Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime Complexity: TRS Innermost pair #487112818
details
property
value
status
complete
benchmark
2.45.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.89794 seconds
cpu usage
16.2019
user time
15.1123
system time
1.08959
max virtual memory
1.8977172E7
max residence set size
3502380.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 29 ms] (10) CdtProblem (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (12) BOUNDS(1, 1) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^1, INF) (20) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: admit(x, nil) -> nil admit(x, .(u, .(v, .(w, z)))) -> cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z))))) cond(true, y) -> y S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: admit(z0, nil) -> nil admit(z0, .(z1, .(z2, .(w, z3)))) -> cond(=(sum(z0, z1, z2), w), .(z1, .(z2, .(w, admit(carry(z0, z1, z2), z3))))) cond(true, z0) -> z0 Tuples: ADMIT(z0, nil) -> c ADMIT(z0, .(z1, .(z2, .(w, z3)))) -> c1(COND(=(sum(z0, z1, z2), w), .(z1, .(z2, .(w, admit(carry(z0, z1, z2), z3))))), ADMIT(carry(z0, z1, z2), z3)) COND(true, z0) -> c2 S tuples: ADMIT(z0, nil) -> c ADMIT(z0, .(z1, .(z2, .(w, z3)))) -> c1(COND(=(sum(z0, z1, z2), w), .(z1, .(z2, .(w, admit(carry(z0, z1, z2), z3))))), ADMIT(carry(z0, z1, z2), z3)) COND(true, z0) -> c2 K tuples:none Defined Rule Symbols: admit_2, cond_2 Defined Pair Symbols: ADMIT_2, COND_2 Compound Symbols: c, c1_2, c2 ---------------------------------------- (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: COND(true, z0) -> c2 ADMIT(z0, nil) -> c ---------------------------------------- (4) Obligation: Complexity Dependency Tuples Problem Rules: admit(z0, nil) -> nil admit(z0, .(z1, .(z2, .(w, z3)))) -> cond(=(sum(z0, z1, z2), w), .(z1, .(z2, .(w, admit(carry(z0, z1, z2), z3))))) cond(true, z0) -> z0 Tuples: ADMIT(z0, .(z1, .(z2, .(w, z3)))) -> c1(COND(=(sum(z0, z1, z2), w), .(z1, .(z2, .(w, admit(carry(z0, z1, z2), z3))))), ADMIT(carry(z0, z1, z2), z3)) S tuples: ADMIT(z0, .(z1, .(z2, .(w, z3)))) -> c1(COND(=(sum(z0, z1, z2), w), .(z1, .(z2, .(w, admit(carry(z0, z1, z2), z3))))), ADMIT(carry(z0, z1, z2), z3)) K tuples:none Defined Rule Symbols: admit_2, cond_2 Defined Pair Symbols: ADMIT_2
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime Complexity: TRS Innermost