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

WORST_CASE(Omega(n^1),?)