YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 R(e(x1:S)) -> R(x1:S)
 R(e(x1:S)) -> W(r(x1:S))
 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
 T(e(x1:S)) -> R(e(x1:S))
 W(r(x1:S)) -> T(x1:S)
-> Rules:
 e(r(x1:S)) -> e(w(x1:S))
 e(w(x1:S)) -> r(i(x1:S))
 i(t(x1:S)) -> e(r(x1:S))
 r(e(x1:S)) -> w(r(x1:S))
 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
 t(e(x1:S)) -> r(e(x1:S))
 w(r(x1:S)) -> i(t(x1:S))
-> Usable rules:
 e(r(x1:S)) -> e(w(x1:S))
 e(w(x1:S)) -> r(i(x1:S))
 i(t(x1:S)) -> e(r(x1:S))
 r(e(x1:S)) -> w(r(x1:S))
 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
 t(e(x1:S)) -> r(e(x1:S))
 w(r(x1:S)) -> i(t(x1:S))
->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) = 2.X + 4/3
[T](X) = 2.X + 2
[W](X) = 4/3.X + 2/3

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.