/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)
(RULES
a -> a | b -> x, c -> x
b -> d | d -> x, e -> x
c -> d | d -> x, e -> x
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 a -> a | b -> x, c -> x
 b -> d | d -> x, e -> x
 c -> d | d -> x, e -> x
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 A -> A | b -> x, c -> x
-> QPairs:
 Empty
-> Rules:
 a -> a | b -> x, c -> x
 b -> d | d -> x, e -> x
 c -> d | d -> x, e -> x

Conditional Termination Problem 2:
-> Pairs:
 A -> B
 A -> C | b -> x
-> QPairs:
 A -> A | b -> x, c -> x
-> Rules:
 a -> a | b -> x, c -> x
 b -> d | d -> x, e -> x
 c -> d | d -> x, e -> x


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 A -> A | b -> x, c -> x
-> QPairs:
 Empty
-> Rules:
 a -> a | b -> x, c -> x
 b -> d | d -> x, e -> x
 c -> d | d -> x, e -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A -> A | b -> x, c -> x
->->-> Rules:
 a -> a | b -> x, c -> x
 b -> d | d -> x, e -> x
 c -> d | d -> x, e -> x

Problem 1.1: 

Simplification and Narrowing on Condition Processor:
-> Pairs:
 A -> A | b -> x, c -> x
-> QPairs:
 Empty
-> Rules:
 a -> a | b -> x, c -> x
 b -> d | d -> x, e -> x
 c -> d | d -> x, e -> x
->Narrowed Pairs:
->->Original Pair:
 A -> A | b -> x, c -> x
->-> Narrowed pairs:
 A -> A | b -> c
 A -> A | c -> b

Problem 1.1: 

SCC Processor:
-> Pairs:
 A -> A | b -> c
 A -> A | c -> b
-> QPairs:
 Empty
-> Rules:
 a -> a | b -> x, c -> x
 b -> d | d -> x, e -> x
 c -> d | d -> x, e -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A -> A | b -> c
 A -> A | c -> b
->->-> Rules:
 a -> a | b -> x, c -> x
 b -> d | d -> x, e -> x
 c -> d | d -> x, e -> x

Problem 1.1: 

Reduction Triple Processor:
-> Pairs:
 A -> A | b -> c
 A -> A | c -> b
-> QPairs:
 Empty
-> Rules:
 a -> a | b -> x, c -> x
 b -> d | d -> x, e -> x
 c -> d | d -> x, e -> x
-> Usable rules:
 b -> d | d -> x, e -> x
 c -> d | d -> x, e -> x
->Interpretation type:
 Linear
->Coefficients:
 Integer Numbers
->Dimension:
 1
->Convex Domain:
 D[(x_1)] = ((1-x_1 >= 0) /\ (1+x_1 >= 0))
->Interpretation:
 
[delta] = 1
[b] = 0
[c] = 1
[d] = 0
[e] = 0
[A] = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 A -> A | c -> b
-> QPairs:
 Empty
-> Rules:
 a -> a | b -> x, c -> x
 b -> d | d -> x, e -> x
 c -> d | d -> x, e -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A -> A | c -> b
->->-> Rules:
 a -> a | b -> x, c -> x
 b -> d | d -> x, e -> x
 c -> d | d -> x, e -> x

Problem 1.1: 

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

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 a -> a | b -> x, c -> x
 b -> d | d -> x, e -> x
 c -> d | d -> x, e -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 A -> B
 A -> C | b -> x
-> QPairs:
 A -> A | b -> x, c -> x
-> Rules:
 a -> a | b -> x, c -> x
 b -> d | d -> x, e -> x
 c -> d | d -> x, e -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.