Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313752
details
property
value
status
complete
benchmark
#3.47.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n119.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.0542 seconds
cpu usage
16.37
user time
15.2535
system time
1.1165
max virtual memory
1.8940616E7
max residence set size
3616128.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
15.98/4.99 WORST_CASE(Omega(n^1), O(n^1)) 15.98/5.00 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 15.98/5.00 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.98/5.00 15.98/5.00 15.98/5.00 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 15.98/5.00 15.98/5.00 (0) CpxTRS 15.98/5.00 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 15.98/5.00 (2) CdtProblem 15.98/5.00 (3) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 50 ms] 15.98/5.00 (4) CdtProblem 15.98/5.00 (5) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] 15.98/5.00 (6) CdtProblem 15.98/5.00 (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 15.98/5.00 (8) CdtProblem 15.98/5.00 (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 15.98/5.00 (10) CdtProblem 15.98/5.00 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 4 ms] 15.98/5.00 (12) CdtProblem 15.98/5.00 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 15.98/5.00 (14) BOUNDS(1, 1) 15.98/5.00 (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 15.98/5.00 (16) TRS for Loop Detection 15.98/5.00 (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 15.98/5.00 (18) BEST 15.98/5.00 (19) proven lower bound 15.98/5.00 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 15.98/5.00 (21) BOUNDS(n^1, INF) 15.98/5.00 (22) TRS for Loop Detection 15.98/5.00 15.98/5.00 15.98/5.00 ---------------------------------------- 15.98/5.00 15.98/5.00 (0) 15.98/5.00 Obligation: 15.98/5.00 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 15.98/5.00 15.98/5.00 15.98/5.00 The TRS R consists of the following rules: 15.98/5.00 15.98/5.00 f(x, c(y)) -> f(x, s(f(y, y))) 15.98/5.00 f(s(x), y) -> f(x, s(c(y))) 15.98/5.00 15.98/5.00 S is empty. 15.98/5.00 Rewrite Strategy: INNERMOST 15.98/5.00 ---------------------------------------- 15.98/5.00 15.98/5.00 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 15.98/5.00 Converted Cpx (relative) TRS to CDT 15.98/5.00 ---------------------------------------- 15.98/5.00 15.98/5.00 (2) 15.98/5.00 Obligation: 15.98/5.00 Complexity Dependency Tuples Problem 15.98/5.00 15.98/5.00 Rules: 15.98/5.00 f(z0, c(z1)) -> f(z0, s(f(z1, z1))) 15.98/5.00 f(s(z0), z1) -> f(z0, s(c(z1))) 15.98/5.00 Tuples: 15.98/5.00 F(z0, c(z1)) -> c1(F(z0, s(f(z1, z1))), F(z1, z1)) 15.98/5.00 F(s(z0), z1) -> c2(F(z0, s(c(z1)))) 15.98/5.00 S tuples: 15.98/5.00 F(z0, c(z1)) -> c1(F(z0, s(f(z1, z1))), F(z1, z1)) 15.98/5.00 F(s(z0), z1) -> c2(F(z0, s(c(z1)))) 15.98/5.00 K tuples:none 15.98/5.00 Defined Rule Symbols: f_2 15.98/5.00 15.98/5.00 Defined Pair Symbols: F_2 15.98/5.00 15.98/5.00 Compound Symbols: c1_2, c2_1 15.98/5.00 15.98/5.00 15.98/5.00 ---------------------------------------- 15.98/5.00 15.98/5.00 (3) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) 15.98/5.00 Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. 15.98/5.00 F(z0, c(z1)) -> c1(F(z0, s(f(z1, z1))), F(z1, z1)) 15.98/5.00 We considered the (Usable) Rules:none 15.98/5.00 And the Tuples: 15.98/5.00 F(z0, c(z1)) -> c1(F(z0, s(f(z1, z1))), F(z1, z1)) 15.98/5.00 F(s(z0), z1) -> c2(F(z0, s(c(z1)))) 15.98/5.00 The order we found is given by the following interpretation: 15.98/5.00 15.98/5.00 Polynomial interpretation : 15.98/5.00 15.98/5.00 POL(F(x_1, x_2)) = x_2 15.98/5.00 POL(c(x_1)) = [1] + x_1 15.98/5.00 POL(c1(x_1, x_2)) = x_1 + x_2 15.98/5.00 POL(c2(x_1)) = x_1 15.98/5.00 POL(f(x_1, x_2)) = [1] + x_2 15.98/5.00 POL(s(x_1)) = 0 15.98/5.00 15.98/5.00 ---------------------------------------- 15.98/5.00 15.98/5.00 (4) 15.98/5.00 Obligation: 15.98/5.00 Complexity Dependency Tuples Problem 15.98/5.00 15.98/5.00 Rules:
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40