/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 x)
(RULES
a(b(x)) -> b(a(a(x)))
a(u(x)) -> x
b(c(x)) -> c(b(b(x)))
b(v(x)) -> x
c(a(x)) -> a(c(c(x)))
c(w(x)) -> x
u(a(x)) -> x
v(b(x)) -> x
w(c(x)) -> x
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(b(x)) -> A(a(x))
 A(b(x)) -> A(x)
 A(b(x)) -> B(a(a(x)))
 B(c(x)) -> B(b(x))
 B(c(x)) -> B(x)
 B(c(x)) -> C(b(b(x)))
 C(a(x)) -> A(c(c(x)))
 C(a(x)) -> C(c(x))
 C(a(x)) -> C(x)
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x

Problem 1: 

SCC Processor:
-> Pairs:
 A(b(x)) -> A(a(x))
 A(b(x)) -> A(x)
 A(b(x)) -> B(a(a(x)))
 B(c(x)) -> B(b(x))
 B(c(x)) -> B(x)
 B(c(x)) -> C(b(b(x)))
 C(a(x)) -> A(c(c(x)))
 C(a(x)) -> C(c(x))
 C(a(x)) -> C(x)
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(b(x)) -> A(a(x))
 A(b(x)) -> A(x)
 A(b(x)) -> B(a(a(x)))
 B(c(x)) -> B(b(x))
 B(c(x)) -> B(x)
 B(c(x)) -> C(b(b(x)))
 C(a(x)) -> A(c(c(x)))
 C(a(x)) -> C(c(x))
 C(a(x)) -> C(x)
->->-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(x)) -> A(a(x))
 A(b(x)) -> A(x)
 A(b(x)) -> B(a(a(x)))
 B(c(x)) -> B(b(x))
 B(c(x)) -> B(x)
 B(c(x)) -> C(b(b(x)))
 C(a(x)) -> A(c(c(x)))
 C(a(x)) -> C(c(x))
 C(a(x)) -> C(x)
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
-> Usable rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[a](X) = [1 0;0 1].X
[b](X) = [1 0;1 1].X + [0;1]
[c](X) = [1 0;1 0].X
[u](X) = [1 1;1 1].X
[v](X) = [1 1;1 1].X
[w](X) = [1 1;0 0].X
[A](X) = [0 1;0 1].X + [0;1]
[B](X) = [1 0;1 0].X + [1;1]
[C](X) = [1 0;1 0].X + [0;1]

Problem 1: 

SCC Processor:
-> Pairs:
 A(b(x)) -> A(x)
 A(b(x)) -> B(a(a(x)))
 B(c(x)) -> B(b(x))
 B(c(x)) -> B(x)
 B(c(x)) -> C(b(b(x)))
 C(a(x)) -> A(c(c(x)))
 C(a(x)) -> C(c(x))
 C(a(x)) -> C(x)
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(b(x)) -> A(x)
 A(b(x)) -> B(a(a(x)))
 B(c(x)) -> B(b(x))
 B(c(x)) -> B(x)
 B(c(x)) -> C(b(b(x)))
 C(a(x)) -> A(c(c(x)))
 C(a(x)) -> C(c(x))
 C(a(x)) -> C(x)
->->-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(x)) -> A(x)
 A(b(x)) -> B(a(a(x)))
 B(c(x)) -> B(b(x))
 B(c(x)) -> B(x)
 B(c(x)) -> C(b(b(x)))
 C(a(x)) -> A(c(c(x)))
 C(a(x)) -> C(c(x))
 C(a(x)) -> C(x)
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
-> Usable rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[a](X) = [1 0;0 1].X
[b](X) = [1 0;1 1].X + [0;1]
[c](X) = [1 0;1 0].X + [0;1]
[u](X) = [1 1;1 1].X
[v](X) = [1 1;0 1].X
[w](X) = [1 1;1 0].X
[A](X) = [0 1;1 0].X + [0;1]
[B](X) = [1 0;1 0].X + [1;1]
[C](X) = [1 0;1 0].X + [1;1]

Problem 1: 

SCC Processor:
-> Pairs:
 A(b(x)) -> B(a(a(x)))
 B(c(x)) -> B(b(x))
 B(c(x)) -> B(x)
 B(c(x)) -> C(b(b(x)))
 C(a(x)) -> A(c(c(x)))
 C(a(x)) -> C(c(x))
 C(a(x)) -> C(x)
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(b(x)) -> B(a(a(x)))
 B(c(x)) -> B(b(x))
 B(c(x)) -> B(x)
 B(c(x)) -> C(b(b(x)))
 C(a(x)) -> A(c(c(x)))
 C(a(x)) -> C(c(x))
 C(a(x)) -> C(x)
->->-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(x)) -> B(a(a(x)))
 B(c(x)) -> B(b(x))
 B(c(x)) -> B(x)
 B(c(x)) -> C(b(b(x)))
 C(a(x)) -> A(c(c(x)))
 C(a(x)) -> C(c(x))
 C(a(x)) -> C(x)
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
-> Usable rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = X + 1
[b](X) = 1/2.X
[c](X) = X
[u](X) = 2.X
[v](X) = 2.X
[w](X) = X
[A](X) = 2.X + 2
[B](X) = 1/2.X
[C](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 B(c(x)) -> B(b(x))
 B(c(x)) -> B(x)
 B(c(x)) -> C(b(b(x)))
 C(a(x)) -> A(c(c(x)))
 C(a(x)) -> C(c(x))
 C(a(x)) -> C(x)
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 C(a(x)) -> C(c(x))
 C(a(x)) -> C(x)
->->-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
->->Cycle:
->->-> Pairs:
 B(c(x)) -> B(b(x))
 B(c(x)) -> B(x)
->->-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 C(a(x)) -> C(c(x))
 C(a(x)) -> C(x)
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
-> Usable rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = X + 2
[b](X) = 1/2.X
[c](X) = X
[u](X) = 2.X
[v](X) = 2.X
[w](X) = X
[C](X) = 1/2.X

Problem 1.1: 

SCC Processor:
-> Pairs:
 C(a(x)) -> C(x)
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 C(a(x)) -> C(x)
->->-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x

Problem 1.1: 

Subterm Processor:
-> Pairs:
 C(a(x)) -> C(x)
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
->Projection:
 pi(C) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 B(c(x)) -> B(b(x))
 B(c(x)) -> B(x)
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
-> Usable rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 1/2.X
[b](X) = X
[c](X) = X + 2
[u](X) = 2.X
[v](X) = 2.X
[w](X) = X
[B](X) = 1/2.X

Problem 1.2: 

SCC Processor:
-> Pairs:
 B(c(x)) -> B(x)
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B(c(x)) -> B(x)
->->-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x

Problem 1.2: 

Subterm Processor:
-> Pairs:
 B(c(x)) -> B(x)
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
->Projection:
 pi(B) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a(b(x)) -> b(a(a(x)))
 a(u(x)) -> x
 b(c(x)) -> c(b(b(x)))
 b(v(x)) -> x
 c(a(x)) -> a(c(c(x)))
 c(w(x)) -> x
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.