/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


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

WORST_CASE(Omega(n^1),?)