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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313294
details
property
value
status
complete
benchmark
elimdupl.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n128.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.642 seconds
cpu usage
322.303
user time
319.207
system time
3.09539
max virtual memory
1.9216744E7
max residence set size
5637936.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
322.15/291.59 WORST_CASE(Omega(n^1), O(n^2)) 322.24/291.60 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 322.24/291.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 322.24/291.60 322.24/291.60 322.24/291.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 322.24/291.60 322.24/291.60 (0) CpxTRS 322.24/291.60 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 322.24/291.60 (2) CdtProblem 322.24/291.60 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 322.24/291.60 (4) CdtProblem 322.24/291.60 (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 322.24/291.60 (6) CdtProblem 322.24/291.60 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 85 ms] 322.24/291.60 (8) CdtProblem 322.24/291.60 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 84 ms] 322.24/291.60 (10) CdtProblem 322.24/291.60 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 83 ms] 322.24/291.60 (12) CdtProblem 322.24/291.60 (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 95 ms] 322.24/291.60 (14) CdtProblem 322.24/291.60 (15) CdtKnowledgeProof [FINISHED, 0 ms] 322.24/291.60 (16) BOUNDS(1, 1) 322.24/291.60 (17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 322.24/291.60 (18) TRS for Loop Detection 322.24/291.60 (19) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 322.24/291.60 (20) BEST 322.24/291.60 (21) proven lower bound 322.24/291.60 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 322.24/291.60 (23) BOUNDS(n^1, INF) 322.24/291.60 (24) TRS for Loop Detection 322.24/291.60 322.24/291.60 322.24/291.60 ---------------------------------------- 322.24/291.60 322.24/291.60 (0) 322.24/291.60 Obligation: 322.24/291.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 322.24/291.60 322.24/291.60 322.24/291.60 The TRS R consists of the following rules: 322.24/291.60 322.24/291.60 eq(0, 0) -> true 322.24/291.60 eq(0, s(X)) -> false 322.24/291.60 eq(s(X), 0) -> false 322.24/291.60 eq(s(X), s(Y)) -> eq(X, Y) 322.24/291.60 rm(N, nil) -> nil 322.24/291.60 rm(N, add(M, X)) -> ifrm(eq(N, M), N, add(M, X)) 322.24/291.60 ifrm(true, N, add(M, X)) -> rm(N, X) 322.24/291.60 ifrm(false, N, add(M, X)) -> add(M, rm(N, X)) 322.24/291.60 purge(nil) -> nil 322.24/291.60 purge(add(N, X)) -> add(N, purge(rm(N, X))) 322.24/291.60 322.24/291.60 S is empty. 322.24/291.60 Rewrite Strategy: INNERMOST 322.24/291.60 ---------------------------------------- 322.24/291.60 322.24/291.60 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 322.24/291.60 Converted Cpx (relative) TRS to CDT 322.24/291.60 ---------------------------------------- 322.24/291.60 322.24/291.60 (2) 322.24/291.60 Obligation: 322.24/291.60 Complexity Dependency Tuples Problem 322.24/291.60 322.24/291.60 Rules: 322.24/291.60 eq(0, 0) -> true 322.24/291.60 eq(0, s(z0)) -> false 322.24/291.60 eq(s(z0), 0) -> false 322.24/291.60 eq(s(z0), s(z1)) -> eq(z0, z1) 322.24/291.61 rm(z0, nil) -> nil 322.24/291.61 rm(z0, add(z1, z2)) -> ifrm(eq(z0, z1), z0, add(z1, z2)) 322.24/291.61 ifrm(true, z0, add(z1, z2)) -> rm(z0, z2) 322.24/291.61 ifrm(false, z0, add(z1, z2)) -> add(z1, rm(z0, z2)) 322.24/291.61 purge(nil) -> nil 322.24/291.61 purge(add(z0, z1)) -> add(z0, purge(rm(z0, z1))) 322.24/291.61 Tuples: 322.24/291.61 EQ(0, 0) -> c 322.24/291.61 EQ(0, s(z0)) -> c1 322.24/291.61 EQ(s(z0), 0) -> c2 322.24/291.61 EQ(s(z0), s(z1)) -> c3(EQ(z0, z1)) 322.24/291.61 RM(z0, nil) -> c4 322.24/291.61 RM(z0, add(z1, z2)) -> c5(IFRM(eq(z0, z1), z0, add(z1, z2)), EQ(z0, z1)) 322.24/291.61 IFRM(true, z0, add(z1, z2)) -> c6(RM(z0, z2)) 322.24/291.61 IFRM(false, z0, add(z1, z2)) -> c7(RM(z0, z2)) 322.24/291.61 PURGE(nil) -> c8 322.24/291.61 PURGE(add(z0, z1)) -> c9(PURGE(rm(z0, z1)), RM(z0, z1)) 322.24/291.61 S tuples: 322.24/291.61 EQ(0, 0) -> c 322.24/291.61 EQ(0, s(z0)) -> c1 322.24/291.61 EQ(s(z0), 0) -> c2 322.24/291.61 EQ(s(z0), s(z1)) -> c3(EQ(z0, z1)) 322.24/291.61 RM(z0, nil) -> c4 322.24/291.61 RM(z0, add(z1, z2)) -> c5(IFRM(eq(z0, z1), z0, add(z1, z2)), EQ(z0, z1)) 322.24/291.61 IFRM(true, z0, add(z1, z2)) -> c6(RM(z0, z2)) 322.24/291.61 IFRM(false, z0, add(z1, z2)) -> c7(RM(z0, z2)) 322.24/291.61 PURGE(nil) -> c8 322.24/291.61 PURGE(add(z0, z1)) -> c9(PURGE(rm(z0, z1)), RM(z0, z1)) 322.24/291.61 K tuples:none
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40