/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:
            empty(cons(x,y)) -> false()
            empty(nil()) -> true()
            head(cons(x,y)) -> x
            if1(false(),x,y) -> cons(0(),int(s(0()),y))
            if1(true(),x,y) -> cons(0(),nil())
            if2(false(),x,y) -> intlist(int(p(x),p(y)))
            if2(true(),x,y) -> nil()
            if_int(false(),b,x,y) -> if2(b,x,y)
            if_int(true(),b,x,y) -> if1(b,x,y)
            if_intlist(false(),x) -> cons(s(head(x)),intlist(tail(x)))
            if_intlist(true(),x) -> nil()
            int(x,y) -> if_int(zero(x),zero(y),x,y)
            intlist(x) -> if_intlist(empty(x),x)
            p(0()) -> 0()
            p(s(0())) -> 0()
            p(s(s(x))) -> s(p(s(x)))
            tail(cons(x,y)) -> y
            tail(nil()) -> nil()
            zero(0()) -> true()
            zero(s(x)) -> false()
        - Signature:
            {empty/1,head/1,if1/3,if2/3,if_int/4,if_intlist/2,int/2,intlist/1,p/1,tail/1,zero/1} / {0/0,cons/2,false/0
            ,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {empty,head,if1,if2,if_int,if_intlist,int,intlist,p,tail
            ,zero} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            empty(cons(x,y)) -> false()
            empty(nil()) -> true()
            head(cons(x,y)) -> x
            if1(false(),x,y) -> cons(0(),int(s(0()),y))
            if1(true(),x,y) -> cons(0(),nil())
            if2(false(),x,y) -> intlist(int(p(x),p(y)))
            if2(true(),x,y) -> nil()
            if_int(false(),b,x,y) -> if2(b,x,y)
            if_int(true(),b,x,y) -> if1(b,x,y)
            if_intlist(false(),x) -> cons(s(head(x)),intlist(tail(x)))
            if_intlist(true(),x) -> nil()
            int(x,y) -> if_int(zero(x),zero(y),x,y)
            intlist(x) -> if_intlist(empty(x),x)
            p(0()) -> 0()
            p(s(0())) -> 0()
            p(s(s(x))) -> s(p(s(x)))
            tail(cons(x,y)) -> y
            tail(nil()) -> nil()
            zero(0()) -> true()
            zero(s(x)) -> false()
        - Signature:
            {empty/1,head/1,if1/3,if2/3,if_int/4,if_intlist/2,int/2,intlist/1,p/1,tail/1,zero/1} / {0/0,cons/2,false/0
            ,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {empty,head,if1,if2,if_int,if_intlist,int,intlist,p,tail
            ,zero} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            empty(cons(x,y)) -> false()
            empty(nil()) -> true()
            head(cons(x,y)) -> x
            if1(false(),x,y) -> cons(0(),int(s(0()),y))
            if1(true(),x,y) -> cons(0(),nil())
            if2(false(),x,y) -> intlist(int(p(x),p(y)))
            if2(true(),x,y) -> nil()
            if_int(false(),b,x,y) -> if2(b,x,y)
            if_int(true(),b,x,y) -> if1(b,x,y)
            if_intlist(false(),x) -> cons(s(head(x)),intlist(tail(x)))
            if_intlist(true(),x) -> nil()
            int(x,y) -> if_int(zero(x),zero(y),x,y)
            intlist(x) -> if_intlist(empty(x),x)
            p(0()) -> 0()
            p(s(0())) -> 0()
            p(s(s(x))) -> s(p(s(x)))
            tail(cons(x,y)) -> y
            tail(nil()) -> nil()
            zero(0()) -> true()
            zero(s(x)) -> false()
        - Signature:
            {empty/1,head/1,if1/3,if2/3,if_int/4,if_intlist/2,int/2,intlist/1,p/1,tail/1,zero/1} / {0/0,cons/2,false/0
            ,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {empty,head,if1,if2,if_int,if_intlist,int,intlist,p,tail
            ,zero} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          p(s(x)){x -> s(x)} =
            p(s(s(x))) ->^+ s(p(s(x)))
              = C[p(s(x)) = p(s(x)){}]

WORST_CASE(Omega(n^1),?)