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


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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
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            if_min(false(),add(n,add(m,x))) -> min(add(m,x))
            if_min(true(),add(n,add(m,x))) -> min(add(n,x))
            if_minsort(false(),add(n,x),y) -> minsort(x,add(n,y))
            if_minsort(true(),add(n,x),y) -> add(n,minsort(app(rm(n,x),y),nil()))
            if_rm(false(),n,add(m,x)) -> add(m,rm(n,x))
            if_rm(true(),n,add(m,x)) -> rm(n,x)
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            min(add(n,add(m,x))) -> if_min(le(n,m),add(n,add(m,x)))
            min(add(n,nil())) -> n
            minsort(add(n,x),y) -> if_minsort(eq(n,min(add(n,x))),add(n,x),y)
            minsort(nil(),nil()) -> nil()
            rm(n,add(m,x)) -> if_rm(eq(n,m),n,add(m,x))
            rm(n,nil()) -> nil()
        - Signature:
            {app/2,eq/2,if_min/2,if_minsort/3,if_rm/3,le/2,min/1,minsort/2,rm/2} / {0/0,add/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {app,eq,if_min,if_minsort,if_rm,le,min,minsort
            ,rm} and constructors {0,add,false,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
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            if_min(false(),add(n,add(m,x))) -> min(add(m,x))
            if_min(true(),add(n,add(m,x))) -> min(add(n,x))
            if_minsort(false(),add(n,x),y) -> minsort(x,add(n,y))
            if_minsort(true(),add(n,x),y) -> add(n,minsort(app(rm(n,x),y),nil()))
            if_rm(false(),n,add(m,x)) -> add(m,rm(n,x))
            if_rm(true(),n,add(m,x)) -> rm(n,x)
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            min(add(n,add(m,x))) -> if_min(le(n,m),add(n,add(m,x)))
            min(add(n,nil())) -> n
            minsort(add(n,x),y) -> if_minsort(eq(n,min(add(n,x))),add(n,x),y)
            minsort(nil(),nil()) -> nil()
            rm(n,add(m,x)) -> if_rm(eq(n,m),n,add(m,x))
            rm(n,nil()) -> nil()
        - Signature:
            {app/2,eq/2,if_min/2,if_minsort/3,if_rm/3,le/2,min/1,minsort/2,rm/2} / {0/0,add/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {app,eq,if_min,if_minsort,if_rm,le,min,minsort
            ,rm} and constructors {0,add,false,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
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            if_min(false(),add(n,add(m,x))) -> min(add(m,x))
            if_min(true(),add(n,add(m,x))) -> min(add(n,x))
            if_minsort(false(),add(n,x),y) -> minsort(x,add(n,y))
            if_minsort(true(),add(n,x),y) -> add(n,minsort(app(rm(n,x),y),nil()))
            if_rm(false(),n,add(m,x)) -> add(m,rm(n,x))
            if_rm(true(),n,add(m,x)) -> rm(n,x)
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            min(add(n,add(m,x))) -> if_min(le(n,m),add(n,add(m,x)))
            min(add(n,nil())) -> n
            minsort(add(n,x),y) -> if_minsort(eq(n,min(add(n,x))),add(n,x),y)
            minsort(nil(),nil()) -> nil()
            rm(n,add(m,x)) -> if_rm(eq(n,m),n,add(m,x))
            rm(n,nil()) -> nil()
        - Signature:
            {app/2,eq/2,if_min/2,if_minsort/3,if_rm/3,le/2,min/1,minsort/2,rm/2} / {0/0,add/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {app,eq,if_min,if_minsort,if_rm,le,min,minsort
            ,rm} and constructors {0,add,false,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),?)