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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(x:S)) -> A(a(x:S))
 A(b(x:S)) -> A(x:S)
 A(b(x:S)) -> B(a(a(x:S)))
 B(c(x:S)) -> B(b(x:S))
 B(c(x:S)) -> B(x:S)
 B(c(x:S)) -> C(b(b(x:S)))
 C(a(x:S)) -> A(c(c(x:S)))
 C(a(x:S)) -> C(c(x:S))
 C(a(x:S)) -> C(x:S)
-> Rules:
 a(b(x:S)) -> b(a(a(x:S)))
 a(u(x:S)) -> x:S
 b(c(x:S)) -> c(b(b(x:S)))
 b(v(x:S)) -> x:S
 c(a(x:S)) -> a(c(c(x:S)))
 c(w(x:S)) -> x:S
 u(a(x:S)) -> x:S
 v(b(x:S)) -> x:S
 w(c(x:S)) -> x:S
-> Usable rules:
 a(b(x:S)) -> b(a(a(x:S)))
 a(u(x:S)) -> x:S
 b(c(x:S)) -> c(b(b(x:S)))
 b(v(x:S)) -> x:S
 c(a(x:S)) -> a(c(c(x:S)))
 c(w(x:S)) -> x:S
->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 0;1 1].X
[w](X) = [1 1;1 1].X
[A](X) = [0 1;0 1].X + [1;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:S)) -> A(x:S)
 A(b(x:S)) -> B(a(a(x:S)))
 B(c(x:S)) -> B(b(x:S))
 B(c(x:S)) -> B(x:S)
 B(c(x:S)) -> C(b(b(x:S)))
 C(a(x:S)) -> A(c(c(x:S)))
 C(a(x:S)) -> C(c(x:S))
 C(a(x:S)) -> C(x:S)
-> Rules:
 a(b(x:S)) -> b(a(a(x:S)))
 a(u(x:S)) -> x:S
 b(c(x:S)) -> c(b(b(x:S)))
 b(v(x:S)) -> x:S
 c(a(x:S)) -> a(c(c(x:S)))
 c(w(x:S)) -> x:S
 u(a(x:S)) -> x:S
 v(b(x:S)) -> x:S
 w(c(x:S)) -> x:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(b(x:S)) -> A(x:S)
 A(b(x:S)) -> B(a(a(x:S)))
 B(c(x:S)) -> B(b(x:S))
 B(c(x:S)) -> B(x:S)
 B(c(x:S)) -> C(b(b(x:S)))
 C(a(x:S)) -> A(c(c(x:S)))
 C(a(x:S)) -> C(c(x:S))
 C(a(x:S)) -> C(x:S)
->->-> Rules:
 a(b(x:S)) -> b(a(a(x:S)))
 a(u(x:S)) -> x:S
 b(c(x:S)) -> c(b(b(x:S)))
 b(v(x:S)) -> x:S
 c(a(x:S)) -> a(c(c(x:S)))
 c(w(x:S)) -> x:S
 u(a(x:S)) -> x:S
 v(b(x:S)) -> x:S
 w(c(x:S)) -> x:S

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

Problem 1.1: 

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

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 B(c(x:S)) -> B(b(x:S))
 B(c(x:S)) -> B(x:S)
-> Rules:
 a(b(x:S)) -> b(a(a(x:S)))
 a(u(x:S)) -> x:S
 b(c(x:S)) -> c(b(b(x:S)))
 b(v(x:S)) -> x:S
 c(a(x:S)) -> a(c(c(x:S)))
 c(w(x:S)) -> x:S
 u(a(x:S)) -> x:S
 v(b(x:S)) -> x:S
 w(c(x:S)) -> x:S
-> Usable rules:
 a(b(x:S)) -> b(a(a(x:S)))
 a(u(x:S)) -> x:S
 b(c(x:S)) -> c(b(b(x:S)))
 b(v(x:S)) -> x:S
 c(a(x:S)) -> a(c(c(x:S)))
 c(w(x:S)) -> x:S
->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) = 2.X

Problem 1.2: 

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

Problem 1.2: 

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

Problem 1.2: 

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

The problem is finite.