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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313757
details
property
value
status
complete
benchmark
#3.23.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n104.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.47405 seconds
cpu usage
14.4109
user time
13.2962
system time
1.11464
max virtual memory
1.8813288E7
max residence set size
3513544.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
13.78/5.17 WORST_CASE(Omega(n^1), O(n^1)) 13.78/5.19 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 13.78/5.19 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 13.78/5.19 13.78/5.19 13.78/5.19 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 13.78/5.19 13.78/5.19 (0) CpxTRS 13.78/5.19 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 13.78/5.19 (2) CdtProblem 13.78/5.19 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 13.78/5.19 (4) CdtProblem 13.78/5.19 (5) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 39 ms] 13.78/5.19 (6) CdtProblem 13.78/5.19 (7) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 13.78/5.19 (8) BOUNDS(1, 1) 13.78/5.19 (9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 13.78/5.19 (10) TRS for Loop Detection 13.78/5.19 (11) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 13.78/5.19 (12) BEST 13.78/5.19 (13) proven lower bound 13.78/5.19 (14) LowerBoundPropagationProof [FINISHED, 0 ms] 13.78/5.19 (15) BOUNDS(n^1, INF) 13.78/5.19 (16) TRS for Loop Detection 13.78/5.19 13.78/5.19 13.78/5.19 ---------------------------------------- 13.78/5.19 13.78/5.19 (0) 13.78/5.19 Obligation: 13.78/5.19 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 13.78/5.19 13.78/5.19 13.78/5.19 The TRS R consists of the following rules: 13.78/5.19 13.78/5.19 f(0, y) -> 0 13.78/5.19 f(s(x), y) -> f(f(x, y), y) 13.78/5.19 13.78/5.19 S is empty. 13.78/5.19 Rewrite Strategy: INNERMOST 13.78/5.19 ---------------------------------------- 13.78/5.19 13.78/5.19 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 13.78/5.19 Converted Cpx (relative) TRS to CDT 13.78/5.19 ---------------------------------------- 13.78/5.19 13.78/5.19 (2) 13.78/5.19 Obligation: 13.78/5.19 Complexity Dependency Tuples Problem 13.78/5.19 13.78/5.19 Rules: 13.78/5.19 f(0, z0) -> 0 13.78/5.19 f(s(z0), z1) -> f(f(z0, z1), z1) 13.78/5.19 Tuples: 13.78/5.19 F(0, z0) -> c 13.78/5.19 F(s(z0), z1) -> c1(F(f(z0, z1), z1), F(z0, z1)) 13.78/5.19 S tuples: 13.78/5.19 F(0, z0) -> c 13.78/5.19 F(s(z0), z1) -> c1(F(f(z0, z1), z1), F(z0, z1)) 13.78/5.19 K tuples:none 13.78/5.19 Defined Rule Symbols: f_2 13.78/5.19 13.78/5.19 Defined Pair Symbols: F_2 13.78/5.19 13.78/5.19 Compound Symbols: c, c1_2 13.78/5.19 13.78/5.19 13.78/5.19 ---------------------------------------- 13.78/5.19 13.78/5.19 (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) 13.78/5.19 Removed 1 trailing nodes: 13.78/5.19 F(0, z0) -> c 13.78/5.19 13.78/5.19 ---------------------------------------- 13.78/5.19 13.78/5.19 (4) 13.78/5.19 Obligation: 13.78/5.19 Complexity Dependency Tuples Problem 13.78/5.19 13.78/5.19 Rules: 13.78/5.19 f(0, z0) -> 0 13.78/5.19 f(s(z0), z1) -> f(f(z0, z1), z1) 13.78/5.19 Tuples: 13.78/5.19 F(s(z0), z1) -> c1(F(f(z0, z1), z1), F(z0, z1)) 13.78/5.19 S tuples: 13.78/5.19 F(s(z0), z1) -> c1(F(f(z0, z1), z1), F(z0, z1)) 13.78/5.19 K tuples:none 13.78/5.19 Defined Rule Symbols: f_2 13.78/5.19 13.78/5.19 Defined Pair Symbols: F_2 13.78/5.19 13.78/5.19 Compound Symbols: c1_2 13.78/5.19 13.78/5.19 13.78/5.19 ---------------------------------------- 13.78/5.19 13.78/5.19 (5) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) 13.78/5.19 Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. 13.78/5.19 F(s(z0), z1) -> c1(F(f(z0, z1), z1), F(z0, z1)) 13.78/5.19 We considered the (Usable) Rules:
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