/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:
            ifMinus(false(),s(X),Y) -> s(minus(X,Y))
            ifMinus(true(),s(X),Y) -> 0()
            le(0(),Y) -> true()
            le(s(X),0()) -> false()
            le(s(X),s(Y)) -> le(X,Y)
            minus(0(),Y) -> 0()
            minus(s(X),Y) -> ifMinus(le(s(X),Y),s(X),Y)
            quot(0(),s(Y)) -> 0()
            quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
        - Signature:
            {ifMinus/3,le/2,minus/2,quot/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {ifMinus,le,minus,quot} 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:
            ifMinus(false(),s(X),Y) -> s(minus(X,Y))
            ifMinus(true(),s(X),Y) -> 0()
            le(0(),Y) -> true()
            le(s(X),0()) -> false()
            le(s(X),s(Y)) -> le(X,Y)
            minus(0(),Y) -> 0()
            minus(s(X),Y) -> ifMinus(le(s(X),Y),s(X),Y)
            quot(0(),s(Y)) -> 0()
            quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
        - Signature:
            {ifMinus/3,le/2,minus/2,quot/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {ifMinus,le,minus,quot} 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:
            ifMinus(false(),s(X),Y) -> s(minus(X,Y))
            ifMinus(true(),s(X),Y) -> 0()
            le(0(),Y) -> true()
            le(s(X),0()) -> false()
            le(s(X),s(Y)) -> le(X,Y)
            minus(0(),Y) -> 0()
            minus(s(X),Y) -> ifMinus(le(s(X),Y),s(X),Y)
            quot(0(),s(Y)) -> 0()
            quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
        - Signature:
            {ifMinus/3,le/2,minus/2,quot/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {ifMinus,le,minus,quot} and constructors {0,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),?)