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


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR x y z)
(RULES
b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 B(a,b(c(z,x,y),a)) -> B(b(z,c(y,z,a)),x)
 B(a,b(c(z,x,y),a)) -> B(z,c(y,z,a))
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
 C(f(c(a,y,a)),x,z) -> F(b(b(z,z),f(b(y,b(x,a)))))
 C(f(c(a,y,a)),x,z) -> F(b(y,b(x,a)))
 F(c(a,b(b(z,a),y),x)) -> B(z,x)
 F(c(a,b(b(z,a),y),x)) -> C(x,b(z,x),y)
 F(c(a,b(b(z,a),y),x)) -> F(c(x,b(z,x),y))
-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))

Problem 1: 

SCC Processor:
-> Pairs:
 B(a,b(c(z,x,y),a)) -> B(b(z,c(y,z,a)),x)
 B(a,b(c(z,x,y),a)) -> B(z,c(y,z,a))
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
 C(f(c(a,y,a)),x,z) -> F(b(b(z,z),f(b(y,b(x,a)))))
 C(f(c(a,y,a)),x,z) -> F(b(y,b(x,a)))
 F(c(a,b(b(z,a),y),x)) -> B(z,x)
 F(c(a,b(b(z,a),y),x)) -> C(x,b(z,x),y)
 F(c(a,b(b(z,a),y),x)) -> F(c(x,b(z,x),y))
-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B(a,b(c(z,x,y),a)) -> B(b(z,c(y,z,a)),x)
 B(a,b(c(z,x,y),a)) -> B(z,c(y,z,a))
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
 C(f(c(a,y,a)),x,z) -> F(b(b(z,z),f(b(y,b(x,a)))))
 C(f(c(a,y,a)),x,z) -> F(b(y,b(x,a)))
 F(c(a,b(b(z,a),y),x)) -> B(z,x)
 F(c(a,b(b(z,a),y),x)) -> C(x,b(z,x),y)
 F(c(a,b(b(z,a),y),x)) -> F(c(x,b(z,x),y))
->->-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 B(a,b(c(z,x,y),a)) -> B(b(z,c(y,z,a)),x)
 B(a,b(c(z,x,y),a)) -> B(z,c(y,z,a))
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
 C(f(c(a,y,a)),x,z) -> F(b(b(z,z),f(b(y,b(x,a)))))
 C(f(c(a,y,a)),x,z) -> F(b(y,b(x,a)))
 F(c(a,b(b(z,a),y),x)) -> B(z,x)
 F(c(a,b(b(z,a),y),x)) -> C(x,b(z,x),y)
 F(c(a,b(b(z,a),y),x)) -> F(c(x,b(z,x),y))
-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
-> Usable rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[b](X1,X2) = 0
[c](X1,X2,X3) = 2
[f](X) = 2.X + 2
[a] = 2
[B](X1,X2) = 2
[C](X1,X2,X3) = 2
[F](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 B(a,b(c(z,x,y),a)) -> B(b(z,c(y,z,a)),x)
 B(a,b(c(z,x,y),a)) -> B(z,c(y,z,a))
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
 C(f(c(a,y,a)),x,z) -> F(b(y,b(x,a)))
 F(c(a,b(b(z,a),y),x)) -> B(z,x)
 F(c(a,b(b(z,a),y),x)) -> C(x,b(z,x),y)
 F(c(a,b(b(z,a),y),x)) -> F(c(x,b(z,x),y))
-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B(a,b(c(z,x,y),a)) -> B(b(z,c(y,z,a)),x)
 B(a,b(c(z,x,y),a)) -> B(z,c(y,z,a))
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
 C(f(c(a,y,a)),x,z) -> F(b(y,b(x,a)))
 F(c(a,b(b(z,a),y),x)) -> B(z,x)
 F(c(a,b(b(z,a),y),x)) -> C(x,b(z,x),y)
 F(c(a,b(b(z,a),y),x)) -> F(c(x,b(z,x),y))
->->-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 B(a,b(c(z,x,y),a)) -> B(b(z,c(y,z,a)),x)
 B(a,b(c(z,x,y),a)) -> B(z,c(y,z,a))
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
 C(f(c(a,y,a)),x,z) -> F(b(y,b(x,a)))
 F(c(a,b(b(z,a),y),x)) -> B(z,x)
 F(c(a,b(b(z,a),y),x)) -> C(x,b(z,x),y)
 F(c(a,b(b(z,a),y),x)) -> F(c(x,b(z,x),y))
-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
-> Usable rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[b](X1,X2) = 0
[c](X1,X2,X3) = 2
[f](X) = 2.X + 2
[a] = 2
[B](X1,X2) = 2
[C](X1,X2,X3) = 2
[F](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 B(a,b(c(z,x,y),a)) -> B(b(z,c(y,z,a)),x)
 B(a,b(c(z,x,y),a)) -> B(z,c(y,z,a))
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
 F(c(a,b(b(z,a),y),x)) -> B(z,x)
 F(c(a,b(b(z,a),y),x)) -> C(x,b(z,x),y)
 F(c(a,b(b(z,a),y),x)) -> F(c(x,b(z,x),y))
-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B(a,b(c(z,x,y),a)) -> B(b(z,c(y,z,a)),x)
 B(a,b(c(z,x,y),a)) -> B(z,c(y,z,a))
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
->->-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
->->Cycle:
->->-> Pairs:
 F(c(a,b(b(z,a),y),x)) -> F(c(x,b(z,x),y))
->->-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 B(a,b(c(z,x,y),a)) -> B(b(z,c(y,z,a)),x)
 B(a,b(c(z,x,y),a)) -> B(z,c(y,z,a))
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
-> Usable rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[b](X1,X2) = X1 + 2.X2 + 1
[c](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 1
[f](X) = 2
[a] = 0
[B](X1,X2) = 2.X2 + 2
[C](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 B(a,b(c(z,x,y),a)) -> B(z,c(y,z,a))
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B(a,b(c(z,x,y),a)) -> B(z,c(y,z,a))
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
->->-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 B(a,b(c(z,x,y),a)) -> B(z,c(y,z,a))
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
-> Usable rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[b](X1,X2) = X1 + 2.X2 + 2
[c](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2
[f](X) = 2
[a] = 0
[B](X1,X2) = 2.X2 + 2
[C](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
->->-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 B(a,b(c(z,x,y),a)) -> C(y,z,a)
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
-> Usable rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[b](X1,X2) = 2.X1 + 2.X2 + 2
[c](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2
[f](X) = 2
[a] = 0
[B](X1,X2) = X2 + 2
[C](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 C(f(c(a,y,a)),x,z) -> B(b(z,z),f(b(y,b(x,a))))
 C(f(c(a,y,a)),x,z) -> B(y,b(x,a))
 C(f(c(a,y,a)),x,z) -> B(z,z)
-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 F(c(a,b(b(z,a),y),x)) -> F(c(x,b(z,x),y))
-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
-> Usable rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[b](X1,X2) = [1 0;1 0].X1 + [0 1;0 1].X2 + [1;1]
[c](X1,X2,X3) = [1 1;0 0].X1 + [0 1;0 1].X2 + [0 1;0 1].X3 + [1;1]
[f](X) = [0;1]
[a] = [1;1]
[F](X) = [0 1;0 1].X

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
 c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.