/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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NO

Problem 1: 

(VAR v_NonEmpty:S)
(RULES
a -> b
a -> c
b -> c | b ->* c
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 a -> b
 a -> c
 b -> c | b ->* c
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 A -> B
-> QPairs:
 Empty
-> Rules:
 a -> b
 a -> c
 b -> c | b ->* c

Conditional Termination Problem 2:
-> Pairs:
 B -> B
-> QPairs:
 Empty
-> Rules:
 a -> b
 a -> c
 b -> c | b ->* c

Problem 1: 

SCC Processor:
-> Pairs:
 B -> B
-> QPairs:
 Empty
-> Rules:
 a -> b
 a -> c
 b -> c | b ->* c
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B -> B
-> QPairs:
 Empty
->->-> Rules:
 a -> b
 a -> c
 b -> c | b ->* c

Problem 1: 

Unsatisfiable Rule Processor:
-> Pairs:
 B -> B
-> QPairs:
 Empty
-> Rules:
 a -> b
 a -> c
 b -> c | b ->* c
->AGES Output:
 
Model Results

System:
mod InTheory is
  sorts S Bool .

op _->*_ : S S -> Bool .
op _->_ : S S -> Bool .
op a :  -> S .
op b :  -> S .
op c :  -> S .
op fSNonEmpty :  -> S .
op gtrsim : S S -> Bool .
op sqsupset : S S -> Bool .

endm


Property:
x:S ->R* x:S
x:S ->R y:S /\ y:S ->R* z:S => x:S ->R* z:S
gtrsim(x:S,y:S) /\ sqsupset(y:S,z:S) => sqsupset(x:S,z:S)
a ->R b
a ->R c
b ->R* c => b ->R c
x:S ->R y:S => gtrsim(x:S,y:S)
sqsupset(c,b)

Results:


Domains:
S: -|N

Function Interpretations:
|[a]| =  - 1
|[b]| = 0
|[c]| =  - 1
|[fSNonEmpty]| =  - 1

Predicate Interpretations:
 x_1_1:S ->* x_2_1:S <=> ((1 >= x_1_1:S) /\ (x_2_1:S >= x_1_1:S))
 x_1_1:S -> x_2_1:S <=> ((x_2_1:S >= x_1_1:S) /\ (1 + x_2_1:S >= 0))
gtrsim(x_1_1:S,x_2_1:S) <=> ((1+3.x_2_1:S >= 2.x_1_1:S) /\ (1 + x_2_1:S >= 0))
sqsupset(x_1_1:S,x_2_1:S) <=> (4.x_2_1:S >= 4+4.x_1_1:S)

Problem 1: 

Infinite Processor:
-> Pairs:
 B -> B
-> QPairs:
 Empty
-> Rules:
 a -> b
 a -> c
-> Pairs in cycle:
 B -> B

The problem is infinite.