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TRS Standard pair #487073876
details
property
value
status
complete
benchmark
aprove1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n182.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
NaTT v.1.6c
configuration
Default
runtime (wallclock)
0.137994 seconds
cpu usage
0.05924
user time
0.025553
system time
0.033687
max virtual memory
113188.0
max residence set size
9312.0
stage attributes
key
value
starexec-result
YES
output
YES Input TRS: 1: ap(ap(map(),f),xs) -> ap(ap(ap(if(),ap(isEmpty(),xs)),f),xs) 2: ap(ap(ap(if(),true()),f),xs) -> null() 3: ap(ap(ap(if(),null()),f),xs) -> ap(ap(cons(),ap(f,ap(last(),xs))),ap(ap(if2(),f),xs)) 4: ap(ap(if2(),f),xs) -> ap(ap(map(),f),ap(dropLast(),xs)) 5: ap(isEmpty(),null()) -> true() 6: ap(isEmpty(),ap(ap(cons(),x),xs)) -> null() 7: ap(last(),ap(ap(cons(),x),null())) -> x 8: ap(last(),ap(ap(cons(),x),ap(ap(cons(),y),ys))) -> ap(last(),ap(ap(cons(),y),ys)) 9: ap(dropLast(),ap(ap(cons(),x),null())) -> null() 10: ap(dropLast(),ap(ap(cons(),x),ap(ap(cons(),y),ys))) -> ap(ap(cons(),x),ap(dropLast(),ap(ap(cons(),y),ys))) Number of strict rules: 10 Direct POLO(bPol) ... failed. Uncurrying ap^1_last ap 1: ap^2_map(f,xs) -> ap^3_if(ap^1_isEmpty(xs),f,xs) 2: ap^3_if(true(),f,xs) -> null() 3: ap^3_if(null(),f,xs) -> ap^2_cons(ap(f,ap^1_last(xs)),ap^2_if2(f,xs)) 4: ap^2_if2(f,xs) -> ap^2_map(f,ap^1_dropLast(xs)) 5: ap^1_isEmpty(null()) -> true() 6: ap^1_isEmpty(ap^2_cons(x,xs)) -> null() 7: ap^1_last^1_ap^2_cons(x,null()) -> x 8: ap^1_last^1_ap^2_cons(x,ap^2_cons(y,ys)) -> ap^1_last^1_ap^2_cons(y,ys) 9: ap^1_dropLast(ap^2_cons(x,null())) -> null() 10: ap^1_dropLast(ap^2_cons(x,ap^2_cons(y,ys))) -> ap^2_cons(x,ap^1_dropLast(ap^2_cons(y,ys))) 11: ap(if2(),_1) ->= ap^1_if2(_1) 12: ap(ap^1_if2(_1),_2) ->= ap^2_if2(_1,_2) 13: ap(if(),_1) ->= ap^1_if(_1) 14: ap(ap^1_if(_1),_2) ->= ap^2_if(_1,_2) 15: ap(ap^2_if(_1,_2),_3) ->= ap^3_if(_1,_2,_3) 16: ap(cons(),_1) ->= ap^1_cons(_1) 17: ap(ap^1_cons(_1),_2) ->= ap^2_cons(_1,_2) 18: ap(isEmpty(),_1) ->= ap^1_isEmpty(_1) 19: ap(dropLast(),_1) ->= ap^1_dropLast(_1) 20: ap(last(),_1) ->= ap^1_last(_1) 21: ap(map(),_1) ->= ap^1_map(_1) 22: ap(ap^1_map(_1),_2) ->= ap^2_map(_1,_2) 23: ap^1_last(ap^2_cons(_1,_2)) ->= ap^1_last^1_ap^2_cons(_1,_2) Number of strict rules: 10 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #ap^1_last(ap^2_cons(_1,_2)) ->? #ap^1_last^1_ap^2_cons(_1,_2) #2: #ap(ap^1_if2(_1),_2) ->? #ap^2_if2(_1,_2) #3: #ap(last(),_1) ->? #ap^1_last(_1) #4: #ap^1_dropLast(ap^2_cons(x,ap^2_cons(y,ys))) -> #ap^1_dropLast(ap^2_cons(y,ys)) #5: #ap(ap^1_map(_1),_2) ->? #ap^2_map(_1,_2) #6: #ap(dropLast(),_1) ->? #ap^1_dropLast(_1) #7: #ap^3_if(null(),f,xs) -> #ap(f,ap^1_last(xs)) #8: #ap^3_if(null(),f,xs) -> #ap^1_last(xs) #9: #ap^3_if(null(),f,xs) -> #ap^2_if2(f,xs) #10: #ap^2_map(f,xs) -> #ap^3_if(ap^1_isEmpty(xs),f,xs) #11: #ap^2_map(f,xs) -> #ap^1_isEmpty(xs) #12: #ap^1_last^1_ap^2_cons(x,ap^2_cons(y,ys)) -> #ap^1_last^1_ap^2_cons(y,ys) #13: #ap(ap^2_if(_1,_2),_3) ->? #ap^3_if(_1,_2,_3) #14: #ap^2_if2(f,xs) -> #ap^2_map(f,ap^1_dropLast(xs)) #15: #ap^2_if2(f,xs) -> #ap^1_dropLast(xs) #16: #ap(isEmpty(),_1) ->? #ap^1_isEmpty(_1) Number of SCCs: 3, DPs: 9 SCC { #12 } POLO(Sum)... succeeded. ap^2_if w: 0 #ap^1_last w: 0 ap^2_map w: 0 ap^1_last w: 0 ap^1_last^1_ap^2_cons w: 0 ap^2_cons w: x2 + 1 ap^1_isEmpty w: 0 ap w: 0 isEmpty w: 0 ap^1_map w: 0 #ap^1_last^1_ap^2_cons w: x2 true w: 0 #ap^3_if w: 0 if2 w: 0 if w: 0 #ap^2_if2 w: 0 #ap^2_map w: 0 null w: 0 dropLast w: 0 last w: 0 map w: 0 #ap^1_dropLast w: 0 #ap w: 0 ap^1_dropLast w: 0 ap^2_if2 w: 0 cons w: 0 ap^3_if w: 0 ap^1_cons w: 0 ap^1_if w: 0 #ap^1_isEmpty w: 0 ap^1_if2 w: 0 USABLE RULES: { } Removed DPs: #12 Number of SCCs: 2, DPs: 8 SCC { #4 } POLO(Sum)... succeeded. ap^2_if w: 0 #ap^1_last w: 0 ap^2_map w: 0 ap^1_last w: 0
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