Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307643
details
property
value
status
complete
benchmark
big.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n094.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.43143 seconds
cpu usage
4.10979
user time
3.94988
system time
0.159906
max virtual memory
1.8277336E7
max residence set size
296064.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
3.83/1.73 WORST_CASE(NON_POLY, ?) 3.83/1.74 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 3.83/1.74 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.83/1.74 3.83/1.74 3.83/1.74 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 3.83/1.74 3.83/1.74 (0) CpxTRS 3.83/1.74 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 3.83/1.74 (2) TRS for Loop Detection 3.83/1.74 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 3.83/1.74 (4) BEST 3.83/1.74 (5) proven lower bound 3.83/1.74 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 3.83/1.74 (7) BOUNDS(n^1, INF) 3.83/1.74 (8) TRS for Loop Detection 3.83/1.74 (9) DecreasingLoopProof [FINISHED, 128 ms] 3.83/1.74 (10) BOUNDS(EXP, INF) 3.83/1.74 3.83/1.74 3.83/1.74 ---------------------------------------- 3.83/1.74 3.83/1.74 (0) 3.83/1.74 Obligation: 3.83/1.74 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 3.83/1.74 3.83/1.74 3.83/1.74 The TRS R consists of the following rules: 3.83/1.74 3.83/1.74 0(#) -> # 3.83/1.74 +(x, #) -> x 3.83/1.74 +(#, x) -> x 3.83/1.74 +(0(x), 0(y)) -> 0(+(x, y)) 3.83/1.74 +(0(x), 1(y)) -> 1(+(x, y)) 3.83/1.74 +(1(x), 0(y)) -> 1(+(x, y)) 3.83/1.74 +(1(x), 1(y)) -> 0(+(+(x, y), 1(#))) 3.83/1.74 +(+(x, y), z) -> +(x, +(y, z)) 3.83/1.74 -(#, x) -> # 3.83/1.74 -(x, #) -> x 3.83/1.74 -(0(x), 0(y)) -> 0(-(x, y)) 3.83/1.74 -(0(x), 1(y)) -> 1(-(-(x, y), 1(#))) 3.83/1.74 -(1(x), 0(y)) -> 1(-(x, y)) 3.83/1.74 -(1(x), 1(y)) -> 0(-(x, y)) 3.83/1.74 not(true) -> false 3.83/1.74 not(false) -> true 3.83/1.74 if(true, x, y) -> x 3.83/1.74 if(false, x, y) -> y 3.83/1.74 eq(#, #) -> true 3.83/1.74 eq(#, 1(y)) -> false 3.83/1.74 eq(1(x), #) -> false 3.83/1.74 eq(#, 0(y)) -> eq(#, y) 3.83/1.74 eq(0(x), #) -> eq(x, #) 3.83/1.74 eq(1(x), 1(y)) -> eq(x, y) 3.83/1.74 eq(0(x), 1(y)) -> false 3.83/1.74 eq(1(x), 0(y)) -> false 3.83/1.74 eq(0(x), 0(y)) -> eq(x, y) 3.83/1.74 ge(0(x), 0(y)) -> ge(x, y) 3.83/1.74 ge(0(x), 1(y)) -> not(ge(y, x)) 3.83/1.74 ge(1(x), 0(y)) -> ge(x, y) 3.83/1.74 ge(1(x), 1(y)) -> ge(x, y) 3.83/1.74 ge(x, #) -> true 3.83/1.74 ge(#, 0(x)) -> ge(#, x) 3.83/1.74 ge(#, 1(x)) -> false 3.83/1.74 log(x) -> -(log'(x), 1(#)) 3.83/1.74 log'(#) -> # 3.83/1.74 log'(1(x)) -> +(log'(x), 1(#)) 3.83/1.74 log'(0(x)) -> if(ge(x, 1(#)), +(log'(x), 1(#)), #) 3.83/1.74 *(#, x) -> # 3.83/1.74 *(0(x), y) -> 0(*(x, y)) 3.83/1.74 *(1(x), y) -> +(0(*(x, y)), y) 3.83/1.74 *(*(x, y), z) -> *(x, *(y, z)) 3.83/1.74 *(x, +(y, z)) -> +(*(x, y), *(x, z)) 3.83/1.74 app(nil, l) -> l 3.83/1.74 app(cons(x, l1), l2) -> cons(x, app(l1, l2)) 3.83/1.74 sum(nil) -> 0(#) 3.83/1.74 sum(cons(x, l)) -> +(x, sum(l)) 3.83/1.74 sum(app(l1, l2)) -> +(sum(l1), sum(l2)) 3.83/1.74 prod(nil) -> 1(#) 3.83/1.74 prod(cons(x, l)) -> *(x, prod(l)) 3.83/1.74 prod(app(l1, l2)) -> *(prod(l1), prod(l2)) 3.83/1.74 mem(x, nil) -> false 3.83/1.74 mem(x, cons(y, l)) -> if(eq(x, y), true, mem(x, l)) 3.83/1.74 inter(x, nil) -> nil 3.83/1.74 inter(nil, x) -> nil 3.83/1.74 inter(app(l1, l2), l3) -> app(inter(l1, l3), inter(l2, l3)) 3.83/1.74 inter(l1, app(l2, l3)) -> app(inter(l1, l2), inter(l1, l3)) 3.83/1.74 inter(cons(x, l1), l2) -> ifinter(mem(x, l2), x, l1, l2) 3.83/1.74 inter(l1, cons(x, l2)) -> ifinter(mem(x, l1), x, l2, l1) 3.83/1.74 ifinter(true, x, l1, l2) -> cons(x, inter(l1, l2)) 3.83/1.74 ifinter(false, x, l1, l2) -> inter(l1, l2) 3.83/1.74 3.83/1.74 S is empty. 3.83/1.74 Rewrite Strategy: FULL 3.83/1.74 ---------------------------------------- 3.83/1.74 3.83/1.74 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 3.83/1.74 Transformed a relative TRS into a decreasing-loop problem. 3.83/1.74 ---------------------------------------- 3.83/1.74 3.83/1.74 (2)
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11