/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 z)
(RULES
pin(a) -> pout(b)
pin(b) -> pout(c)
tc(x) -> x
tc(x) -> y | pin(x) -> pout(z), tc(z) -> y
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 pin(a) -> pout(b)
 pin(b) -> pout(c)
 tc(x) -> x
 tc(x) -> y | pin(x) -> pout(z), tc(z) -> y
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 pin(a) -> pout(b)
 pin(b) -> pout(c)
 tc(x) -> x
 tc(x) -> y | pin(x) -> pout(z), tc(z) -> y

Conditional Termination Problem 2:
-> Pairs:
 TC(x) -> PIN(x)
 TC(x) -> TC(z) | pin(x) -> pout(z)
-> QPairs:
 Empty
-> Rules:
 pin(a) -> pout(b)
 pin(b) -> pout(c)
 tc(x) -> x
 tc(x) -> y | pin(x) -> pout(z), tc(z) -> y


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 pin(a) -> pout(b)
 pin(b) -> pout(c)
 tc(x) -> x
 tc(x) -> y | pin(x) -> pout(z), tc(z) -> y
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 TC(x) -> PIN(x)
 TC(x) -> TC(z) | pin(x) -> pout(z)
-> QPairs:
 Empty
-> Rules:
 pin(a) -> pout(b)
 pin(b) -> pout(c)
 tc(x) -> x
 tc(x) -> y | pin(x) -> pout(z), tc(z) -> y
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 TC(x) -> TC(z) | pin(x) -> pout(z)
->->-> Rules:
 pin(a) -> pout(b)
 pin(b) -> pout(c)
 tc(x) -> x
 tc(x) -> y | pin(x) -> pout(z), tc(z) -> y

Problem 1.2: 

Reduction Triple Processor:
-> Pairs:
 TC(x) -> TC(z) | pin(x) -> pout(z)
-> QPairs:
 Empty
-> Rules:
 pin(a) -> pout(b)
 pin(b) -> pout(c)
 tc(x) -> x
 tc(x) -> y | pin(x) -> pout(z), tc(z) -> y
-> Usable rules:
 pin(a) -> pout(b)
 pin(b) -> pout(c)
->Interpretation type:
 Linear
->Coefficients:
 Integer Numbers
->Dimension:
 1
->Convex Domain:
 D[(x_1)] = ((1 >= 0) /\ (x_1 >= 0))
->Interpretation:
 
[delta] = 1
[pin](x_1) = x_1
[a] = 2
[b] = 1
[c] = 0
[pout](x_1) = 1+x_1
[TC](x_1) = 2.x_1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 pin(a) -> pout(b)
 pin(b) -> pout(c)
 tc(x) -> x
 tc(x) -> y | pin(x) -> pout(z), tc(z) -> y
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.