1 + x1 + x2    
          p(otimes) = 0              
        
        Following rules are strictly oriented:
        *(1(),y) = 1 + 2*y
                 > y      
                 = y      
        
        
        Following rules are (at-least) weakly oriented:
            *(x,*(y,z)) =  x + x*y + x*y*z + x*z + y + y*z + z
                        >= z                                  
                        =  *(otimes(x,y),z)                   
        
        *(x,oplus(y,z)) =  1 + 2*x + x*y + x*z + y + z        
                        >= 1 + 2*x + x*y + x*z + y + z        
                        =  oplus(*(x,y),*(x,z))               
        
            *(+(x,y),z) =  1 + x + x*z + y + y*z + 2*z        
                        >= 1 + x + x*z + y + y*z + 2*z        
                        =  oplus(*(x,z),*(y,z))               
        
** Step 1.b:2: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(x,*(y,z)) -> *(otimes(x,y),z)
            *(x,oplus(y,z)) -> oplus(*(x,y),*(x,z))
            *(+(x,y),z) -> oplus(*(x,z),*(y,z))
        - Weak TRS:
            *(1(),y) -> y
        - Signature:
            {*/2} / {+/2,1/0,oplus/2,otimes/2}
        - Obligation:
             runtime complexity wrt. defined symbols {*} and constructors {+,1,oplus,otimes}
    + Applied Processor:

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