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


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YES

Problem 1: 

(VAR x1)
(RULES
e(r(x1)) -> e(w(x1))
e(w(x1)) -> r(i(x1))
i(t(x1)) -> e(r(x1))
r(e(x1)) -> w(r(x1))
r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
t(e(x1)) -> r(e(x1))
w(r(x1)) -> i(t(x1))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 E(r(x1)) -> E(w(x1))
 E(r(x1)) -> W(x1)
 E(w(x1)) -> I(x1)
 E(w(x1)) -> R(i(x1))
 I(t(x1)) -> E(r(x1))
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> E(w(r(i(t(e(x1))))))
 R(i(t(e(r(x1))))) -> E(x1)
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))

Problem 1: 

SCC Processor:
-> Pairs:
 E(r(x1)) -> E(w(x1))
 E(r(x1)) -> W(x1)
 E(w(x1)) -> I(x1)
 E(w(x1)) -> R(i(x1))
 I(t(x1)) -> E(r(x1))
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> E(w(r(i(t(e(x1))))))
 R(i(t(e(r(x1))))) -> E(x1)
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 E(r(x1)) -> E(w(x1))
 E(r(x1)) -> W(x1)
 E(w(x1)) -> I(x1)
 E(w(x1)) -> R(i(x1))
 I(t(x1)) -> E(r(x1))
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> E(w(r(i(t(e(x1))))))
 R(i(t(e(r(x1))))) -> E(x1)
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
->->-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 E(r(x1)) -> E(w(x1))
 E(r(x1)) -> W(x1)
 E(w(x1)) -> I(x1)
 E(w(x1)) -> R(i(x1))
 I(t(x1)) -> E(r(x1))
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> E(w(r(i(t(e(x1))))))
 R(i(t(e(r(x1))))) -> E(x1)
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
-> Usable rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[e](X) = X + 1/2
[i](X) = 2/3.X
[r](X) = 4/3.X + 3/4
[t](X) = 2.X + 2
[w](X) = X + 2/3
[E](X) = 4/3.X + 4/3
[I](X) = X + 1/3
[R](X) = 2.X + 2
[T](X) = 2.X + 2
[W](X) = 3/2.X + 4/3

Problem 1: 

SCC Processor:
-> Pairs:
 E(r(x1)) -> W(x1)
 E(w(x1)) -> I(x1)
 E(w(x1)) -> R(i(x1))
 I(t(x1)) -> E(r(x1))
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> E(w(r(i(t(e(x1))))))
 R(i(t(e(r(x1))))) -> E(x1)
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 E(r(x1)) -> W(x1)
 E(w(x1)) -> I(x1)
 E(w(x1)) -> R(i(x1))
 I(t(x1)) -> E(r(x1))
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> E(w(r(i(t(e(x1))))))
 R(i(t(e(r(x1))))) -> E(x1)
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
->->-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 E(r(x1)) -> W(x1)
 E(w(x1)) -> I(x1)
 E(w(x1)) -> R(i(x1))
 I(t(x1)) -> E(r(x1))
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> E(w(r(i(t(e(x1))))))
 R(i(t(e(r(x1))))) -> E(x1)
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
-> Usable rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[e](X) = X + 1/2
[i](X) = 1/2.X + 1/3
[r](X) = 3/2.X + 1/2
[t](X) = 3.X + 4/3
[w](X) = X + 1/2
[E](X) = 1/2.X + 1/3
[I](X) = 1/4.X + 1/4
[R](X) = 3/4.X + 1/3
[T](X) = 3/4.X + 1/3
[W](X) = 1/2.X + 1/3

Problem 1: 

SCC Processor:
-> Pairs:
 E(w(x1)) -> I(x1)
 E(w(x1)) -> R(i(x1))
 I(t(x1)) -> E(r(x1))
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> E(w(r(i(t(e(x1))))))
 R(i(t(e(r(x1))))) -> E(x1)
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 E(w(x1)) -> I(x1)
 E(w(x1)) -> R(i(x1))
 I(t(x1)) -> E(r(x1))
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> E(w(r(i(t(e(x1))))))
 R(i(t(e(r(x1))))) -> E(x1)
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
->->-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 E(w(x1)) -> I(x1)
 E(w(x1)) -> R(i(x1))
 I(t(x1)) -> E(r(x1))
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> E(w(r(i(t(e(x1))))))
 R(i(t(e(r(x1))))) -> E(x1)
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
-> Usable rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[e](X) = 4/3.X + 2/3
[i](X) = 2/3.X
[r](X) = 2.X + 3/2
[t](X) = 4.X + 4
[w](X) = 4/3.X + 3/4
[E](X) = 1/2.X + 2/3
[I](X) = 1/4.X + 1/2
[R](X) = X + 1
[T](X) = X + 3/2
[W](X) = 2/3.X + 1/2

