/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)
(RULES
a(y,c(b(a(0,x),0))) -> b(a(c(b(0,y)),x),0)
a(y,x) -> y
b(x,y) -> c(a(c(y),a(0,x)))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(y,c(b(a(0,x),0))) -> A(c(b(0,y)),x)
 A(y,c(b(a(0,x),0))) -> B(a(c(b(0,y)),x),0)
 A(y,c(b(a(0,x),0))) -> B(0,y)
 B(x,y) -> A(0,x)
 B(x,y) -> A(c(y),a(0,x))
-> Rules:
 a(y,c(b(a(0,x),0))) -> b(a(c(b(0,y)),x),0)
 a(y,x) -> y
 b(x,y) -> c(a(c(y),a(0,x)))

Problem 1: 

SCC Processor:
-> Pairs:
 A(y,c(b(a(0,x),0))) -> A(c(b(0,y)),x)
 A(y,c(b(a(0,x),0))) -> B(a(c(b(0,y)),x),0)
 A(y,c(b(a(0,x),0))) -> B(0,y)
 B(x,y) -> A(0,x)
 B(x,y) -> A(c(y),a(0,x))
-> Rules:
 a(y,c(b(a(0,x),0))) -> b(a(c(b(0,y)),x),0)
 a(y,x) -> y
 b(x,y) -> c(a(c(y),a(0,x)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(y,c(b(a(0,x),0))) -> A(c(b(0,y)),x)
 A(y,c(b(a(0,x),0))) -> B(a(c(b(0,y)),x),0)
 A(y,c(b(a(0,x),0))) -> B(0,y)
 B(x,y) -> A(0,x)
 B(x,y) -> A(c(y),a(0,x))
->->-> Rules:
 a(y,c(b(a(0,x),0))) -> b(a(c(b(0,y)),x),0)
 a(y,x) -> y
 b(x,y) -> c(a(c(y),a(0,x)))

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 A(y,c(b(a(0,x),0))) -> B(a(c(b(0,y)),x),0)
 A(y,c(b(a(0,x),0))) -> B(0,y)
 B(x,y) -> A(0,x)
 B(x,y) -> A(c(y),a(0,x))
-> Rules:
 a(y,c(b(a(0,x),0))) -> b(a(c(b(0,y)),x),0)
 a(y,x) -> y
 b(x,y) -> c(a(c(y),a(0,x)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(y,c(b(a(0,x),0))) -> B(a(c(b(0,y)),x),0)
 A(y,c(b(a(0,x),0))) -> B(0,y)
 B(x,y) -> A(0,x)
 B(x,y) -> A(c(y),a(0,x))
->->-> Rules:
 a(y,c(b(a(0,x),0))) -> b(a(c(b(0,y)),x),0)
 a(y,x) -> y
 b(x,y) -> c(a(c(y),a(0,x)))

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 A(y,c(b(a(0,x),0))) -> B(0,y)
 B(x,y) -> A(0,x)
 B(x,y) -> A(c(y),a(0,x))
-> Rules:
 a(y,c(b(a(0,x),0))) -> b(a(c(b(0,y)),x),0)
 a(y,x) -> y
 b(x,y) -> c(a(c(y),a(0,x)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(y,c(b(a(0,x),0))) -> B(0,y)
 B(x,y) -> A(0,x)
 B(x,y) -> A(c(y),a(0,x))
->->-> Rules:
 a(y,c(b(a(0,x),0))) -> b(a(c(b(0,y)),x),0)
 a(y,x) -> y
 b(x,y) -> c(a(c(y),a(0,x)))

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 B(x,y) -> A(0,x)
 B(x,y) -> A(c(y),a(0,x))
-> Rules:
 a(y,c(b(a(0,x),0))) -> b(a(c(b(0,y)),x),0)
 a(y,x) -> y
 b(x,y) -> c(a(c(y),a(0,x)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.