/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 x0 y z)
(STRATEGY CONTEXTSENSITIVE
(*top*_0 1)
(f_0 1 2)
(f_1)
(a_1)
(c_0)
)
(RULES
*top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
f_1(f_0(x,y),z) -> c_0
f_1(f_1(x,y),z) -> c_0
f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 *TOP*_0(a_1) -> *TOP*_0(f_0(a_1,a_1))
 *TOP*_0(a_1) -> F_0(a_1,a_1)
 F_0(a_1,x0) -> F_1(f_0(a_1,a_1),x0)
 F_0(x0,a_1) -> F_1(x0,f_0(a_1,a_1))
 F_1(x,f_0(y,z)) -> F_1(f_0(x,y),z)
 F_1(x,f_0(y,z)) -> F_1(f_1(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z)
-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
-> Unhiding Rules:
 Empty

Problem 1: 

SCC Processor:
-> Pairs:
 *TOP*_0(a_1) -> *TOP*_0(f_0(a_1,a_1))
 *TOP*_0(a_1) -> F_0(a_1,a_1)
 F_0(a_1,x0) -> F_1(f_0(a_1,a_1),x0)
 F_0(x0,a_1) -> F_1(x0,f_0(a_1,a_1))
 F_1(x,f_0(y,z)) -> F_1(f_0(x,y),z)
 F_1(x,f_0(y,z)) -> F_1(f_1(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z)
-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
-> Unhiding rules:
 Empty
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F_1(x,f_0(y,z)) -> F_1(f_0(x,y),z)
 F_1(x,f_0(y,z)) -> F_1(f_1(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z)
->->-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
->->-> Unhiding rules:
 Empty
->->Cycle:
->->-> Pairs:
 *TOP*_0(a_1) -> *TOP*_0(f_0(a_1,a_1))
->->-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
->->-> Unhiding rules:
 Empty


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Reduction Pairs Processor:
-> Pairs:
 F_1(x,f_0(y,z)) -> F_1(f_0(x,y),z)
 F_1(x,f_0(y,z)) -> F_1(f_1(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z)
-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
-> Unhiding rules:
 Empty
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f_0](X1,X2) = X1 + 2.X2 + 2
[f_1](X1,X2) = X1 + 2.X2 + 2
[F_1](X1,X2) = X1 + 2.X2

Problem 1.1: 

SCC Processor:
-> Pairs:
 F_1(x,f_0(y,z)) -> F_1(f_1(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z)
-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
-> Unhiding rules:
 Empty
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F_1(x,f_0(y,z)) -> F_1(f_1(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z)
->->-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
->->-> Unhiding rules:
 Empty

Problem 1.1: 

Reduction Pairs Processor:
-> Pairs:
 F_1(x,f_0(y,z)) -> F_1(f_1(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z)
-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
-> Unhiding rules:
 Empty
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f_0](X1,X2) = X1 + 2.X2 + 2
[f_1](X1,X2) = X1 + X2 + 2
[F_1](X1,X2) = X1 + 2.X2

Problem 1.1: 

SCC Processor:
-> Pairs:
 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z)
-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
-> Unhiding rules:
 Empty
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z)
->->-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
->->-> Unhiding rules:
 Empty

Problem 1.1: 

Reduction Pairs Processor:
-> Pairs:
 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z)
 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z)
-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
-> Unhiding rules:
 Empty
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f_0](X1,X2) = 2.X2 + 2
[f_1](X1,X2) = X1 + 2.X2 + 2
[F_1](X1,X2) = X1 + 2.X2

Problem 1.1: 

SCC Processor:
-> Pairs:
 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z)
-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
-> Unhiding rules:
 Empty
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z)
->->-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
->->-> Unhiding rules:
 Empty

Problem 1.1: 

Reduction Pairs Processor:
-> Pairs:
 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z)
-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
-> Unhiding rules:
 Empty
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f_1](X1,X2) = X1 + X2 + 1
[F_1](X1,X2) = X1 + 2.X2

Problem 1.1: 

Basic Processor:
-> Pairs:
 Empty
-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
-> Unhiding rules:
 Empty
-> Result:
 Set P is empty

The problem is finite.

Problem 1.2: 

Reduction Pairs Processor:
-> Pairs:
 *TOP*_0(a_1) -> *TOP*_0(f_0(a_1,a_1))
-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
-> Unhiding rules:
 Empty
-> Usable rules:
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f_0](X1,X2) = 1
[f_1](X1,X2) = 0
[a_1] = 2
[c_0] = 0
[*TOP*_0](X) = 2.X

Problem 1.2: 

Basic Processor:
-> Pairs:
 Empty
-> Rules:
 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1))
 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0)
 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1))
 f_1(f_0(x,y),z) -> c_0
 f_1(f_1(x,y),z) -> c_0
 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z)
 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z)
-> Unhiding rules:
 Empty
-> Result:
 Set P is empty

The problem is finite.