/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(NON_POLY,?)
* Step 1: Sum.  WORST_CASE(NON_POLY,?)
    + Considered Problem:
        - Strict TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            f(0()) -> 0()
            f(s(0())) -> s(0())
            f(s(s(x))) -> +(p(g(x)),q(g(x)))
            f(s(s(x))) -> p(h(g(x)))
            g(0()) -> pair(s(0()),s(0()))
            g(s(x)) -> h(g(x))
            g(s(x)) -> pair(+(p(g(x)),q(g(x))),p(g(x)))
            h(x) -> pair(+(p(x),q(x)),p(x))
            p(pair(x,y)) -> x
            q(pair(x,y)) -> y
        - Signature:
            {+/2,f/1,g/1,h/1,p/1,q/1} / {0/0,pair/2,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {+,f,g,h,p,q} and constructors {0,pair,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(NON_POLY,?)
    + Considered Problem:
        - Strict TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            f(0()) -> 0()
            f(s(0())) -> s(0())
            f(s(s(x))) -> +(p(g(x)),q(g(x)))
            f(s(s(x))) -> p(h(g(x)))
            g(0()) -> pair(s(0()),s(0()))
            g(s(x)) -> h(g(x))
            g(s(x)) -> pair(+(p(g(x)),q(g(x))),p(g(x)))
            h(x) -> pair(+(p(x),q(x)),p(x))
            p(pair(x,y)) -> x
            q(pair(x,y)) -> y
        - Signature:
            {+/2,f/1,g/1,h/1,p/1,q/1} / {0/0,pair/2,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {+,f,g,h,p,q} and constructors {0,pair,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(NON_POLY,?)
    + Considered Problem:
        - Strict TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            f(0()) -> 0()
            f(s(0())) -> s(0())
            f(s(s(x))) -> +(p(g(x)),q(g(x)))
            f(s(s(x))) -> p(h(g(x)))
            g(0()) -> pair(s(0()),s(0()))
            g(s(x)) -> h(g(x))
            g(s(x)) -> pair(+(p(g(x)),q(g(x))),p(g(x)))
            h(x) -> pair(+(p(x),q(x)),p(x))
            p(pair(x,y)) -> x
            q(pair(x,y)) -> y
        - Signature:
            {+/2,f/1,g/1,h/1,p/1,q/1} / {0/0,pair/2,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {+,f,g,h,p,q} and constructors {0,pair,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          g(x){x -> s(x)} =
            g(s(x)) ->^+ pair(+(p(g(x)),q(g(x))),p(g(x)))
              = C[g(x) = g(x){}]
          g(x){x -> s(x)} =
            g(s(x)) ->^+ pair(+(p(g(x)),q(g(x))),p(g(x)))
              = C[g(x) = g(x){}]

WORST_CASE(NON_POLY,?)