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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.