/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 x y)
(RULES
f(k(a),k(b),x) -> f(x,x,x)
g(x) -> k(y) | h(x) -> d, h(x) -> c(y)
h(d) -> c(a)
h(d) -> c(b)
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 f(k(a),k(b),x) -> f(x,x,x)
 g(x) -> k(y) | h(x) -> d, h(x) -> c(y)
 h(d) -> c(a)
 h(d) -> c(b)
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 F(k(a),k(b),x) -> F(x,x,x)
-> QPairs:
 Empty
-> Rules:
 f(k(a),k(b),x) -> f(x,x,x)
 g(x) -> k(y) | h(x) -> d, h(x) -> c(y)
 h(d) -> c(a)
 h(d) -> c(b)

Conditional Termination Problem 2:
-> Pairs:
 G(x) -> H(x)
 G(x) -> H(x) | h(x) -> d
-> QPairs:
 F(k(a),k(b),x) -> F(x,x,x)
-> Rules:
 f(k(a),k(b),x) -> f(x,x,x)
 g(x) -> k(y) | h(x) -> d, h(x) -> c(y)
 h(d) -> c(a)
 h(d) -> c(b)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 F(k(a),k(b),x) -> F(x,x,x)
-> QPairs:
 Empty
-> Rules:
 f(k(a),k(b),x) -> f(x,x,x)
 g(x) -> k(y) | h(x) -> d, h(x) -> c(y)
 h(d) -> c(a)
 h(d) -> c(b)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(k(a),k(b),x) -> F(x,x,x)
->->-> Rules:
 f(k(a),k(b),x) -> f(x,x,x)
 g(x) -> k(y) | h(x) -> d, h(x) -> c(y)
 h(d) -> c(a)
 h(d) -> c(b)

Problem 1.1: 

Unsatisfiable Rule Processor:
-> Pairs:
 F(k(a),k(b),x) -> F(x,x,x)
-> QPairs:
 Empty
-> Rules:
 f(k(a),k(b),x) -> f(x,x,x)
 g(x) -> k(y) | h(x) -> d, h(x) -> c(y)
 h(d) -> c(a)
 h(d) -> c(b)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X1,X2,X3) = 0
[g](X) = 2.X + 2
[h](X) = 1
[a] = 0
[b] = 2
[c](X) = 1
[d] = 2
[k](X) = 2
[F](X1,X2,X3) = 0
[G](X) = 0
[H](X) = 0

Problem 1.1: 

SCC Processor:
-> Pairs:
 F(k(a),k(b),x) -> F(x,x,x)
-> QPairs:
 Empty
-> Rules:
 f(k(a),k(b),x) -> f(x,x,x)
 h(d) -> c(a)
 h(d) -> c(b)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(k(a),k(b),x) -> F(x,x,x)
->->-> Rules:
 f(k(a),k(b),x) -> f(x,x,x)
 h(d) -> c(a)
 h(d) -> c(b)

Problem 1.1: 

Shift to Dependency Pair Processor:
-> Pairs:
 F(k(a),k(b),x) -> F(x,x,x)
-> Rules:
 f(k(a),k(b),x) -> f(x,x,x)
 h(d) -> c(a)
 h(d) -> c(b)

Problem 1.1: 

SCC Processor:
-> Pairs:
 F(k(a),k(b),x) -> F(x,x,x)
-> Rules:
 f(k(a),k(b),x) -> f(x,x,x)
 h(d) -> c(a)
 h(d) -> c(b)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(k(a),k(b),x) -> F(x,x,x)
->->-> Rules:
 f(k(a),k(b),x) -> f(x,x,x)
 h(d) -> c(a)
 h(d) -> c(b)

Problem 1.1: 

Forward Instantiation Processor:
-> Pairs:
 F(k(a),k(b),x) -> F(x,x,x)
-> Rules:
 f(k(a),k(b),x) -> f(x,x,x)
 h(d) -> c(a)
 h(d) -> c(b)
->Instantiated Pairs:
->->Original Pair:
 F(k(a),k(b),x) -> F(x,x,x)
->-> Instantiated pairs:
 Empty

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 G(x) -> H(x)
 G(x) -> H(x) | h(x) -> d
-> QPairs:
 F(k(a),k(b),x) -> F(x,x,x)
-> Rules:
 f(k(a),k(b),x) -> f(x,x,x)
 g(x) -> k(y) | h(x) -> d, h(x) -> c(y)
 h(d) -> c(a)
 h(d) -> c(b)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.