details

property	value
status	complete
benchmark	wiehe01.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n175.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	NaTT v.1.6c
configuration	Default
runtime (wallclock)	0.104611 seconds
cpu usage	0.037486
user time	0.018968
system time	0.018518
max virtual memory	113188.0
max residence set size	7024.0

stage attributes

key	value
starexec-result	YES

output

YES Input TRS: 1: times(x,0()) -> 0() 2: times(x,s(y)) -> plus(times(x,y),x) 3: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) 4: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x)) 5: plus(zero(),y) -> y 6: plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y)))) 7: id(x) -> x 8: if(true(),x,y) -> x 9: if(false(),x,y) -> y 10: not(x) -> if(x,false(),true()) 11: gt(s(x),zero()) -> true() 12: gt(zero(),y) -> false() 13: gt(s(x),s(y)) -> gt(x,y) Number of strict rules: 13 Direct POLO(bPol) ... failed. Uncurrying gt 1: times(x,0()) -> 0() 2: times(x,s(y)) -> plus(times(x,y),x) 3: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) 4: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x)) 5: plus(zero(),y) -> y 6: plus(id(x),s(y)) -> s(plus(x,if(gt^1_s(y,y),y,s(y)))) 7: id(x) -> x 8: if(true(),x,y) -> x 9: if(false(),x,y) -> y 10: not(x) -> if(x,false(),true()) 11: gt^1_s(x,zero()) -> true() 12: gt^1_zero(y) -> false() 13: gt^1_s(x,s(y)) -> gt(x,y) 14: gt(zero(),_1) ->= gt^1_zero(_1) 15: gt(s(_1),_2) ->= gt^1_s(_1,_2) Number of strict rules: 13 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #times(x,s(y)) -> #plus(times(x,y),x) #2: #times(x,s(y)) -> #times(x,y) #3: #plus(id(x),s(y)) -> #plus(x,if(gt^1_s(y,y),y,s(y))) #4: #plus(id(x),s(y)) -> #if(gt^1_s(y,y),y,s(y)) #5: #plus(id(x),s(y)) -> #gt^1_s(y,y) #6: #gt^1_s(x,s(y)) -> #gt(x,y) #7: #gt(zero(),_1) ->? #gt^1_zero(_1) #8: #not(x) -> #if(x,false(),true()) #9: #plus(s(x),s(y)) -> #plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))) #10: #plus(s(x),s(y)) -> #if(gt(x,y),x,y) #11: #plus(s(x),s(y)) -> #gt(x,y) #12: #plus(s(x),s(y)) -> #if(not(gt(x,y)),id(x),id(y)) #13: #plus(s(x),s(y)) -> #not(gt(x,y)) #14: #plus(s(x),s(y)) -> #gt(x,y) #15: #plus(s(x),s(y)) -> #id(x) #16: #plus(s(x),s(y)) -> #id(y) #17: #gt(s(_1),_2) ->? #gt^1_s(_1,_2) #18: #plus(s(x),x) -> #plus(if(gt(x,x),id(x),id(x)),s(x)) #19: #plus(s(x),x) -> #if(gt(x,x),id(x),id(x)) #20: #plus(s(x),x) -> #gt(x,x) #21: #plus(s(x),x) -> #id(x) #22: #plus(s(x),x) -> #id(x) Number of SCCs: 3, DPs: 6 SCC { #2 } POLO(Sum)... succeeded. zero w: 0 s w: x1 + 1 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 #not w: 0 #times w: x2 0 w: 0 if w: 0 times w: 0 #gt w: 0 plus w: 0 gt^1_s w: 0 #if w: 0 id w: 0 #gt^1_s w: 0 not w: 0 USABLE RULES: { } Removed DPs: #2 Number of SCCs: 2, DPs: 5 SCC { #6 #17 } POLO(Sum)... succeeded. zero w: 0 s w: x1 + 2 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 #not w: 0 #times w: 0 0 w: 0 if w: 0 popout

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all output return to TRS Standard