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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308328
details
property
value
status
complete
benchmark
Ex15_Luc98_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n031.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.1466 seconds
cpu usage
27.0872
user time
25.3708
system time
1.71648
max virtual memory
1.9142876E7
max residence set size
3739228.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
26.78/8.47 WORST_CASE(Omega(n^1), O(n^1)) 26.78/8.48 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 26.78/8.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 26.78/8.48 26.78/8.48 26.78/8.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 26.78/8.48 26.78/8.48 (0) CpxTRS 26.78/8.48 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 7 ms] 26.78/8.48 (2) CpxTRS 26.78/8.48 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 26.78/8.48 (4) CpxTRS 26.78/8.48 (5) CpxTrsMatchBoundsTAProof [FINISHED, 123 ms] 26.78/8.48 (6) BOUNDS(1, n^1) 26.78/8.48 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 26.78/8.48 (8) TRS for Loop Detection 26.78/8.48 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 26.78/8.48 (10) BEST 26.78/8.48 (11) proven lower bound 26.78/8.48 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 26.78/8.48 (13) BOUNDS(n^1, INF) 26.78/8.48 (14) TRS for Loop Detection 26.78/8.48 26.78/8.48 26.78/8.48 ---------------------------------------- 26.78/8.48 26.78/8.48 (0) 26.78/8.48 Obligation: 26.78/8.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 26.78/8.48 26.78/8.48 26.78/8.48 The TRS R consists of the following rules: 26.78/8.48 26.78/8.48 active(and(true, X)) -> mark(X) 26.78/8.48 active(and(false, Y)) -> mark(false) 26.78/8.48 active(if(true, X, Y)) -> mark(X) 26.78/8.48 active(if(false, X, Y)) -> mark(Y) 26.78/8.48 active(add(0, X)) -> mark(X) 26.78/8.48 active(add(s(X), Y)) -> mark(s(add(X, Y))) 26.78/8.48 active(first(0, X)) -> mark(nil) 26.78/8.48 active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))) 26.78/8.48 active(from(X)) -> mark(cons(X, from(s(X)))) 26.78/8.48 active(and(X1, X2)) -> and(active(X1), X2) 26.78/8.48 active(if(X1, X2, X3)) -> if(active(X1), X2, X3) 26.78/8.48 active(add(X1, X2)) -> add(active(X1), X2) 26.78/8.48 active(first(X1, X2)) -> first(active(X1), X2) 26.78/8.48 active(first(X1, X2)) -> first(X1, active(X2)) 26.78/8.48 and(mark(X1), X2) -> mark(and(X1, X2)) 26.78/8.48 if(mark(X1), X2, X3) -> mark(if(X1, X2, X3)) 26.78/8.48 add(mark(X1), X2) -> mark(add(X1, X2)) 26.78/8.48 first(mark(X1), X2) -> mark(first(X1, X2)) 26.78/8.48 first(X1, mark(X2)) -> mark(first(X1, X2)) 26.78/8.48 proper(and(X1, X2)) -> and(proper(X1), proper(X2)) 26.78/8.48 proper(true) -> ok(true) 26.78/8.48 proper(false) -> ok(false) 26.78/8.48 proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3)) 26.78/8.48 proper(add(X1, X2)) -> add(proper(X1), proper(X2)) 26.78/8.48 proper(0) -> ok(0) 26.78/8.48 proper(s(X)) -> s(proper(X)) 26.78/8.48 proper(first(X1, X2)) -> first(proper(X1), proper(X2)) 26.78/8.48 proper(nil) -> ok(nil) 26.78/8.48 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 26.78/8.48 proper(from(X)) -> from(proper(X)) 26.78/8.48 and(ok(X1), ok(X2)) -> ok(and(X1, X2)) 26.78/8.48 if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3)) 26.78/8.48 add(ok(X1), ok(X2)) -> ok(add(X1, X2)) 26.78/8.48 s(ok(X)) -> ok(s(X)) 26.78/8.48 first(ok(X1), ok(X2)) -> ok(first(X1, X2)) 26.78/8.48 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 26.78/8.48 from(ok(X)) -> ok(from(X)) 26.78/8.48 top(mark(X)) -> top(proper(X)) 26.78/8.48 top(ok(X)) -> top(active(X)) 26.78/8.48 26.78/8.48 S is empty. 26.78/8.48 Rewrite Strategy: FULL 26.78/8.48 ---------------------------------------- 26.78/8.48 26.78/8.48 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 26.78/8.48 The following defined symbols can occur below the 0th argument of top: proper, active 26.78/8.48 The following defined symbols can occur below the 0th argument of proper: proper, active 26.78/8.48 The following defined symbols can occur below the 0th argument of active: proper, active 26.78/8.48 26.78/8.48 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 26.78/8.48 active(and(true, X)) -> mark(X) 26.78/8.48 active(and(false, Y)) -> mark(false) 26.78/8.48 active(if(true, X, Y)) -> mark(X) 26.78/8.48 active(if(false, X, Y)) -> mark(Y) 26.78/8.48 active(add(0, X)) -> mark(X) 26.78/8.48 active(add(s(X), Y)) -> mark(s(add(X, Y))) 26.78/8.48 active(first(0, X)) -> mark(nil) 26.78/8.48 active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))) 26.78/8.48 active(from(X)) -> mark(cons(X, from(s(X)))) 26.78/8.48 active(and(X1, X2)) -> and(active(X1), X2) 26.78/8.48 active(if(X1, X2, X3)) -> if(active(X1), X2, X3) 26.78/8.48 active(add(X1, X2)) -> add(active(X1), X2) 26.78/8.48 active(first(X1, X2)) -> first(active(X1), X2) 26.78/8.48 active(first(X1, X2)) -> first(X1, active(X2)) 26.78/8.48 proper(and(X1, X2)) -> and(proper(X1), proper(X2)) 26.78/8.48 proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3)) 26.78/8.48 proper(add(X1, X2)) -> add(proper(X1), proper(X2))
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