/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:
            active(and(X1,X2)) -> and(active(X1),X2)
            active(and(tt(),X)) -> mark(X)
            active(plus(N,0())) -> mark(N)
            active(plus(N,s(M))) -> mark(s(plus(N,M)))
            active(plus(X1,X2)) -> plus(X1,active(X2))
            active(plus(X1,X2)) -> plus(active(X1),X2)
            active(s(X)) -> s(active(X))
            active(x(N,0())) -> mark(0())
            active(x(N,s(M))) -> mark(plus(x(N,M),N))
            active(x(X1,X2)) -> x(X1,active(X2))
            active(x(X1,X2)) -> x(active(X1),X2)
            and(mark(X1),X2) -> mark(and(X1,X2))
            and(ok(X1),ok(X2)) -> ok(and(X1,X2))
            plus(X1,mark(X2)) -> mark(plus(X1,X2))
            plus(mark(X1),X2) -> mark(plus(X1,X2))
            plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
            proper(0()) -> ok(0())
            proper(and(X1,X2)) -> and(proper(X1),proper(X2))
            proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
            proper(s(X)) -> s(proper(X))
            proper(tt()) -> ok(tt())
            proper(x(X1,X2)) -> x(proper(X1),proper(X2))
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
            x(X1,mark(X2)) -> mark(x(X1,X2))
            x(mark(X1),X2) -> mark(x(X1,X2))
            x(ok(X1),ok(X2)) -> ok(x(X1,X2))
        - Signature:
            {active/1,and/2,plus/2,proper/1,s/1,top/1,x/2} / {0/0,mark/1,ok/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {active,and,plus,proper,s,top,x} and constructors {0,mark,ok,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            active(and(X1,X2)) -> and(active(X1),X2)
            active(and(tt(),X)) -> mark(X)
            active(plus(N,0())) -> mark(N)
            active(plus(N,s(M))) -> mark(s(plus(N,M)))
            active(plus(X1,X2)) -> plus(X1,active(X2))
            active(plus(X1,X2)) -> plus(active(X1),X2)
            active(s(X)) -> s(active(X))
            active(x(N,0())) -> mark(0())
            active(x(N,s(M))) -> mark(plus(x(N,M),N))
            active(x(X1,X2)) -> x(X1,active(X2))
            active(x(X1,X2)) -> x(active(X1),X2)
            and(mark(X1),X2) -> mark(and(X1,X2))
            and(ok(X1),ok(X2)) -> ok(and(X1,X2))
            plus(X1,mark(X2)) -> mark(plus(X1,X2))
            plus(mark(X1),X2) -> mark(plus(X1,X2))
            plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
            proper(0()) -> ok(0())
            proper(and(X1,X2)) -> and(proper(X1),proper(X2))
            proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
            proper(s(X)) -> s(proper(X))
            proper(tt()) -> ok(tt())
            proper(x(X1,X2)) -> x(proper(X1),proper(X2))
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
            x(X1,mark(X2)) -> mark(x(X1,X2))
            x(mark(X1),X2) -> mark(x(X1,X2))
            x(ok(X1),ok(X2)) -> ok(x(X1,X2))
        - Signature:
            {active/1,and/2,plus/2,proper/1,s/1,top/1,x/2} / {0/0,mark/1,ok/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {active,and,plus,proper,s,top,x} and constructors {0,mark,ok,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            active(and(X1,X2)) -> and(active(X1),X2)
            active(and(tt(),X)) -> mark(X)
            active(plus(N,0())) -> mark(N)
            active(plus(N,s(M))) -> mark(s(plus(N,M)))
            active(plus(X1,X2)) -> plus(X1,active(X2))
            active(plus(X1,X2)) -> plus(active(X1),X2)
            active(s(X)) -> s(active(X))
            active(x(N,0())) -> mark(0())
            active(x(N,s(M))) -> mark(plus(x(N,M),N))
            active(x(X1,X2)) -> x(X1,active(X2))
            active(x(X1,X2)) -> x(active(X1),X2)
            and(mark(X1),X2) -> mark(and(X1,X2))
            and(ok(X1),ok(X2)) -> ok(and(X1,X2))
            plus(X1,mark(X2)) -> mark(plus(X1,X2))
            plus(mark(X1),X2) -> mark(plus(X1,X2))
            plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
            proper(0()) -> ok(0())
            proper(and(X1,X2)) -> and(proper(X1),proper(X2))
            proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
            proper(s(X)) -> s(proper(X))
            proper(tt()) -> ok(tt())
            proper(x(X1,X2)) -> x(proper(X1),proper(X2))
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
            x(X1,mark(X2)) -> mark(x(X1,X2))
            x(mark(X1),X2) -> mark(x(X1,X2))
            x(ok(X1),ok(X2)) -> ok(x(X1,X2))
        - Signature:
            {active/1,and/2,plus/2,proper/1,s/1,top/1,x/2} / {0/0,mark/1,ok/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {active,and,plus,proper,s,top,x} and constructors {0,mark,ok,tt}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          and(x,y){x -> mark(x)} =
            and(mark(x),y) ->^+ mark(and(x,y))
              = C[and(x,y) = and(x,y){}]

WORST_CASE(Omega(n^1),?)