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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308147
details
property
value
status
complete
benchmark
MYNAT_nosorts_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n124.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.15745 seconds
cpu usage
23.8743
user time
22.1467
system time
1.72765
max virtual memory
1.9214084E7
max residence set size
3887696.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
23.63/8.10 WORST_CASE(Omega(n^1), O(n^1)) 23.63/8.11 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 23.63/8.11 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 23.63/8.11 23.63/8.11 23.63/8.11 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 23.63/8.11 23.63/8.11 (0) CpxTRS 23.63/8.11 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 23.63/8.11 (2) CpxTRS 23.63/8.11 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 23.63/8.11 (4) CpxTRS 23.63/8.11 (5) CpxTrsMatchBoundsTAProof [FINISHED, 44 ms] 23.63/8.11 (6) BOUNDS(1, n^1) 23.63/8.11 (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 23.63/8.11 (8) CpxTRS 23.63/8.11 (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 23.63/8.11 (10) typed CpxTrs 23.63/8.11 (11) OrderProof [LOWER BOUND(ID), 0 ms] 23.63/8.11 (12) typed CpxTrs 23.63/8.11 (13) RewriteLemmaProof [LOWER BOUND(ID), 456 ms] 23.63/8.11 (14) BEST 23.63/8.11 (15) proven lower bound 23.63/8.11 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 23.63/8.11 (17) BOUNDS(n^1, INF) 23.63/8.11 (18) typed CpxTrs 23.63/8.11 (19) RewriteLemmaProof [LOWER BOUND(ID), 143 ms] 23.63/8.11 (20) typed CpxTrs 23.63/8.11 (21) RewriteLemmaProof [LOWER BOUND(ID), 118 ms] 23.63/8.11 (22) typed CpxTrs 23.63/8.11 (23) RewriteLemmaProof [LOWER BOUND(ID), 66 ms] 23.63/8.11 (24) typed CpxTrs 23.63/8.11 23.63/8.11 23.63/8.11 ---------------------------------------- 23.63/8.11 23.63/8.11 (0) 23.63/8.11 Obligation: 23.63/8.11 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 23.63/8.11 23.63/8.11 23.63/8.11 The TRS R consists of the following rules: 23.63/8.11 23.63/8.11 active(and(tt, X)) -> mark(X) 23.63/8.11 active(plus(N, 0)) -> mark(N) 23.63/8.11 active(plus(N, s(M))) -> mark(s(plus(N, M))) 23.63/8.11 active(x(N, 0)) -> mark(0) 23.63/8.11 active(x(N, s(M))) -> mark(plus(x(N, M), N)) 23.63/8.11 active(and(X1, X2)) -> and(active(X1), X2) 23.63/8.11 active(plus(X1, X2)) -> plus(active(X1), X2) 23.63/8.11 active(plus(X1, X2)) -> plus(X1, active(X2)) 23.63/8.11 active(s(X)) -> s(active(X)) 23.63/8.11 active(x(X1, X2)) -> x(active(X1), X2) 23.63/8.11 active(x(X1, X2)) -> x(X1, active(X2)) 23.63/8.11 and(mark(X1), X2) -> mark(and(X1, X2)) 23.63/8.11 plus(mark(X1), X2) -> mark(plus(X1, X2)) 23.63/8.11 plus(X1, mark(X2)) -> mark(plus(X1, X2)) 23.63/8.11 s(mark(X)) -> mark(s(X)) 23.63/8.11 x(mark(X1), X2) -> mark(x(X1, X2)) 23.63/8.11 x(X1, mark(X2)) -> mark(x(X1, X2)) 23.63/8.11 proper(and(X1, X2)) -> and(proper(X1), proper(X2)) 23.63/8.11 proper(tt) -> ok(tt) 23.63/8.11 proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) 23.63/8.11 proper(0) -> ok(0) 23.63/8.11 proper(s(X)) -> s(proper(X)) 23.63/8.11 proper(x(X1, X2)) -> x(proper(X1), proper(X2)) 23.63/8.11 and(ok(X1), ok(X2)) -> ok(and(X1, X2)) 23.63/8.11 plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) 23.63/8.11 s(ok(X)) -> ok(s(X)) 23.63/8.11 x(ok(X1), ok(X2)) -> ok(x(X1, X2)) 23.63/8.11 top(mark(X)) -> top(proper(X)) 23.63/8.11 top(ok(X)) -> top(active(X)) 23.63/8.11 23.63/8.11 S is empty. 23.63/8.11 Rewrite Strategy: FULL 23.63/8.11 ---------------------------------------- 23.63/8.11 23.63/8.11 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 23.63/8.11 The following defined symbols can occur below the 0th argument of top: proper, active 23.63/8.11 The following defined symbols can occur below the 0th argument of proper: proper, active 23.63/8.11 The following defined symbols can occur below the 0th argument of active: proper, active 23.63/8.11 23.63/8.11 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 23.63/8.11 active(and(tt, X)) -> mark(X) 23.63/8.11 active(plus(N, 0)) -> mark(N) 23.63/8.11 active(plus(N, s(M))) -> mark(s(plus(N, M))) 23.63/8.11 active(x(N, 0)) -> mark(0) 23.63/8.11 active(x(N, s(M))) -> mark(plus(x(N, M), N)) 23.63/8.11 active(and(X1, X2)) -> and(active(X1), X2) 23.63/8.11 active(plus(X1, X2)) -> plus(active(X1), X2) 23.63/8.11 active(plus(X1, X2)) -> plus(X1, active(X2)) 23.63/8.11 active(s(X)) -> s(active(X)) 23.63/8.11 active(x(X1, X2)) -> x(active(X1), X2) 23.63/8.11 active(x(X1, X2)) -> x(X1, active(X2)) 23.63/8.11 proper(and(X1, X2)) -> and(proper(X1), proper(X2)) 23.63/8.11 proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) 23.63/8.11 proper(s(X)) -> s(proper(X)) 23.63/8.11 proper(x(X1, X2)) -> x(proper(X1), proper(X2)) 23.63/8.11 23.63/8.11 ----------------------------------------
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