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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(b(b(x,f(y)),z)) -> F(b(b(f(a),y),y))
-> Rules:
 c(b(a,a),b(y,z),x) -> b(a,b(z,z))
 f(c(c(a,y,a),b(x,z),a)) -> b(y,f(c(f(a),z,z)))
 f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a),y),y)))
-> Usable rules:
 c(b(a,a),b(y,z),x) -> b(a,b(z,z))
 f(c(c(a,y,a),b(x,z),a)) -> b(y,f(c(f(a),z,z)))
 f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a),y),y)))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[c](X1,X2,X3) = 2/3.X1 + 3.X2 + 3/2
[f](X) = 3.X + 1
[a] = 0
[b](X1,X2) = X1 + 4/3.X2 + 4
[F](X) = 4/3.X

Problem 1: 

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

The problem is finite.