/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:
            function(if(),false(),x,y) -> function(plus(),function(third(),x,y,y),function(p(),x,x,y),s(y))
            function(if(),true(),x,y) -> y
            function(iszero(),0(),dummy,dummy2) -> true()
            function(iszero(),s(x),dummy,dummy2) -> false()
            function(p(),0(),dummy,dummy2) -> 0()
            function(p(),s(0()),dummy,dummy2) -> 0()
            function(p(),s(s(x)),dummy,dummy2) -> s(function(p(),s(x),x,x))
            function(plus(),dummy,x,y) -> function(if(),function(iszero(),x,x,x),x,y)
            function(third(),x,y,z) -> z
        - Signature:
            {function/4} / {0/0,false/0,if/0,iszero/0,p/0,plus/0,s/1,third/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {function} and constructors {0,false,if,iszero,p,plus,s,third,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            function(if(),false(),x,y) -> function(plus(),function(third(),x,y,y),function(p(),x,x,y),s(y))
            function(if(),true(),x,y) -> y
            function(iszero(),0(),dummy,dummy2) -> true()
            function(iszero(),s(x),dummy,dummy2) -> false()
            function(p(),0(),dummy,dummy2) -> 0()
            function(p(),s(0()),dummy,dummy2) -> 0()
            function(p(),s(s(x)),dummy,dummy2) -> s(function(p(),s(x),x,x))
            function(plus(),dummy,x,y) -> function(if(),function(iszero(),x,x,x),x,y)
            function(third(),x,y,z) -> z
        - Signature:
            {function/4} / {0/0,false/0,if/0,iszero/0,p/0,plus/0,s/1,third/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {function} and constructors {0,false,if,iszero,p,plus,s,third,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            function(if(),false(),x,y) -> function(plus(),function(third(),x,y,y),function(p(),x,x,y),s(y))
            function(if(),true(),x,y) -> y
            function(iszero(),0(),dummy,dummy2) -> true()
            function(iszero(),s(x),dummy,dummy2) -> false()
            function(p(),0(),dummy,dummy2) -> 0()
            function(p(),s(0()),dummy,dummy2) -> 0()
            function(p(),s(s(x)),dummy,dummy2) -> s(function(p(),s(x),x,x))
            function(plus(),dummy,x,y) -> function(if(),function(iszero(),x,x,x),x,y)
            function(third(),x,y,z) -> z
        - Signature:
            {function/4} / {0/0,false/0,if/0,iszero/0,p/0,plus/0,s/1,third/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {function} and constructors {0,false,if,iszero,p,plus,s,third,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          function(p(),s(x),y,z){x -> s(x)} =
            function(p(),s(s(x)),y,z) ->^+ s(function(p(),s(x),x,x))
              = C[function(p(),s(x),x,x) = function(p(),s(x),y,z){y -> x,z -> x}]

WORST_CASE(Omega(n^1),?)