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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.