/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:
            id(0()) -> 0()
            id(s(x)) -> s(id(x))
            if2(false(),b2,x,y) -> if3(b2,x,y)
            if2(true(),b2,x,y) -> 0()
            if3(false(),x,y) -> x
            if3(true(),x,y) -> mod(minus(x,y),s(y))
            if_mod(false(),b1,b2,x,y) -> if2(b1,b2,x,y)
            if_mod(true(),b1,b2,x,y) -> 0()
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            mod(x,y) -> if_mod(zero(x),zero(y),le(y,x),id(x),id(y))
            zero(0()) -> true()
            zero(s(x)) -> false()
        - Signature:
            {id/1,if2/4,if3/3,if_mod/5,le/2,minus/2,mod/2,zero/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {id,if2,if3,if_mod,le,minus,mod,zero} and constructors {0,false,s
            ,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            id(0()) -> 0()
            id(s(x)) -> s(id(x))
            if2(false(),b2,x,y) -> if3(b2,x,y)
            if2(true(),b2,x,y) -> 0()
            if3(false(),x,y) -> x
            if3(true(),x,y) -> mod(minus(x,y),s(y))
            if_mod(false(),b1,b2,x,y) -> if2(b1,b2,x,y)
            if_mod(true(),b1,b2,x,y) -> 0()
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            mod(x,y) -> if_mod(zero(x),zero(y),le(y,x),id(x),id(y))
            zero(0()) -> true()
            zero(s(x)) -> false()
        - Signature:
            {id/1,if2/4,if3/3,if_mod/5,le/2,minus/2,mod/2,zero/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {id,if2,if3,if_mod,le,minus,mod,zero} and constructors {0,false,s
            ,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            id(0()) -> 0()
            id(s(x)) -> s(id(x))
            if2(false(),b2,x,y) -> if3(b2,x,y)
            if2(true(),b2,x,y) -> 0()
            if3(false(),x,y) -> x
            if3(true(),x,y) -> mod(minus(x,y),s(y))
            if_mod(false(),b1,b2,x,y) -> if2(b1,b2,x,y)
            if_mod(true(),b1,b2,x,y) -> 0()
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            mod(x,y) -> if_mod(zero(x),zero(y),le(y,x),id(x),id(y))
            zero(0()) -> true()
            zero(s(x)) -> false()
        - Signature:
            {id/1,if2/4,if3/3,if_mod/5,le/2,minus/2,mod/2,zero/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {id,if2,if3,if_mod,le,minus,mod,zero} and constructors {0,false,s
            ,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          id(x){x -> s(x)} =
            id(s(x)) ->^+ s(id(x))
              = C[id(x) = id(x){}]

WORST_CASE(Omega(n^1),?)