/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem 1: 

(VAR x1)
(RULES
a(l(x1)) -> a(t(x1))
n(s(x1)) -> a(l(a(t(x1))))
o(m(a(x1))) -> t(e(n(x1)))
s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
t(o(x1)) -> m(a(x1))
t(e(x1)) -> n(s(x1))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(l(x1)) -> A(t(x1))
 A(l(x1)) -> T(x1)
 N(s(x1)) -> A(t(x1))
 N(s(x1)) -> A(l(a(t(x1))))
 N(s(x1)) -> T(x1)
 O(m(a(x1))) -> N(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> N(s(x1))
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))

Problem 1: 

SCC Processor:
-> Pairs:
 A(l(x1)) -> A(t(x1))
 A(l(x1)) -> T(x1)
 N(s(x1)) -> A(t(x1))
 N(s(x1)) -> A(l(a(t(x1))))
 N(s(x1)) -> T(x1)
 O(m(a(x1))) -> N(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> N(s(x1))
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(l(x1)) -> A(t(x1))
 A(l(x1)) -> T(x1)
 N(s(x1)) -> A(t(x1))
 N(s(x1)) -> A(l(a(t(x1))))
 N(s(x1)) -> T(x1)
 O(m(a(x1))) -> N(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> N(s(x1))
 T(e(x1)) -> S(x1)
->->-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(l(x1)) -> A(t(x1))
 A(l(x1)) -> T(x1)
 N(s(x1)) -> A(t(x1))
 N(s(x1)) -> A(l(a(t(x1))))
 N(s(x1)) -> T(x1)
 O(m(a(x1))) -> N(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> N(s(x1))
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
-> Usable rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = X + 1/2
[n](X) = 1/2.X
[o](X) = X + 1/2
[s](X) = 2.X + 2
[t](X) = X
[e](X) = 2.X + 1
[l](X) = X
[m](X) = X
[A](X) = X
[N](X) = 1/2.X
[O](X) = X + 1/2
[S](X) = 2.X + 1
[T](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 A(l(x1)) -> A(t(x1))
 A(l(x1)) -> T(x1)
 N(s(x1)) -> A(l(a(t(x1))))
 N(s(x1)) -> T(x1)
 O(m(a(x1))) -> N(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> N(s(x1))
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(l(x1)) -> A(t(x1))
 A(l(x1)) -> T(x1)
 N(s(x1)) -> A(l(a(t(x1))))
 N(s(x1)) -> T(x1)
 O(m(a(x1))) -> N(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> N(s(x1))
 T(e(x1)) -> S(x1)
->->-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(l(x1)) -> A(t(x1))
 A(l(x1)) -> T(x1)
 N(s(x1)) -> A(l(a(t(x1))))
 N(s(x1)) -> T(x1)
 O(m(a(x1))) -> N(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> N(s(x1))
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
-> Usable rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = X + 1/2
[n](X) = 1/2.X
[o](X) = X + 1/2
[s](X) = 2.X + 2
[t](X) = X
[e](X) = 2.X + 1
[l](X) = X
[m](X) = X
[A](X) = X
[N](X) = 1/2.X
[O](X) = X + 1/2
[S](X) = 2.X + 1
[T](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 A(l(x1)) -> A(t(x1))
 A(l(x1)) -> T(x1)
 N(s(x1)) -> T(x1)
 O(m(a(x1))) -> N(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> N(s(x1))
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(l(x1)) -> A(t(x1))
 A(l(x1)) -> T(x1)
 N(s(x1)) -> T(x1)
 O(m(a(x1))) -> N(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> N(s(x1))
 T(e(x1)) -> S(x1)
->->-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(l(x1)) -> A(t(x1))
 A(l(x1)) -> T(x1)
 N(s(x1)) -> T(x1)
 O(m(a(x1))) -> N(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> N(s(x1))
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
-> Usable rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = X + 1/2
[n](X) = 1/2.X
[o](X) = 2.X + 1/2
[s](X) = 2.X + 2
[t](X) = X
[e](X) = 2.X + 1
[l](X) = X
[m](X) = 1/2.X
[A](X) = X
[N](X) = 1/2.X
[O](X) = 2.X + 1/2
[S](X) = 2.X + 1
[T](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 A(l(x1)) -> A(t(x1))
 A(l(x1)) -> T(x1)
 O(m(a(x1))) -> N(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> N(s(x1))
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(l(x1)) -> A(t(x1))
 A(l(x1)) -> T(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> S(x1)
->->-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(l(x1)) -> A(t(x1))
 A(l(x1)) -> T(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
-> Usable rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 0
[n](X) = 0
[o](X) = 2.X
[s](X) = 2.X + 2
[t](X) = 0
[e](X) = 0
[l](X) = 2.X + 1
[m](X) = 0
[A](X) = 2.X + 2
[O](X) = 2
[S](X) = 2
[T](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A(l(x1)) -> T(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(l(x1)) -> T(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> S(x1)
->->-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(l(x1)) -> T(x1)
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
-> Usable rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2
[n](X) = 2
[o](X) = X + 1
[s](X) = 2.X + 2
[t](X) = 2
[e](X) = 2
[l](X) = 2.X + 2
[m](X) = 1
[A](X) = X
[O](X) = 2
[S](X) = 2
[T](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> A(t(o(m(a(t(e(x1)))))))
 S(a(x1)) -> A(t(e(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(o(x1)) -> A(x1)
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(e(x1)) -> S(x1)
->->-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(o(m(a(t(e(x1))))))
 S(a(x1)) -> T(e(x1))
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
-> Usable rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 0
[n](X) = 0
[o](X) = 2.X
[s](X) = 2.X + 2
[t](X) = 0
[e](X) = 1
[l](X) = 2
[m](X) = 0
[O](X) = 2
[S](X) = 2
[T](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(e(x1))
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(e(x1))
 T(e(x1)) -> S(x1)
->->-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 S(a(x1)) -> T(e(x1))
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
-> Usable rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = X + 1/2
[n](X) = 1/2.X
[o](X) = 2.X + 1
[s](X) = 2.X + 2
[t](X) = X
[e](X) = 2.X + 1
[l](X) = X
[m](X) = 1/2.X
[O](X) = 2.X + 1/2
[S](X) = 2.X + 1
[T](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 T(e(x1)) -> S(x1)
->->-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 O(m(a(x1))) -> T(e(n(x1)))
 S(a(x1)) -> O(m(a(t(e(x1)))))
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
-> Usable rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[a](X) = 1/4.X + 1
[n](X) = 1/4.X + 1/2
[o](X) = 3.X + 4
[s](X) = 3.X + 4
[t](X) = 3/2.X + 1/3
[e](X) = 2/3.X + 1
[l](X) = 3/2.X + 1/3
[m](X) = 1/2.X + 1/3
[O](X) = 4.X + 3/4
[S](X) = 2.X + 3
[T](X) = 3.X

Problem 1: 

SCC Processor:
-> Pairs:
 S(a(x1)) -> O(m(a(t(e(x1)))))
 T(e(x1)) -> S(x1)
-> Rules:
 a(l(x1)) -> a(t(x1))
 n(s(x1)) -> a(l(a(t(x1))))
 o(m(a(x1))) -> t(e(n(x1)))
 s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
 t(o(x1)) -> m(a(x1))
 t(e(x1)) -> n(s(x1))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.