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TRS Standard pair #516967164
details
property
value
status
complete
benchmark
#3.17a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n092.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
1.05291008949 seconds
cpu usage
2.800343776
max memory
3.73137408E8
stage attributes
key
value
output-size
7094
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: app(nil(),k) -> k app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) sum(plus(cons(0(),x),cons(y,l))) -> pred(sum(cons(s(x),cons(y,l)))) pred(cons(s(x),nil())) -> cons(x,nil()) Proof: Matrix Interpretation Processor: dim=1 interpretation: [plus](x0, x1) = x0 + x1 + 2, [app](x0, x1) = 2x0 + x1 + 2, [sum](x0) = x0, [0] = 6, [nil] = 0, [pred](x0) = x0 + 1, [s](x0) = x0 + 6, [cons](x0, x1) = x0 + x1 + 2 orientation: app(nil(),k) = k + 2 >= k = k app(l,nil()) = 2l + 2 >= l = l app(cons(x,l),k) = k + 2l + 2x + 6 >= k + 2l + x + 4 = cons(x,app(l,k)) sum(cons(x,nil())) = x + 2 >= x + 2 = cons(x,nil()) sum(cons(x,cons(y,l))) = l + x + y + 4 >= l + x + y + 4 = sum(cons(plus(x,y),l)) sum(app(l,cons(x,cons(y,k)))) = k + 2l + x + y + 6 >= k + 2l + x + y + 6 = sum(app(l,sum(cons(x,cons(y,k))))) plus(0(),y) = y + 8 >= y = y plus(s(x),y) = x + y + 8 >= x + y + 8 = s(plus(x,y)) sum(plus(cons(0(),x),cons(y,l))) = l + x + y + 12 >= l + x + y + 11 = pred(sum(cons(s(x),cons(y,l)))) pred(cons(s(x),nil())) = x + 9 >= x + 2 = cons(x,nil()) problem: sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) plus(s(x),y) -> s(plus(x,y)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [plus](x0, x1) = [0 1 0]x0 + [1 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [app](x0, x1) = [0 1 0]x0 + [0 0 1]x1 [0 0 0] [1 0 0] , [sum](x0) = x0 , [0] [nil] = [0] [0], [1 0 0] [s](x0) = [1 0 1]x0 [0 0 0] , [1 0 1] [1 0 1] [0] [cons](x0, x1) = [1 0 0]x0 + [0 1 0]x1 + [0] [0 1 0] [0 1 0] [1] orientation: [1 0 1] [0] [1 0 1] [0] sum(cons(x,nil())) = [1 0 0]x + [0] >= [1 0 0]x + [0] = cons(x,nil()) [0 1 0] [1] [0 1 0] [1] [1 1 1] [1 0 1] [1 1 1] [1] [1 0 1] [1 0 0] [1 0 0] [0] sum(cons(x,cons(y,l))) = [0 1 0]l + [1 0 0]x + [1 0 0]y + [0] >= [0 1 0]l + [1 0 0]x + [1 0 0]y + [0] = sum(cons(plus(x,y),l)) [0 1 0] [0 1 0] [1 0 0] [1] [0 1 0] [0 1 0] [1 0 0] [1] [1 1 1] [1 0 0] [1 0 1] [1 1 1] [1] [1 1 1] [1 0 0] [1 0 1] [1 1 1] [1]
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