/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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__diff(X1,X2)) -> diff(activate(X1),activate(X2))
            activate(n__p(X)) -> p(activate(X))
            activate(n__s(X)) -> s(activate(X))
            diff(X,Y) -> if(leq(X,Y),n__0(),n__s(n__diff(n__p(X),Y)))
            diff(X1,X2) -> n__diff(X1,X2)
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> activate(X)
            leq(0(),Y) -> true()
            leq(s(X),0()) -> false()
            leq(s(X),s(Y)) -> leq(X,Y)
            p(X) -> n__p(X)
            p(0()) -> 0()
            p(s(X)) -> X
            s(X) -> n__s(X)
        - Signature:
            {0/0,activate/1,diff/2,if/3,leq/2,p/1,s/1} / {false/0,n__0/0,n__diff/2,n__p/1,n__s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,diff,if,leq,p,s} and constructors {false,n__0,n__diff
            ,n__p,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__diff(X1,X2)) -> diff(activate(X1),activate(X2))
            activate(n__p(X)) -> p(activate(X))
            activate(n__s(X)) -> s(activate(X))
            diff(X,Y) -> if(leq(X,Y),n__0(),n__s(n__diff(n__p(X),Y)))
            diff(X1,X2) -> n__diff(X1,X2)
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> activate(X)
            leq(0(),Y) -> true()
            leq(s(X),0()) -> false()
            leq(s(X),s(Y)) -> leq(X,Y)
            p(X) -> n__p(X)
            p(0()) -> 0()
            p(s(X)) -> X
            s(X) -> n__s(X)
        - Signature:
            {0/0,activate/1,diff/2,if/3,leq/2,p/1,s/1} / {false/0,n__0/0,n__diff/2,n__p/1,n__s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,diff,if,leq,p,s} and constructors {false,n__0,n__diff
            ,n__p,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__diff(X1,X2)) -> diff(activate(X1),activate(X2))
            activate(n__p(X)) -> p(activate(X))
            activate(n__s(X)) -> s(activate(X))
            diff(X,Y) -> if(leq(X,Y),n__0(),n__s(n__diff(n__p(X),Y)))
            diff(X1,X2) -> n__diff(X1,X2)
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> activate(X)
            leq(0(),Y) -> true()
            leq(s(X),0()) -> false()
            leq(s(X),s(Y)) -> leq(X,Y)
            p(X) -> n__p(X)
            p(0()) -> 0()
            p(s(X)) -> X
            s(X) -> n__s(X)
        - Signature:
            {0/0,activate/1,diff/2,if/3,leq/2,p/1,s/1} / {false/0,n__0/0,n__diff/2,n__p/1,n__s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,diff,if,leq,p,s} and constructors {false,n__0,n__diff
            ,n__p,n__s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__diff(x,y)} =
            activate(n__diff(x,y)) ->^+ diff(activate(x),activate(y))
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)