/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 B(z,b(c(a,y,a),f(f(x)))) -> C(c(y,a,z),z,x)
 B(z,b(c(a,y,a),f(f(x)))) -> C(y,a,z)
 C(c(z,y,a),a,a) -> B(z,y)
-> Rules:
 b(z,b(c(a,y,a),f(f(x)))) -> c(c(y,a,z),z,x)
 c(c(z,y,a),a,a) -> b(z,y)
 f(c(x,y,z)) -> c(z,f(b(y,z)),a)
-> Usable rules:
 b(z,b(c(a,y,a),f(f(x)))) -> c(c(y,a,z),z,x)
 c(c(z,y,a),a,a) -> b(z,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 + 2.X2 + 2
[f](X) = 2.X
[a] = 1
[B](X1,X2) = 2.X1 + 2.X2 + 2
[C](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2

Problem 1.1: 

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

Problem 1.1: 

Subterm Processor:
-> Pairs:
 B(z,b(c(a,y,a),f(f(x)))) -> C(y,a,z)
 C(c(z,y,a),a,a) -> B(z,y)
-> Rules:
 b(z,b(c(a,y,a),f(f(x)))) -> c(c(y,a,z),z,x)
 c(c(z,y,a),a,a) -> b(z,y)
 f(c(x,y,z)) -> c(z,f(b(y,z)),a)
->Projection:
 pi(B) = 2
 pi(C) = 1

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

Problem 1.2: 

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

The problem is finite.