/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 x:S)
(RULES
a -> b
b -> a
f(x:S,x:S) -> a
g(x:S) -> a | g(x:S) ->* b
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 a -> b
 b -> a
 f(x:S,x:S) -> a
 g(x:S) -> a | g(x:S) ->* b
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 A -> B
 B -> A
 F(x:S,x:S) -> A
 G(x:S) -> A | g(x:S) ->* b
-> QPairs:
 Empty
-> Rules:
 a -> b
 b -> a
 f(x:S,x:S) -> a
 g(x:S) -> a | g(x:S) ->* b

Conditional Termination Problem 2:
-> Pairs:
 G(x:S) -> G(x:S)
-> QPairs:
 A -> B
 B -> A
 G(x:S) -> A | g(x:S) ->* b
-> Rules:
 a -> b
 b -> a
 f(x:S,x:S) -> a
 g(x:S) -> a | g(x:S) ->* b

Problem 1: 

SCC Processor:
-> Pairs:
 A -> B
 B -> A
 F(x:S,x:S) -> A
 G(x:S) -> A | g(x:S) ->* b
-> QPairs:
 Empty
-> Rules:
 a -> b
 b -> a
 f(x:S,x:S) -> a
 g(x:S) -> a | g(x:S) ->* b
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A -> B
 B -> A
-> QPairs:
 Empty
->->-> Rules:
 a -> b
 b -> a
 f(x:S,x:S) -> a
 g(x:S) -> a | g(x:S) ->* b

Problem 1: 

Unsatisfiable Rule Processor:
-> Pairs:
 A -> B
 B -> A
-> QPairs:
 Empty
-> Rules:
 a -> b
 b -> a
 f(x:S,x:S) -> a
 g(x:S) -> a | g(x:S) ->* b
->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 f : S S -> S .
op g : S -> 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)
x1:S ->R y1:S => f(x1:S,x2:S) ->R f(y1:S,x2:S)
x2:S ->R y2:S => f(x1:S,x2:S) ->R f(x1:S,y2:S)
x1:S ->R y1:S => g(x1:S) ->R g(y1:S)
a ->R b
b ->R a
f(x:S,x:S) ->R a
g(x:S) ->R* b => g(x:S) ->R a
x:S ->R y:S => gtrsim(x:S,y:S)
sqsupset(b,g(x:S))

Results:


Domains:
S: -|N

Function Interpretations:
|[a]| =  - 1
|[b]| =  - 1
|[f(x_1_1:S,x_2_1:S)]| =  - 1
|[g(x_1_1:S)]| = 0
|[fSNonEmpty]| =  - 1

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

Problem 1: 

SCC Processor:
-> Pairs:
 A -> B
 B -> A
-> QPairs:
 Empty
-> Rules:
 a -> b
 b -> a
 f(x:S,x:S) -> a
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A -> B
 B -> A
-> QPairs:
 Empty
->->-> Rules:
 a -> b
 b -> a
 f(x:S,x:S) -> a

Problem 1: 

Infinite Processor:
-> Pairs:
 A -> B
 B -> A
-> QPairs:
 Empty
-> Rules:
 a -> b
 b -> a
 f(x:S,x:S) -> a
-> Pairs in cycle:
 A -> B
 B -> A

The problem is infinite.