/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:
            10() -> s(s(s(s(s(s(s(s(s(s(0()))))))))))
            gen(x) -> if1(le(x,10()),x)
            if1(false(),x) -> nil()
            if1(true(),x) -> if2(x,x)
            if2(x,y) -> if3(le(y,10()),x,y)
            if3(false(),x,y) -> gen(s(x))
            if3(true(),x,y) -> cons(entry(x,y,times(x,y)),if2(x,s(y)))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            table() -> gen(s(0()))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
        - Signature:
            {10/0,gen/1,if1/2,if2/2,if3/3,le/2,plus/2,table/0,times/2} / {0/0,cons/2,entry/3,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {10,gen,if1,if2,if3,le,plus,table,times} and constructors {0,cons
            ,entry,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            10() -> s(s(s(s(s(s(s(s(s(s(0()))))))))))
            gen(x) -> if1(le(x,10()),x)
            if1(false(),x) -> nil()
            if1(true(),x) -> if2(x,x)
            if2(x,y) -> if3(le(y,10()),x,y)
            if3(false(),x,y) -> gen(s(x))
            if3(true(),x,y) -> cons(entry(x,y,times(x,y)),if2(x,s(y)))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            table() -> gen(s(0()))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
        - Signature:
            {10/0,gen/1,if1/2,if2/2,if3/3,le/2,plus/2,table/0,times/2} / {0/0,cons/2,entry/3,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {10,gen,if1,if2,if3,le,plus,table,times} and constructors {0,cons
            ,entry,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            10() -> s(s(s(s(s(s(s(s(s(s(0()))))))))))
            gen(x) -> if1(le(x,10()),x)
            if1(false(),x) -> nil()
            if1(true(),x) -> if2(x,x)
            if2(x,y) -> if3(le(y,10()),x,y)
            if3(false(),x,y) -> gen(s(x))
            if3(true(),x,y) -> cons(entry(x,y,times(x,y)),if2(x,s(y)))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            table() -> gen(s(0()))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
        - Signature:
            {10/0,gen/1,if1/2,if2/2,if3/3,le/2,plus/2,table/0,times/2} / {0/0,cons/2,entry/3,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {10,gen,if1,if2,if3,le,plus,table,times} and constructors {0,cons
            ,entry,false,nil,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),?)