/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:
            cond1(false(),x,y) -> cond2(gt(x,y),x,y)
            cond1(true(),x,y) -> 0()
            cond2(false(),x,y) -> s(diff(s(x),y))
            cond2(true(),x,y) -> s(diff(x,s(y)))
            diff(x,y) -> cond1(equal(x,y),x,y)
            equal(0(),0()) -> true()
            equal(0(),s(y)) -> false()
            equal(s(x),0()) -> false()
            equal(s(x),s(y)) -> equal(x,y)
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
        - Signature:
            {cond1/3,cond2/3,diff/2,equal/2,gt/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {cond1,cond2,diff,equal,gt} 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:
            cond1(false(),x,y) -> cond2(gt(x,y),x,y)
            cond1(true(),x,y) -> 0()
            cond2(false(),x,y) -> s(diff(s(x),y))
            cond2(true(),x,y) -> s(diff(x,s(y)))
            diff(x,y) -> cond1(equal(x,y),x,y)
            equal(0(),0()) -> true()
            equal(0(),s(y)) -> false()
            equal(s(x),0()) -> false()
            equal(s(x),s(y)) -> equal(x,y)
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
        - Signature:
            {cond1/3,cond2/3,diff/2,equal/2,gt/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {cond1,cond2,diff,equal,gt} 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:
            cond1(false(),x,y) -> cond2(gt(x,y),x,y)
            cond1(true(),x,y) -> 0()
            cond2(false(),x,y) -> s(diff(s(x),y))
            cond2(true(),x,y) -> s(diff(x,s(y)))
            diff(x,y) -> cond1(equal(x,y),x,y)
            equal(0(),0()) -> true()
            equal(0(),s(y)) -> false()
            equal(s(x),0()) -> false()
            equal(s(x),s(y)) -> equal(x,y)
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
        - Signature:
            {cond1/3,cond2/3,diff/2,equal/2,gt/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {cond1,cond2,diff,equal,gt} and constructors {0,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          equal(x,y){x -> s(x),y -> s(y)} =
            equal(s(x),s(y)) ->^+ equal(x,y)
              = C[equal(x,y) = equal(x,y){}]

WORST_CASE(Omega(n^1),?)