/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 t(N) -> cs(r(q(N)),nt(ns(N)))
 q(0()) -> 0()
 q(s(X)) -> s(p(q(X),d(X)))
 d(0()) -> 0()
 d(s(X)) -> s(s(d(X)))
 p(0(),X) -> X
 p(X,0()) -> X
 p(s(X),s(Y)) -> s(s(p(X,Y)))
 f(0(),X) -> nil()
 f(s(X),cs(Y,Z)) -> cs(Y,nf(X,a(Z)))
 t(X) -> nt(X)
 s(X) -> ns(X)
 f(X1,X2) -> nf(X1,X2)
 a(nt(X)) -> t(a(X))
 a(ns(X)) -> s(a(X))
 a(nf(X1,X2)) -> f(a(X1),a(X2))
 a(X) -> X

Proof:
 WPO Processor:
  algebra: Max
  weight function:
   w0 = 0
   w(nf) = 5
   w(0) = 3
   w(nil) = 2
   w(f) = w(cs) = w(nt) = w(r) = w(q) = w(t) = 1
   w(a) = w(p) = w(d) = w(s) = w(ns) = 0
  status function:
   st(nf) = [0, 1]
   st(a) = [0]
   st(nil) = []
   st(f) = st(p) = [0, 1]
   st(d) = st(s) = [0]
   st(0) = []
   st(cs) = [0, 1]
   st(nt) = st(ns) = st(r) = st(q) = st(t) = [0]
  subterm penalty function:
   sp(nf, 1) = sp(f, 1) = 5
   sp(nt, 0) = sp(q, 0) = sp(t, 0) = 1
   sp(nf, 0) = sp(a, 0) = sp(f, 0) = sp(p, 1) = sp(p, 0) = sp(d, 0) = sp(
   s, 0) = sp(cs, 1) = sp(cs, 0) = sp(ns, 0) = sp(r, 0) = 0
  precedence:
   a > t > q > p > d > s > f > nf ~ nil ~ 0 ~ cs ~ nt ~ ns ~ r
  problem:
   
  Qed