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


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YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S)
(RULES
a(x:S,y:S) -> b(x:S,b(0,c(y:S)))
b(y:S,0) -> y:S
c(b(y:S,c(x:S))) -> c(c(b(a(0,0),y:S)))
)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.