Runti Compl Full Rewri 10127 pair #381902573

details

property	value
status	complete
benchmark	31.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n049.star.cs.uiowa.edu
space	Der95

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	0.941478967667 seconds
cpu usage	2.671001078
max memory	7.9392768E7

stage attributes

key	value
output-size	6313
starexec-result	WORST_CASE(Omega(n^1),O(n^2))

output

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

** Step 1.b:1: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            :(z,+(x,f(y))) -> :(g(z,y),+(x,a()))
            :(+(x,y),z) -> +(:(x,z),:(y,z))
            :(:(x,y),z) -> :(x,:(y,z))
        - Signature:
            {:/2} / {+/2,a/0,f/1,g/2}
        - Obligation:
             runtime complexity wrt. defined symbols {:} and constructors {+,a,f,g}
    + 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},
          uargs(:) = {2}
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(+) = 1 + x1 + x2            
          p(:) = 1 + 2*x1 + 2*x1*x2 + x2
          p(a) = 0                      
          p(f) = 1 + x1                 
          p(g) = x1                     
        
        Following rules are strictly oriented:
        :(z,+(x,f(y))) = 3 + x + 2*x*z + y + 2*y*z + 6*z                      
                       > 2 + x + 2*x*z + 4*z                                  
                       = :(g(z,y),+(x,a()))                                   
        
           :(:(x,y),z) = 3 + 4*x + 4*x*y + 4*x*y*z + 4*x*z + 2*y + 2*y*z + 3*z
                       > 2 + 4*x + 4*x*y + 4*x*y*z + 2*x*z + 2*y + 2*y*z + z  
                       = :(x,:(y,z))                                          
        
        
        Following rules are (at-least) weakly oriented:
        :(+(x,y),z) =  3 + 2*x + 2*x*z + 2*y + 2*y*z + 3*z
                    >= 3 + 2*x + 2*x*z + 2*y + 2*y*z + 2*z
                    =  +(:(x,z),:(y,z))                   
        
** Step 1.b:2: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            :(+(x,y),z) -> +(:(x,z),:(y,z))
        - Weak TRS:
            :(z,+(x,f(y))) -> :(g(z,y),+(x,a()))
            :(:(x,y),z) -> :(x,:(y,z))
        - Signature:
            {:/2} / {+/2,a/0,f/1,g/2}
        - Obligation:
             runtime complexity wrt. defined symbols {:} and constructors {+,a,f,g}
    + 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},
          uargs(:) = {2}

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