/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__fact(X)) -> fact(activate(X))
            activate(n__p(X)) -> p(activate(X))
            activate(n__prod(X1,X2)) -> prod(activate(X1),activate(X2))
            activate(n__s(X)) -> s(activate(X))
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            fact(X) -> if(zero(X),n__s(n__0()),n__prod(X,n__fact(n__p(X))))
            fact(X) -> n__fact(X)
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> activate(X)
            p(X) -> n__p(X)
            p(s(X)) -> X
            prod(X1,X2) -> n__prod(X1,X2)
            prod(0(),X) -> 0()
            prod(s(X),Y) -> add(Y,prod(X,Y))
            s(X) -> n__s(X)
            zero(0()) -> true()
            zero(s(X)) -> false()
        - Signature:
            {0/0,activate/1,add/2,fact/1,if/3,p/1,prod/2,s/1,zero/1} / {false/0,n__0/0,n__fact/1,n__p/1,n__prod/2,n__s/1
            ,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,add,fact,if,p,prod,s,zero} and constructors {false,n__0
            ,n__fact,n__p,n__prod,n__s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__fact(X)) -> fact(activate(X))
            activate(n__p(X)) -> p(activate(X))
            activate(n__prod(X1,X2)) -> prod(activate(X1),activate(X2))
            activate(n__s(X)) -> s(activate(X))
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            fact(X) -> if(zero(X),n__s(n__0()),n__prod(X,n__fact(n__p(X))))
            fact(X) -> n__fact(X)
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> activate(X)
            p(X) -> n__p(X)
            p(s(X)) -> X
            prod(X1,X2) -> n__prod(X1,X2)
            prod(0(),X) -> 0()
            prod(s(X),Y) -> add(Y,prod(X,Y))
            s(X) -> n__s(X)
            zero(0()) -> true()
            zero(s(X)) -> false()
        - Signature:
            {0/0,activate/1,add/2,fact/1,if/3,p/1,prod/2,s/1,zero/1} / {false/0,n__0/0,n__fact/1,n__p/1,n__prod/2,n__s/1
            ,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,add,fact,if,p,prod,s,zero} and constructors {false,n__0
            ,n__fact,n__p,n__prod,n__s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__fact(X)) -> fact(activate(X))
            activate(n__p(X)) -> p(activate(X))
            activate(n__prod(X1,X2)) -> prod(activate(X1),activate(X2))
            activate(n__s(X)) -> s(activate(X))
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            fact(X) -> if(zero(X),n__s(n__0()),n__prod(X,n__fact(n__p(X))))
            fact(X) -> n__fact(X)
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> activate(X)
            p(X) -> n__p(X)
            p(s(X)) -> X
            prod(X1,X2) -> n__prod(X1,X2)
            prod(0(),X) -> 0()
            prod(s(X),Y) -> add(Y,prod(X,Y))
            s(X) -> n__s(X)
            zero(0()) -> true()
            zero(s(X)) -> false()
        - Signature:
            {0/0,activate/1,add/2,fact/1,if/3,p/1,prod/2,s/1,zero/1} / {false/0,n__0/0,n__fact/1,n__p/1,n__prod/2,n__s/1
            ,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,add,fact,if,p,prod,s,zero} and constructors {false,n__0
            ,n__fact,n__p,n__prod,n__s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__fact(x)} =
            activate(n__fact(x)) ->^+ fact(activate(x))
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)