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


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


YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.