Problem 1: 

SCC Processor:
-> Pairs:
 E(w(x1)) -> R(i(x1))
 I(t(x1)) -> E(r(x1))
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> E(w(r(i(t(e(x1))))))
 R(i(t(e(r(x1))))) -> E(x1)
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 E(w(x1)) -> R(i(x1))
 I(t(x1)) -> E(r(x1))
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> E(w(r(i(t(e(x1))))))
 R(i(t(e(r(x1))))) -> E(x1)
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
->->-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 E(w(x1)) -> R(i(x1))
 I(t(x1)) -> E(r(x1))
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> E(w(r(i(t(e(x1))))))
 R(i(t(e(r(x1))))) -> E(x1)
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
-> Usable rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[e](X) = X + 1/2
[i](X) = 2/3.X + 1/4
[r](X) = 4/3.X + 2/3
[t](X) = 2.X + 3/2
[w](X) = X + 2/3
[E](X) = 3/2.X + 1/4
[I](X) = X
[R](X) = 2.X + 1/2
[T](X) = 2.X + 4/3
[W](X) = 3/2.X + 1/2

Problem 1: 

SCC Processor:
-> Pairs:
 I(t(x1)) -> E(r(x1))
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> E(w(r(i(t(e(x1))))))
 R(i(t(e(r(x1))))) -> E(x1)
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
->->-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 I(t(x1)) -> R(x1)
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
-> Usable rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[e](X) = 4/3.X + 2/3
[i](X) = 2/3.X
[r](X) = 2.X + 3/2
[t](X) = 4.X + 4
[w](X) = 4/3.X + 2/3
[I](X) = 1/2.X + 1/4
[R](X) = 3/2.X + 4/3
[T](X) = 2.X + 1
[W](X) = X + 3/4

Problem 1: 

SCC Processor:
-> Pairs:
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> I(t(e(x1)))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> I(t(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> T(x1)
->->-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 R(e(x1)) -> R(x1)
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
-> Usable rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[e](X) = X + 1/3
[i](X) = 1/2.X
[r](X) = 3/2.X + 1/2
[t](X) = 3.X + 2
[w](X) = X + 1/2
[R](X) = 1/2.X + 3
[T](X) = 1/2.X + 3
[W](X) = 1/3.X + 3

Problem 1: 

SCC Processor:
-> Pairs:
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> T(x1)
->->-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 R(e(x1)) -> W(r(x1))
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
-> Usable rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[e](X) = X + 3/2
[i](X) = 1/2.X + 1
[r](X) = 3/2.X + 3/2
[t](X) = 3.X + 4
[w](X) = X + 3/2
[R](X) = 3/2.X + 1/4
[T](X) = 3/2.X + 1
[W](X) = X + 1/4

Problem 1: 

SCC Processor:
-> Pairs:
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> T(x1)
->->-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 R(i(t(e(r(x1))))) -> R(i(t(e(x1))))
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
-> Usable rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[e](X) = X + 1/3
[i](X) = 1/3.X
[r](X) = X + 2/3
[t](X) = 3.X + 3
[w](X) = X + 1/3
[R](X) = 1/4.X
[T](X) = 1/4.X
[W](X) = 1/4.X

Problem 1: 

SCC Processor:
-> Pairs:
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> T(x1)
->->-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 R(i(t(e(r(x1))))) -> T(e(x1))
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
-> Usable rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[e](X) = X + 1/3
[i](X) = 1/2.X
[r](X) = 3/2.X + 1/3
[t](X) = 3.X + 4/3
[w](X) = X + 1/3
[R](X) = 4/3.X
[T](X) = 3/2.X + 1/3
[W](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> T(x1)
->->-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 R(i(t(e(r(x1))))) -> W(r(i(t(e(x1)))))
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
-> Usable rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[e](X) = X + 3/4
[i](X) = 1/3.X + 1/2
[r](X) = 4/3.X + 1
[t](X) = 4.X + 4
[w](X) = X + 1
[R](X) = 2/3.X + 3/2
[T](X) = 2/3.X + 3/2
[W](X) = 2/3.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 T(e(x1)) -> R(e(x1))
 W(r(x1)) -> T(x1)
-> Rules:
 e(r(x1)) -> e(w(x1))
 e(w(x1)) -> r(i(x1))
 i(t(x1)) -> e(r(x1))
 r(e(x1)) -> w(r(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.