TRS Standard pair #487071032

details

property	value
status	complete
benchmark	Ex14_AEGL02_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n182.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	20.0111 seconds
cpu usage	55.4494
user time	52.9316
system time	2.51781
max virtual memory	6333908.0
max residence set size	472280.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 active(from(X)) -> mark(cons(X,from(s(X))))
 active(length(nil())) -> mark(0())
 active(length(cons(X,Y))) -> mark(s(length1(Y)))
 active(length1(X)) -> mark(length(X))
 active(from(X)) -> from(active(X))
 active(cons(X1,X2)) -> cons(active(X1),X2)
 active(s(X)) -> s(active(X))
 from(mark(X)) -> mark(from(X))
 cons(mark(X1),X2) -> mark(cons(X1,X2))
 s(mark(X)) -> mark(s(X))
 proper(from(X)) -> from(proper(X))
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(s(X)) -> s(proper(X))
 proper(length(X)) -> length(proper(X))
 proper(nil()) -> ok(nil())
 proper(0()) -> ok(0())
 proper(length1(X)) -> length1(proper(X))
 from(ok(X)) -> ok(from(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 s(ok(X)) -> ok(s(X))
 length(ok(X)) -> ok(length(X))
 length1(ok(X)) -> ok(length1(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                [1 1]  
   [mark](x0) = [0 0]x0,
   
                   [1 0]     [0]
   [length1](x0) = [2 0]x0 + [2],
   
                  [2 1]  
   [active](x0) = [0 0]x0,
   
                         [1 0]  
   [cons](x0, x1) = x0 + [0 0]x1,
   
           [0]
   [nil] = [0],
   
              [2 0]  
   [ok](x0) = [0 1]x0,
   
                  
   [from](x0) = x0,
   
         [0]
   [0] = [0],
   
               [1 1]     [0]
   [top](x0) = [0 0]x0 + [2],
   
                    
   [proper](x0) = x0,
   
                  [2 0]     [0]
   [length](x0) = [0 0]x0 + [2],
   
               
   [s](x0) = x0
  orientation:
                     [2 1]     [2 1]                            
   active(from(X)) = [0 0]X >= [0 0]X = mark(cons(X,from(s(X))))
   
                           [2]    [0]            
   active(length(nil())) = [0] >= [0] = mark(0())
   
                               [4 0]    [4 0]    [2]    [3 0]    [2]                      
   active(length(cons(X,Y))) = [0 0]X + [0 0]Y + [0] >= [0 0]Y + [0] = mark(s(length1(Y)))
   
                        [4 0]    [2]    [2 0]    [2]                  
   active(length1(X)) = [0 0]X + [0] >= [0 0]X + [0] = mark(length(X))
   
                     [2 1]     [2 1]                   
   active(from(X)) = [0 0]X >= [0 0]X = from(active(X))
   
                         [2 1]     [2 0]      [2 1]     [1 0]                        
   active(cons(X1,X2)) = [0 0]X1 + [0 0]X2 >= [0 0]X1 + [0 0]X2 = cons(active(X1),X2)
   
                  [2 1]     [2 1]                
   active(s(X)) = [0 0]X >= [0 0]X = s(active(X))
   
                   [1 1]     [1 1]                 
   from(mark(X)) = [0 0]X >= [0 0]X = mark(from(X))
   
                       [1 1]     [1 0]      [1 1]     [1 0]                      
   cons(mark(X1),X2) = [0 0]X1 + [0 0]X2 >= [0 0]X1 + [0 0]X2 = mark(cons(X1,X2))
   
                [1 1]     [1 1]              
   s(mark(X)) = [0 0]X >= [0 0]X = mark(s(X))
   
                                             
   proper(from(X)) = X >= X = from(proper(X))

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