TRS Standard pair #615301586

details

property	value
status	complete
benchmark	Ex6_Luc98_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n005.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	2.08521008492 seconds
cpu usage	6.649245668
max memory	4.09325568E8

stage attributes

key	value
output-size	20639
starexec-result	"YES"

output

/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

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

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

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