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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313789
details
property
value
status
complete
benchmark
mul.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n153.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.91145 seconds
cpu usage
15.3703
user time
14.3344
system time
1.03597
max virtual memory
1.9011912E7
max residence set size
3504964.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), O(n^3))
output
14.92/4.69 WORST_CASE(Omega(n^3), O(n^3)) 14.92/4.70 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 14.92/4.70 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 14.92/4.70 14.92/4.70 14.92/4.70 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 14.92/4.70 14.92/4.70 (0) CpxTRS 14.92/4.70 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 14.92/4.70 (2) CdtProblem 14.92/4.70 (3) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] 14.92/4.70 (4) CdtProblem 14.92/4.70 (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 14.92/4.70 (6) CdtProblem 14.92/4.70 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 69 ms] 14.92/4.70 (8) CdtProblem 14.92/4.70 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 164 ms] 14.92/4.70 (10) CdtProblem 14.92/4.70 (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 14.92/4.70 (12) BOUNDS(1, 1) 14.92/4.70 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 14.92/4.70 (14) CpxTRS 14.92/4.70 (15) SlicingProof [LOWER BOUND(ID), 0 ms] 14.92/4.70 (16) CpxTRS 14.92/4.70 (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 14.92/4.70 (18) typed CpxTrs 14.92/4.70 (19) OrderProof [LOWER BOUND(ID), 0 ms] 14.92/4.70 (20) typed CpxTrs 14.92/4.70 (21) RewriteLemmaProof [LOWER BOUND(ID), 300 ms] 14.92/4.70 (22) BEST 14.92/4.70 (23) proven lower bound 14.92/4.70 (24) LowerBoundPropagationProof [FINISHED, 0 ms] 14.92/4.70 (25) BOUNDS(n^1, INF) 14.92/4.70 (26) typed CpxTrs 14.92/4.70 (27) RewriteLemmaProof [LOWER BOUND(ID), 78 ms] 14.92/4.70 (28) proven lower bound 14.92/4.70 (29) LowerBoundPropagationProof [FINISHED, 0 ms] 14.92/4.70 (30) BOUNDS(n^3, INF) 14.92/4.70 14.92/4.70 14.92/4.70 ---------------------------------------- 14.92/4.70 14.92/4.70 (0) 14.92/4.70 Obligation: 14.92/4.70 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 14.92/4.70 14.92/4.70 14.92/4.70 The TRS R consists of the following rules: 14.92/4.70 14.92/4.70 mul0(Cons(x, xs), y) -> add0(mul0(xs, y), y) 14.92/4.70 add0(Cons(x, xs), y) -> add0(xs, Cons(S, y)) 14.92/4.70 mul0(Nil, y) -> Nil 14.92/4.70 add0(Nil, y) -> y 14.92/4.70 goal(xs, ys) -> mul0(xs, ys) 14.92/4.70 14.92/4.70 S is empty. 14.92/4.70 Rewrite Strategy: INNERMOST 14.92/4.70 ---------------------------------------- 14.92/4.70 14.92/4.70 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 14.92/4.70 Converted Cpx (relative) TRS to CDT 14.92/4.70 ---------------------------------------- 14.92/4.70 14.92/4.70 (2) 14.92/4.70 Obligation: 14.92/4.70 Complexity Dependency Tuples Problem 14.92/4.70 14.92/4.70 Rules: 14.92/4.70 mul0(Cons(z0, z1), z2) -> add0(mul0(z1, z2), z2) 14.92/4.70 mul0(Nil, z0) -> Nil 14.92/4.70 add0(Cons(z0, z1), z2) -> add0(z1, Cons(S, z2)) 14.92/4.70 add0(Nil, z0) -> z0 14.92/4.70 goal(z0, z1) -> mul0(z0, z1) 14.92/4.70 Tuples: 14.92/4.70 MUL0(Cons(z0, z1), z2) -> c(ADD0(mul0(z1, z2), z2), MUL0(z1, z2)) 14.92/4.70 MUL0(Nil, z0) -> c1 14.92/4.70 ADD0(Cons(z0, z1), z2) -> c2(ADD0(z1, Cons(S, z2))) 14.92/4.70 ADD0(Nil, z0) -> c3 14.92/4.70 GOAL(z0, z1) -> c4(MUL0(z0, z1)) 14.92/4.70 S tuples: 14.92/4.70 MUL0(Cons(z0, z1), z2) -> c(ADD0(mul0(z1, z2), z2), MUL0(z1, z2)) 14.92/4.70 MUL0(Nil, z0) -> c1 14.92/4.70 ADD0(Cons(z0, z1), z2) -> c2(ADD0(z1, Cons(S, z2))) 14.92/4.70 ADD0(Nil, z0) -> c3 14.92/4.70 GOAL(z0, z1) -> c4(MUL0(z0, z1)) 14.92/4.70 K tuples:none 14.92/4.70 Defined Rule Symbols: mul0_2, add0_2, goal_2 14.92/4.70 14.92/4.70 Defined Pair Symbols: MUL0_2, ADD0_2, GOAL_2 14.92/4.70 14.92/4.70 Compound Symbols: c_2, c1, c2_1, c3, c4_1 14.92/4.70 14.92/4.70 14.92/4.70 ---------------------------------------- 14.92/4.70 14.92/4.70 (3) CdtLeafRemovalProof (ComplexityIfPolyImplication) 14.92/4.70 Removed 1 leading nodes: 14.92/4.70 GOAL(z0, z1) -> c4(MUL0(z0, z1)) 14.92/4.70 Removed 2 trailing nodes: 14.92/4.70 ADD0(Nil, z0) -> c3
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