/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),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            if(false(),x,y,z,u) -> if2(le(y,s(u)),x,y,s(z),s(u))
            if(true(),x,y,z,u) -> u
            if2(false(),x,y,z,u) -> modIter(x,y,z,u)
            if2(true(),x,y,z,u) -> modIter(x,y,z,0())
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            mod(x,0()) -> modZeroErro()
            mod(x,s(y)) -> modIter(x,s(y),0(),0())
            modIter(x,s(y),z,u) -> if(le(x,z),x,s(y),z,u)
        - Signature:
            {if/5,if2/5,le/2,mod/2,modIter/4} / {0/0,false/0,modZeroErro/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {if,if2,le,mod,modIter} and constructors {0,false,modZeroErro,s
            ,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            if(false(),x,y,z,u) -> if2(le(y,s(u)),x,y,s(z),s(u))
            if(true(),x,y,z,u) -> u
            if2(false(),x,y,z,u) -> modIter(x,y,z,u)
            if2(true(),x,y,z,u) -> modIter(x,y,z,0())
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            mod(x,0()) -> modZeroErro()
            mod(x,s(y)) -> modIter(x,s(y),0(),0())
            modIter(x,s(y),z,u) -> if(le(x,z),x,s(y),z,u)
        - Signature:
            {if/5,if2/5,le/2,mod/2,modIter/4} / {0/0,false/0,modZeroErro/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {if,if2,le,mod,modIter} and constructors {0,false,modZeroErro,s
            ,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            if(false(),x,y,z,u) -> if2(le(y,s(u)),x,y,s(z),s(u))
            if(true(),x,y,z,u) -> u
            if2(false(),x,y,z,u) -> modIter(x,y,z,u)
            if2(true(),x,y,z,u) -> modIter(x,y,z,0())
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            mod(x,0()) -> modZeroErro()
            mod(x,s(y)) -> modIter(x,s(y),0(),0())
            modIter(x,s(y),z,u) -> if(le(x,z),x,s(y),z,u)
        - Signature:
            {if/5,if2/5,le/2,mod/2,modIter/4} / {0/0,false/0,modZeroErro/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {if,if2,le,mod,modIter} and constructors {0,false,modZeroErro,s
            ,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          le(x,y){x -> s(x),y -> s(y)} =
            le(s(x),s(y)) ->^+ le(x,y)
              = C[le(x,y) = le(x,y){}]

WORST_CASE(Omega(n^1),?)