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TRS Equat 89423 pair #381732634
details
property
value
status
complete
benchmark
AC50.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n107.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
NaTT
configuration
Default
runtime (wallclock)
0.0730400085449 seconds
cpu usage
0.080308548
max memory
1.118208E7
stage attributes
key
value
output-size
3035
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: AC symbols: plus 1: app(nil(),k) -> k 2: app(l,nil()) -> l 3: app(cons(x,l),k) -> cons(x,app(l,k)) 4: sum(cons(x,nil())) -> cons(x,nil()) 5: sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) 6: sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) 7: sum(cons(0(),cons(plus(x,y),l))) -> pred(sum(cons(s(x),cons(y,l)))) 8: plus(0(),y) -> y 9: plus(s(x),y) -> s(plus(x,y)) 10: pred(cons(s(x),nil())) -> cons(x,nil()) Number of strict rules: 10 Direct POLO(bPol) ... removes: 8 1 3 5 10 7 2 s w: x1 + 1 pred w: x1 + 1 sum w: x1 0 w: 1 nil w: 1 plus w: x1 + x2 + 1 cons w: 2 * x1 + x2 + 3 app w: 2 * x1 + 2 * x2 + 1 Number of strict rules: 3 Direct POLO(bPol) ... failed. Uncurrying sum AC symbols: plus 4: sum^1_cons(x,nil()) -> cons(x,nil()) 6: sum^1_app(l,cons(x,cons(y,k))) -> sum^1_app(l,sum^1_cons(x,cons(y,k))) 9: plus(s(x),y) -> s(plus(x,y)) 11: sum(cons(_1,_2)) ->= sum^1_cons(_1,_2) 12: sum(app(_1,_2)) ->= sum^1_app(_1,_2) Number of strict rules: 3 Direct POLO(bPol) ... removes: 12 11 sum^1_app w: x1 + x2 s w: x1 sum^1_cons w: x1 + x2 + 1 pred w: x1 sum w: 2 * x1 + 1 0 w: 0 nil w: 1 plus w: x1 + x2 + 1 cons w: x1 + x2 + 1 app w: 2 * x1 + x2 + 1 Number of strict rules: 3 Direct POLO(bPol) ... removes: 4 6 sum^1_app w: x1 + x2 s w: x1 sum^1_cons w: x1 + x2 + 5 pred w: x1 sum w: 2 * x1 + 1 0 w: 0 nil w: 1 plus w: x1 + x2 + 1 cons w: x1 + 2 * x2 + 3 app w: 2 * x1 + x2 + 1 Number of strict rules: 1 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) #2: #plus(x,plus(y,z)) ->= #plus(x,y) #3: #plus(s(x),y) -> #plus(x,y) Number of SCCs: 1, DPs: 3 SCC { #1..3 } POLO(Sum)... succeeded. sum^1_app w: 0 s w: x1 + 1 sum^1_cons w: 0 #plus w: x1 + x2 pred w: 0 sum w: 0 0 w: 0 nil w: 0 plus w: x1 + x2 + 1 cons w: 0 app w: 0 USABLE RULES: { 9 13 } Removed DPs: #2 #3 Number of SCCs: 1, DPs: 1 SCC { #1 } only weak rules. Number of SCCs: 0, DPs: 0 Next Dependency Pairs: #4: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) #5: #plus(x,plus(y,z)) ->= #plus(x,y) #6: #plus(plus(s(x),y),_1) -> #plus(s(plus(x,y)),_1) Number of SCCs: 1, DPs: 3 SCC { #4..6 } POLO(Sum)... succeeded. sum^1_app w: 0 s w: 1 sum^1_cons w: 0 #plus w: x1 + x2 pred w: 0
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