Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime Complexity: TRS Innermost pair #487111898
details
property
value
status
complete
benchmark
fgh.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n147.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.61985 seconds
cpu usage
3.65168
user time
3.49797
system time
0.153717
max virtual memory
1.827736E7
max residence set size
247892.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection (9) DecreasingLoopProof [FINISHED, 0 ms] (10) BOUNDS(EXP, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: f(S(x'), S(x)) -> h(g(x', S(x)), f(S(S(S(x'))), x)) g(S(x), S(x')) -> h(f(S(x), S(x')), g(x, S(S(S(x'))))) h(0, S(x)) -> h(0, x) h(0, 0) -> 0 g(S(x), 0) -> 0 f(S(x), 0) -> 0 h(S(x), x2) -> h(x, x2) g(0, x2) -> 0 f(0, x2) -> 0 S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: f(S(x'), S(x)) -> h(g(x', S(x)), f(S(S(S(x'))), x)) g(S(x), S(x')) -> h(f(S(x), S(x')), g(x, S(S(S(x'))))) h(0, S(x)) -> h(0, x) h(0, 0) -> 0 g(S(x), 0) -> 0 f(S(x), 0) -> 0 h(S(x), x2) -> h(x, x2) g(0, x2) -> 0 f(0, x2) -> 0 S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence f(S(x'), S(x)) ->^+ h(g(x', S(x)), f(S(S(S(x'))), x)) gives rise to a decreasing loop by considering the right hand sides subterm at position [1]. The pumping substitution is [x / S(x)]. The result substitution is [x' / S(S(x'))]. ---------------------------------------- (4) Complex Obligation (BEST) ---------------------------------------- (5) Obligation: Proved the lower bound n^1 for the following obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime Complexity: TRS Innermost