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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313389
details
property
value
status
complete
benchmark
perfect.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n093.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.55049 seconds
cpu usage
26.0329
user time
24.3174
system time
1.71557
max virtual memory
1.9345636E7
max residence set size
4097272.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
25.69/7.46 WORST_CASE(Omega(n^1), O(n^1)) 25.88/7.49 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 25.88/7.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 25.88/7.49 25.88/7.49 25.88/7.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 25.88/7.49 25.88/7.49 (0) CpxTRS 25.88/7.49 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 25.88/7.49 (2) CdtProblem 25.88/7.49 (3) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] 25.88/7.49 (4) CdtProblem 25.88/7.49 (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 25.88/7.49 (6) CdtProblem 25.88/7.49 (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 25.88/7.49 (8) CdtProblem 25.88/7.49 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 24 ms] 25.88/7.49 (10) CdtProblem 25.88/7.49 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 8 ms] 25.88/7.49 (12) CdtProblem 25.88/7.49 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 25.88/7.49 (14) BOUNDS(1, 1) 25.88/7.49 (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 25.88/7.49 (16) TRS for Loop Detection 25.88/7.49 (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 25.88/7.49 (18) BEST 25.88/7.49 (19) proven lower bound 25.88/7.49 (20) LowerBoundPropagationProof [FINISHED, 1 ms] 25.88/7.49 (21) BOUNDS(n^1, INF) 25.88/7.49 (22) TRS for Loop Detection 25.88/7.49 25.88/7.49 25.88/7.49 ---------------------------------------- 25.88/7.49 25.88/7.49 (0) 25.88/7.49 Obligation: 25.88/7.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 25.88/7.49 25.88/7.49 25.88/7.49 The TRS R consists of the following rules: 25.88/7.49 25.88/7.49 perfectp(0) -> false 25.88/7.49 perfectp(s(x)) -> f(x, s(0), s(x), s(x)) 25.88/7.49 f(0, y, 0, u) -> true 25.88/7.49 f(0, y, s(z), u) -> false 25.88/7.49 f(s(x), 0, z, u) -> f(x, u, minus(z, s(x)), u) 25.88/7.49 f(s(x), s(y), z, u) -> if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u)) 25.88/7.49 25.88/7.49 S is empty. 25.88/7.49 Rewrite Strategy: INNERMOST 25.88/7.49 ---------------------------------------- 25.88/7.49 25.88/7.49 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 25.88/7.49 Converted Cpx (relative) TRS to CDT 25.88/7.49 ---------------------------------------- 25.88/7.49 25.88/7.49 (2) 25.88/7.49 Obligation: 25.88/7.49 Complexity Dependency Tuples Problem 25.88/7.49 25.88/7.49 Rules: 25.88/7.49 perfectp(0) -> false 25.88/7.49 perfectp(s(z0)) -> f(z0, s(0), s(z0), s(z0)) 25.88/7.49 f(0, z0, 0, z1) -> true 25.88/7.49 f(0, z0, s(z1), z2) -> false 25.88/7.49 f(s(z0), 0, z1, z2) -> f(z0, z2, minus(z1, s(z0)), z2) 25.88/7.49 f(s(z0), s(z1), z2, z3) -> if(le(z0, z1), f(s(z0), minus(z1, z0), z2, z3), f(z0, z3, z2, z3)) 25.88/7.49 Tuples: 25.88/7.49 PERFECTP(0) -> c 25.88/7.49 PERFECTP(s(z0)) -> c1(F(z0, s(0), s(z0), s(z0))) 25.88/7.49 F(0, z0, 0, z1) -> c2 25.88/7.49 F(0, z0, s(z1), z2) -> c3 25.88/7.49 F(s(z0), 0, z1, z2) -> c4(F(z0, z2, minus(z1, s(z0)), z2)) 25.88/7.49 F(s(z0), s(z1), z2, z3) -> c5(F(s(z0), minus(z1, z0), z2, z3), F(z0, z3, z2, z3)) 25.88/7.49 S tuples: 25.88/7.49 PERFECTP(0) -> c 25.88/7.49 PERFECTP(s(z0)) -> c1(F(z0, s(0), s(z0), s(z0))) 25.88/7.49 F(0, z0, 0, z1) -> c2 25.88/7.49 F(0, z0, s(z1), z2) -> c3 25.88/7.49 F(s(z0), 0, z1, z2) -> c4(F(z0, z2, minus(z1, s(z0)), z2)) 25.88/7.49 F(s(z0), s(z1), z2, z3) -> c5(F(s(z0), minus(z1, z0), z2, z3), F(z0, z3, z2, z3)) 25.88/7.49 K tuples:none 25.88/7.49 Defined Rule Symbols: perfectp_1, f_4 25.88/7.49 25.88/7.49 Defined Pair Symbols: PERFECTP_1, F_4 25.88/7.49 25.88/7.49 Compound Symbols: c, c1_1, c2, c3, c4_1, c5_2 25.88/7.49 25.88/7.49 25.88/7.49 ---------------------------------------- 25.88/7.49 25.88/7.49 (3) CdtLeafRemovalProof (ComplexityIfPolyImplication) 25.88/7.49 Removed 1 leading nodes: 25.88/7.49 PERFECTP(s(z0)) -> c1(F(z0, s(0), s(z0), s(z0))) 25.88/7.49 Removed 3 trailing nodes: 25.88/7.49 F(0, z0, 0, z1) -> c2 25.88/7.49 F(0, z0, s(z1), z2) -> c3 25.88/7.49 PERFECTP(0) -> c 25.88/7.49 25.88/7.49 ----------------------------------------
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40
