/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:
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> times(x,exp(x,y))
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z))
            help(true(),c,x,y,z) -> z
            plus(0(),x) -> x
            plus(s(x),y) -> s(plus(x,y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
            tower(x,y) -> towerIter(0(),x,y,s(0()))
            towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z)
        - Signature:
            {exp/2,ge/2,help/5,plus/2,times/2,tower/2,towerIter/4} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {exp,ge,help,plus,times,tower,towerIter} 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:
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> times(x,exp(x,y))
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z))
            help(true(),c,x,y,z) -> z
            plus(0(),x) -> x
            plus(s(x),y) -> s(plus(x,y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
            tower(x,y) -> towerIter(0(),x,y,s(0()))
            towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z)
        - Signature:
            {exp/2,ge/2,help/5,plus/2,times/2,tower/2,towerIter/4} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {exp,ge,help,plus,times,tower,towerIter} 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:
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> times(x,exp(x,y))
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z))
            help(true(),c,x,y,z) -> z
            plus(0(),x) -> x
            plus(s(x),y) -> s(plus(x,y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
            tower(x,y) -> towerIter(0(),x,y,s(0()))
            towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z)
        - Signature:
            {exp/2,ge/2,help/5,plus/2,times/2,tower/2,towerIter/4} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {exp,ge,help,plus,times,tower,towerIter} and constructors {0,false
            ,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          exp(x,y){y -> s(y)} =
            exp(x,s(y)) ->^+ times(x,exp(x,y))
              = C[exp(x,y) = exp(x,y){}]

WORST_CASE(Omega(n^1),?)