/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:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__div(X1,X2)) -> div(activate(X1),X2)
            activate(n__minus(X1,X2)) -> minus(X1,X2)
            activate(n__s(X)) -> s(activate(X))
            div(X1,X2) -> n__div(X1,X2)
            div(0(),n__s(Y)) -> 0()
            div(s(X),n__s(Y)) -> if(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0())
            geq(X,n__0()) -> true()
            geq(n__0(),n__s(Y)) -> false()
            geq(n__s(X),n__s(Y)) -> geq(activate(X),activate(Y))
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> activate(X)
            minus(X1,X2) -> n__minus(X1,X2)
            minus(n__0(),Y) -> 0()
            minus(n__s(X),n__s(Y)) -> minus(activate(X),activate(Y))
            s(X) -> n__s(X)
        - Signature:
            {0/0,activate/1,div/2,geq/2,if/3,minus/2,s/1} / {false/0,n__0/0,n__div/2,n__minus/2,n__s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,div,geq,if,minus,s} and constructors {false,n__0,n__div
            ,n__minus,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__div(X1,X2)) -> div(activate(X1),X2)
            activate(n__minus(X1,X2)) -> minus(X1,X2)
            activate(n__s(X)) -> s(activate(X))
            div(X1,X2) -> n__div(X1,X2)
            div(0(),n__s(Y)) -> 0()
            div(s(X),n__s(Y)) -> if(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0())
            geq(X,n__0()) -> true()
            geq(n__0(),n__s(Y)) -> false()
            geq(n__s(X),n__s(Y)) -> geq(activate(X),activate(Y))
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> activate(X)
            minus(X1,X2) -> n__minus(X1,X2)
            minus(n__0(),Y) -> 0()
            minus(n__s(X),n__s(Y)) -> minus(activate(X),activate(Y))
            s(X) -> n__s(X)
        - Signature:
            {0/0,activate/1,div/2,geq/2,if/3,minus/2,s/1} / {false/0,n__0/0,n__div/2,n__minus/2,n__s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,div,geq,if,minus,s} and constructors {false,n__0,n__div
            ,n__minus,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__div(X1,X2)) -> div(activate(X1),X2)
            activate(n__minus(X1,X2)) -> minus(X1,X2)
            activate(n__s(X)) -> s(activate(X))
            div(X1,X2) -> n__div(X1,X2)
            div(0(),n__s(Y)) -> 0()
            div(s(X),n__s(Y)) -> if(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0())
            geq(X,n__0()) -> true()
            geq(n__0(),n__s(Y)) -> false()
            geq(n__s(X),n__s(Y)) -> geq(activate(X),activate(Y))
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> activate(X)
            minus(X1,X2) -> n__minus(X1,X2)
            minus(n__0(),Y) -> 0()
            minus(n__s(X),n__s(Y)) -> minus(activate(X),activate(Y))
            s(X) -> n__s(X)
        - Signature:
            {0/0,activate/1,div/2,geq/2,if/3,minus/2,s/1} / {false/0,n__0/0,n__div/2,n__minus/2,n__s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,div,geq,if,minus,s} and constructors {false,n__0,n__div
            ,n__minus,n__s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__div(x,y)} =
            activate(n__div(x,y)) ->^+ div(activate(x),y)
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)