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TRS Standard pair #487073111
details
property
value
status
complete
benchmark
wiehe02.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n187.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
NaTT v.1.6c
configuration
Default
runtime (wallclock)
0.242484 seconds
cpu usage
0.052366
user time
0.027825
system time
0.024541
max virtual memory
113188.0
max residence set size
9288.0
stage attributes
key
value
starexec-result
YES
output
YES Input TRS: 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: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) 8: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x)) 9: plus(zero(),y) -> y 10: plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y)))) 11: id(x) -> x 12: if(true(),x,y) -> x 13: if(false(),x,y) -> y 14: not(x) -> if(x,false(),true()) 15: gt(s(x),zero()) -> true() 16: gt(zero(),y) -> false() 17: gt(s(x),s(y)) -> gt(x,y) Number of strict rules: 17 Direct POLO(bPol) ... failed. Uncurrying gt 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: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) 8: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x)) 9: plus(zero(),y) -> y 10: plus(id(x),s(y)) -> s(plus(x,if(gt^1_s(y,y),y,s(y)))) 11: id(x) -> x 12: if(true(),x,y) -> x 13: if(false(),x,y) -> y 14: not(x) -> if(x,false(),true()) 15: gt^1_s(x,zero()) -> true() 16: gt^1_zero(y) -> false() 17: gt^1_s(x,s(y)) -> gt(x,y) 18: gt(zero(),_1) ->= gt^1_zero(_1) 19: gt(s(_1),_2) ->= gt^1_s(_1,_2) Number of strict rules: 17 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #sum(app(l,cons(x,cons(y,k)))) -> #sum(app(l,sum(cons(x,cons(y,k))))) #2: #sum(app(l,cons(x,cons(y,k)))) -> #app(l,sum(cons(x,cons(y,k)))) #3: #sum(app(l,cons(x,cons(y,k)))) -> #sum(cons(x,cons(y,k))) #4: #not(x) -> #if(x,false(),true()) #5: #plus(s(x),s(y)) -> #plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))) #6: #plus(s(x),s(y)) -> #if(gt(x,y),x,y) #7: #plus(s(x),s(y)) -> #gt(x,y) #8: #plus(s(x),s(y)) -> #if(not(gt(x,y)),id(x),id(y)) #9: #plus(s(x),s(y)) -> #not(gt(x,y)) #10: #plus(s(x),s(y)) -> #gt(x,y) #11: #plus(s(x),s(y)) -> #id(x) #12: #plus(s(x),s(y)) -> #id(y) #13: #plus(id(x),s(y)) -> #plus(x,if(gt^1_s(y,y),y,s(y))) #14: #plus(id(x),s(y)) -> #if(gt^1_s(y,y),y,s(y)) #15: #plus(id(x),s(y)) -> #gt^1_s(y,y) #16: #sum(cons(x,cons(y,l))) -> #sum(cons(plus(x,y),l)) #17: #sum(cons(x,cons(y,l))) -> #plus(x,y) #18: #gt^1_s(x,s(y)) -> #gt(x,y) #19: #gt(s(_1),_2) ->? #gt^1_s(_1,_2) #20: #app(cons(x,l),k) -> #app(l,k) #21: #plus(s(x),x) -> #plus(if(gt(x,x),id(x),id(x)),s(x)) #22: #plus(s(x),x) -> #if(gt(x,x),id(x),id(x)) #23: #plus(s(x),x) -> #gt(x,x) #24: #plus(s(x),x) -> #id(x) #25: #plus(s(x),x) -> #id(x) #26: #gt(zero(),_1) ->? #gt^1_zero(_1) Number of SCCs: 5, DPs: 8 SCC { #20 } POLO(Sum)... succeeded. zero w: 0 s w: 0 gt w: 0 #gt^1_zero w: 0 #plus w: 0 false w: 0 #id w: 0 gt^1_zero w: 0 true w: 0 sum w: 0 #not w: 0 if w: 0 nil w: 0 #gt w: 0 #app w: x1 plus w: 0 cons w: x2 + 1 gt^1_s w: 0 #if w: 0 id w: 0 #sum w: 0 #gt^1_s w: 0 not w: 0 app w: 0 USABLE RULES: { } Removed DPs: #20 Number of SCCs: 4, DPs: 7
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