/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),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            *(x,0()) -> 0()
            *(x,s(y)) -> +(*(x,y),x)
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            f(x,0(),z) -> z
            f(x,s(y),z) -> if(odd(s(y)),f(x,y,*(x,z)),f(*(x,x),half(s(y)),z))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            if(false(),x,y) -> y
            if(false(),x,y) -> false()
            if(true(),x,y) -> x
            if(true(),x,y) -> true()
            odd(0()) -> false()
            odd(s(0())) -> true()
            odd(s(s(x))) -> odd(x)
            pow(x,y) -> f(x,y,s(0()))
        - Signature:
            {*/2,-/2,f/3,half/1,if/3,odd/1,pow/2} / {+/2,0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {*,-,f,half,if,odd,pow} and constructors {+,0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            *(x,0()) -> 0()
            *(x,s(y)) -> +(*(x,y),x)
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            f(x,0(),z) -> z
            f(x,s(y),z) -> if(odd(s(y)),f(x,y,*(x,z)),f(*(x,x),half(s(y)),z))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            if(false(),x,y) -> y
            if(false(),x,y) -> false()
            if(true(),x,y) -> x
            if(true(),x,y) -> true()
            odd(0()) -> false()
            odd(s(0())) -> true()
            odd(s(s(x))) -> odd(x)
            pow(x,y) -> f(x,y,s(0()))
        - Signature:
            {*/2,-/2,f/3,half/1,if/3,odd/1,pow/2} / {+/2,0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {*,-,f,half,if,odd,pow} and constructors {+,0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            *(x,0()) -> 0()
            *(x,s(y)) -> +(*(x,y),x)
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            f(x,0(),z) -> z
            f(x,s(y),z) -> if(odd(s(y)),f(x,y,*(x,z)),f(*(x,x),half(s(y)),z))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            if(false(),x,y) -> y
            if(false(),x,y) -> false()
            if(true(),x,y) -> x
            if(true(),x,y) -> true()
            odd(0()) -> false()
            odd(s(0())) -> true()
            odd(s(s(x))) -> odd(x)
            pow(x,y) -> f(x,y,s(0()))
        - Signature:
            {*/2,-/2,f/3,half/1,if/3,odd/1,pow/2} / {+/2,0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {*,-,f,half,if,odd,pow} and constructors {+,0,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          *(x,y){y -> s(y)} =
            *(x,s(y)) ->^+ +(*(x,y),x)
              = C[*(x,y) = *(x,y){}]

WORST_CASE(Omega(n^1),?)