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


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


tct-trs: Prelude.head: empty list
tct-trs: Prelude.head: empty list
tct-trs: Prelude.head: empty list
tct-trs: Prelude.head: empty list
WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(cons(h,t),x) -> cons(h,app(t,x))
            app(nil(),x) -> x
            empty(cons(h,t)) -> false()
            empty(nil()) -> true()
            fstsplit(0(),x) -> nil()
            fstsplit(s(n),cons(h,t)) -> cons(h,fstsplit(n,t))
            fstsplit(s(n),nil()) -> nil()
            if1(store,m,false()) -> if3(store,m,empty(fstsplit(m,app(map_f(self(),nil()),store))))
            if1(store,m,true()) -> if2(store,m,empty(fstsplit(m,store)))
            if2(store,m,false()) -> process(app(map_f(self(),nil()),sndsplit(m,store)),m)
            if3(store,m,false()) -> process(sndsplit(m,app(map_f(self(),nil()),store)),m)
            length(cons(h,t)) -> s(length(t))
            length(nil()) -> 0()
            leq(0(),m) -> true()
            leq(s(n),0()) -> false()
            leq(s(n),s(m)) -> leq(n,m)
            map_f(pid,cons(h,t)) -> app(f(pid,h),map_f(pid,t))
            map_f(pid,nil()) -> nil()
            process(store,m) -> if1(store,m,leq(m,length(store)))
            sndsplit(0(),x) -> x
            sndsplit(s(n),cons(h,t)) -> sndsplit(n,t)
            sndsplit(s(n),nil()) -> nil()
        - Signature:
            {app/2,empty/1,fstsplit/2,if1/3,if2/3,if3/3,length/1,leq/2,map_f/2,process/2,sndsplit/2} / {0/0,cons/2,f/2
            ,false/0,nil/0,s/1,self/0,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app,empty,fstsplit,if1,if2,if3,length,leq,map_f,process
            ,sndsplit} and constructors {0,cons,f,false,nil,s,self,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(cons(h,t),x) -> cons(h,app(t,x))
            app(nil(),x) -> x
            empty(cons(h,t)) -> false()
            empty(nil()) -> true()
            fstsplit(0(),x) -> nil()
            fstsplit(s(n),cons(h,t)) -> cons(h,fstsplit(n,t))
            fstsplit(s(n),nil()) -> nil()
            if1(store,m,false()) -> if3(store,m,empty(fstsplit(m,app(map_f(self(),nil()),store))))
            if1(store,m,true()) -> if2(store,m,empty(fstsplit(m,store)))
            if2(store,m,false()) -> process(app(map_f(self(),nil()),sndsplit(m,store)),m)
            if3(store,m,false()) -> process(sndsplit(m,app(map_f(self(),nil()),store)),m)
            length(cons(h,t)) -> s(length(t))
            length(nil()) -> 0()
            leq(0(),m) -> true()
            leq(s(n),0()) -> false()
            leq(s(n),s(m)) -> leq(n,m)
            map_f(pid,cons(h,t)) -> app(f(pid,h),map_f(pid,t))
            map_f(pid,nil()) -> nil()
            process(store,m) -> if1(store,m,leq(m,length(store)))
            sndsplit(0(),x) -> x
            sndsplit(s(n),cons(h,t)) -> sndsplit(n,t)
            sndsplit(s(n),nil()) -> nil()
        - Signature:
            {app/2,empty/1,fstsplit/2,if1/3,if2/3,if3/3,length/1,leq/2,map_f/2,process/2,sndsplit/2} / {0/0,cons/2,f/2
            ,false/0,nil/0,s/1,self/0,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app,empty,fstsplit,if1,if2,if3,length,leq,map_f,process
            ,sndsplit} and constructors {0,cons,f,false,nil,s,self,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(cons(h,t),x) -> cons(h,app(t,x))
            app(nil(),x) -> x
            empty(cons(h,t)) -> false()
            empty(nil()) -> true()
            fstsplit(0(),x) -> nil()
            fstsplit(s(n),cons(h,t)) -> cons(h,fstsplit(n,t))
            fstsplit(s(n),nil()) -> nil()
            if1(store,m,false()) -> if3(store,m,empty(fstsplit(m,app(map_f(self(),nil()),store))))
            if1(store,m,true()) -> if2(store,m,empty(fstsplit(m,store)))
            if2(store,m,false()) -> process(app(map_f(self(),nil()),sndsplit(m,store)),m)
            if3(store,m,false()) -> process(sndsplit(m,app(map_f(self(),nil()),store)),m)
            length(cons(h,t)) -> s(length(t))
            length(nil()) -> 0()
            leq(0(),m) -> true()
            leq(s(n),0()) -> false()
            leq(s(n),s(m)) -> leq(n,m)
            map_f(pid,cons(h,t)) -> app(f(pid,h),map_f(pid,t))
            map_f(pid,nil()) -> nil()
            process(store,m) -> if1(store,m,leq(m,length(store)))
            sndsplit(0(),x) -> x
            sndsplit(s(n),cons(h,t)) -> sndsplit(n,t)
            sndsplit(s(n),nil()) -> nil()
        - Signature:
            {app/2,empty/1,fstsplit/2,if1/3,if2/3,if3/3,length/1,leq/2,map_f/2,process/2,sndsplit/2} / {0/0,cons/2,f/2
            ,false/0,nil/0,s/1,self/0,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app,empty,fstsplit,if1,if2,if3,length,leq,map_f,process
            ,sndsplit} and constructors {0,cons,f,false,nil,s,self,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          app(y,z){y -> cons(x,y)} =
            app(cons(x,y),z) ->^+ cons(x,app(y,z))
              = C[app(y,z) = app(y,z){}]

WORST_CASE(Omega(n^1),?)