/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:
            if_mod(false(),false(),x,y,z) -> x
            if_mod(false(),true(),x,y,z) -> mod(z,y)
            if_mod(true(),b,x,y,z) -> divByZeroError()
            isZero(0()) -> true()
            isZero(s(x)) -> false()
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,x) -> 0()
            minus(x,0()) -> x
            minus(0(),x) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            mod(x,y) -> if_mod(isZero(y),le(y,x),x,y,minus(x,y))
        - Signature:
            {if_mod/5,isZero/1,le/2,minus/2,mod/2} / {0/0,divByZeroError/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {if_mod,isZero,le,minus,mod} and constructors {0,divByZeroError
            ,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            if_mod(false(),false(),x,y,z) -> x
            if_mod(false(),true(),x,y,z) -> mod(z,y)
            if_mod(true(),b,x,y,z) -> divByZeroError()
            isZero(0()) -> true()
            isZero(s(x)) -> false()
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,x) -> 0()
            minus(x,0()) -> x
            minus(0(),x) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            mod(x,y) -> if_mod(isZero(y),le(y,x),x,y,minus(x,y))
        - Signature:
            {if_mod/5,isZero/1,le/2,minus/2,mod/2} / {0/0,divByZeroError/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {if_mod,isZero,le,minus,mod} and constructors {0,divByZeroError
            ,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            if_mod(false(),false(),x,y,z) -> x
            if_mod(false(),true(),x,y,z) -> mod(z,y)
            if_mod(true(),b,x,y,z) -> divByZeroError()
            isZero(0()) -> true()
            isZero(s(x)) -> false()
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,x) -> 0()
            minus(x,0()) -> x
            minus(0(),x) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            mod(x,y) -> if_mod(isZero(y),le(y,x),x,y,minus(x,y))
        - Signature:
            {if_mod/5,isZero/1,le/2,minus/2,mod/2} / {0/0,divByZeroError/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {if_mod,isZero,le,minus,mod} and constructors {0,divByZeroError
            ,false,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),?)