/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:
            a(X) -> X
            a(nf(X1,X2)) -> f(a(X1),a(X2))
            a(ns(X)) -> s(a(X))
            a(nt(X)) -> t(a(X))
            d(0()) -> 0()
            d(s(X)) -> s(s(d(X)))
            f(X1,X2) -> nf(X1,X2)
            f(0(),X) -> nil()
            f(s(X),cs(Y,Z)) -> cs(Y,nf(X,a(Z)))
            p(X,0()) -> X
            p(0(),X) -> X
            p(s(X),s(Y)) -> s(s(p(X,Y)))
            q(0()) -> 0()
            q(s(X)) -> s(p(q(X),d(X)))
            s(X) -> ns(X)
            t(N) -> cs(r(q(N)),nt(ns(N)))
            t(X) -> nt(X)
        - Signature:
            {a/1,d/1,f/2,p/2,q/1,s/1,t/1} / {0/0,cs/2,nf/2,nil/0,ns/1,nt/1,r/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a,d,f,p,q,s,t} and constructors {0,cs,nf,nil,ns,nt,r}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a(X) -> X
            a(nf(X1,X2)) -> f(a(X1),a(X2))
            a(ns(X)) -> s(a(X))
            a(nt(X)) -> t(a(X))
            d(0()) -> 0()
            d(s(X)) -> s(s(d(X)))
            f(X1,X2) -> nf(X1,X2)
            f(0(),X) -> nil()
            f(s(X),cs(Y,Z)) -> cs(Y,nf(X,a(Z)))
            p(X,0()) -> X
            p(0(),X) -> X
            p(s(X),s(Y)) -> s(s(p(X,Y)))
            q(0()) -> 0()
            q(s(X)) -> s(p(q(X),d(X)))
            s(X) -> ns(X)
            t(N) -> cs(r(q(N)),nt(ns(N)))
            t(X) -> nt(X)
        - Signature:
            {a/1,d/1,f/2,p/2,q/1,s/1,t/1} / {0/0,cs/2,nf/2,nil/0,ns/1,nt/1,r/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a,d,f,p,q,s,t} and constructors {0,cs,nf,nil,ns,nt,r}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a(X) -> X
            a(nf(X1,X2)) -> f(a(X1),a(X2))
            a(ns(X)) -> s(a(X))
            a(nt(X)) -> t(a(X))
            d(0()) -> 0()
            d(s(X)) -> s(s(d(X)))
            f(X1,X2) -> nf(X1,X2)
            f(0(),X) -> nil()
            f(s(X),cs(Y,Z)) -> cs(Y,nf(X,a(Z)))
            p(X,0()) -> X
            p(0(),X) -> X
            p(s(X),s(Y)) -> s(s(p(X,Y)))
            q(0()) -> 0()
            q(s(X)) -> s(p(q(X),d(X)))
            s(X) -> ns(X)
            t(N) -> cs(r(q(N)),nt(ns(N)))
            t(X) -> nt(X)
        - Signature:
            {a/1,d/1,f/2,p/2,q/1,s/1,t/1} / {0/0,cs/2,nf/2,nil/0,ns/1,nt/1,r/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a,d,f,p,q,s,t} and constructors {0,cs,nf,nil,ns,nt,r}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          a(x){x -> nf(x,y)} =
            a(nf(x,y)) ->^+ f(a(x),a(y))
              = C[a(x) = a(x){}]

WORST_CASE(Omega(n^1),?)