/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:
            app(add(n,x),y) -> add(n,app(x,y))
            app(nil(),y) -> y
            concat(cons(u,v),y) -> cons(u,concat(v,y))
            concat(leaf(),y) -> y
            less_leaves(x,leaf()) -> false()
            less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
            less_leaves(leaf(),cons(w,z)) -> true()
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
            reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
            reverse(nil()) -> nil()
            shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
            shuffle(nil()) -> nil()
        - Signature:
            {app/2,concat/2,less_leaves/2,minus/2,quot/2,reverse/1,shuffle/1} / {0/0,add/2,cons/2,false/0,leaf/0,nil/0
            ,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {app,concat,less_leaves,minus,quot,reverse
            ,shuffle} and constructors {0,add,cons,false,leaf,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(add(n,x),y) -> add(n,app(x,y))
            app(nil(),y) -> y
            concat(cons(u,v),y) -> cons(u,concat(v,y))
            concat(leaf(),y) -> y
            less_leaves(x,leaf()) -> false()
            less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
            less_leaves(leaf(),cons(w,z)) -> true()
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
            reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
            reverse(nil()) -> nil()
            shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
            shuffle(nil()) -> nil()
        - Signature:
            {app/2,concat/2,less_leaves/2,minus/2,quot/2,reverse/1,shuffle/1} / {0/0,add/2,cons/2,false/0,leaf/0,nil/0
            ,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {app,concat,less_leaves,minus,quot,reverse
            ,shuffle} and constructors {0,add,cons,false,leaf,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(add(n,x),y) -> add(n,app(x,y))
            app(nil(),y) -> y
            concat(cons(u,v),y) -> cons(u,concat(v,y))
            concat(leaf(),y) -> y
            less_leaves(x,leaf()) -> false()
            less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
            less_leaves(leaf(),cons(w,z)) -> true()
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
            reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
            reverse(nil()) -> nil()
            shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
            shuffle(nil()) -> nil()
        - Signature:
            {app/2,concat/2,less_leaves/2,minus/2,quot/2,reverse/1,shuffle/1} / {0/0,add/2,cons/2,false/0,leaf/0,nil/0
            ,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {app,concat,less_leaves,minus,quot,reverse
            ,shuffle} and constructors {0,add,cons,false,leaf,nil,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          app(y,z){y -> add(x,y)} =
            app(add(x,y),z) ->^+ add(x,app(y,z))
              = C[app(y,z) = app(y,z){}]

WORST_CASE(Omega(n^1),?)