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TRS Standard pair #516968188
details
property
value
status
complete
benchmark
t001.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n035.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
NaTT 2.1
configuration
default
runtime (wallclock)
0.150701999664 seconds
cpu usage
0.098512198
max memory
1.3299712E7
stage attributes
key
value
output-size
5510
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: -(x,0()) -> x 2: -(s(x),s(y)) -> -(x,y) 3: *(x,0()) -> 0() 4: *(x,s(y)) -> +(*(x,y),x) 5: if(true(),x,y) -> x 6: if(false(),x,y) -> y 7: odd(0()) -> false() 8: odd(s(0())) -> true() 9: odd(s(s(x))) -> odd(x) 10: half(0()) -> 0() 11: half(s(0())) -> 0() 12: half(s(s(x))) -> s(half(x)) 13: if(true(),x,y) -> true() 14: if(false(),x,y) -> false() 15: pow(x,y) -> f(x,y,s(0())) 16: f(x,0(),z) -> z 17: f(x,s(y),z) -> if(odd(s(y)),f(x,y,*(x,z)),f(*(x,x),half(s(y)),z)) Number of strict rules: 17 Direct poly ... failed. Freezing half odd 1: -(x,0()) -> x 2: -(s(x),s(y)) -> -(x,y) 3: *(x,0()) -> 0() 4: *(x,s(y)) -> +(*(x,y),x) 5: if(true(),x,y) -> x 6: if(false(),x,y) -> y 7: odd❆1_0() -> false() 8: odd❆1_s(0()) -> true() 9: odd❆1_s(s(x)) -> odd(x) 10: half❆1_0() -> 0() 11: half❆1_s(0()) -> 0() 12: half❆1_s(s(x)) -> s(half(x)) 13: if(true(),x,y) -> true() 14: if(false(),x,y) -> false() 15: pow(x,y) -> f(x,y,s(0())) 16: f(x,0(),z) -> z 17: f(x,s(y),z) -> if(odd❆1_s(y),f(x,y,*(x,z)),f(*(x,x),half❆1_s(y),z)) 18: odd(0()) ->= odd❆1_0() 19: odd(s(_1)) ->= odd❆1_s(_1) 20: half(0()) ->= half❆1_0() 21: half(s(_1)) ->= half❆1_s(_1) Number of strict rules: 17 Direct poly ... failed. Dependency Pairs: #1: #-(s(x),s(y)) -> #-(x,y) #2: #odd❆1_s(s(x)) -> #odd(x) #3: #half❆1_s(s(x)) -> #half(x) #4: #half(0()) ->? #half❆1_0() #5: #f(x,s(y),z) -> #if(odd❆1_s(y),f(x,y,*(x,z)),f(*(x,x),half❆1_s(y),z)) #6: #f(x,s(y),z) -> #odd❆1_s(y) #7: #f(x,s(y),z) -> #f(x,y,*(x,z)) #8: #f(x,s(y),z) -> #*(x,z) #9: #f(x,s(y),z) -> #f(*(x,x),half❆1_s(y),z) #10: #f(x,s(y),z) -> #*(x,x) #11: #f(x,s(y),z) -> #half❆1_s(y) #12: #odd(s(_1)) ->? #odd❆1_s(_1) #13: #half(s(_1)) ->? #half❆1_s(_1) #14: #pow(x,y) -> #f(x,y,s(0())) #15: #*(x,s(y)) -> #*(x,y) #16: #odd(0()) ->? #odd❆1_0() Number of SCCs: 5, DPs: 8 SCC { #15 } Sum... succeeded. #odd❆1_0() w: (0) s(x1) w: (1 + x1) #half❆1_s(x1) w: (0) pow(x1,x2) w: (0) false() w: (0) #*(x1,x2) w: (x2) #half(x1) w: (0) true() w: (0) #pow(x1,x2) w: (0) f(x1,x2,x3) w: (0) #half❆1_0() w: (0) half(x1) w: (0) half❆1_s(x1) w: (0) 0() w: (0) if(x1,x2,x3) w: (0) odd❆1_s(x1) w: (0) -(x1,x2) w: (0) #f(x1,x2,x3) w: (0) #odd(x1) w: (0) #odd❆1_s(x1) w: (0) odd(x1) w: (0) #-(x1,x2) w: (0) odd❆1_0() w: (0) #if(x1,x2,x3) w: (0) +(x1,x2) w: (0) half❆1_0() w: (0) *(x1,x2) w: (0) USABLE RULES: { } Removed DPs: #15
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