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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308105
details
property
value
status
complete
benchmark
Ex4_7_77_Bor03_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.605 seconds
cpu usage
1097.21
user time
1082.96
system time
14.2454
max virtual memory
3.8036072E7
max residence set size
1.504144E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
1096.78/291.51 WORST_CASE(Omega(n^1), O(n^1)) 1097.04/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1097.04/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1097.04/291.53 1097.04/291.53 1097.04/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 1097.04/291.53 1097.04/291.53 (0) CpxTRS 1097.04/291.53 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 1097.04/291.53 (2) CpxTRS 1097.04/291.53 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 1097.04/291.53 (4) CpxTRS 1097.04/291.53 (5) CpxTrsMatchBoundsTAProof [FINISHED, 369 ms] 1097.04/291.53 (6) BOUNDS(1, n^1) 1097.04/291.53 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1097.04/291.53 (8) TRS for Loop Detection 1097.04/291.53 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1097.04/291.53 (10) BEST 1097.04/291.53 (11) proven lower bound 1097.04/291.53 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 1097.04/291.53 (13) BOUNDS(n^1, INF) 1097.04/291.53 (14) TRS for Loop Detection 1097.04/291.53 1097.04/291.53 1097.04/291.53 ---------------------------------------- 1097.04/291.53 1097.04/291.53 (0) 1097.04/291.53 Obligation: 1097.04/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 1097.04/291.53 1097.04/291.53 1097.04/291.53 The TRS R consists of the following rules: 1097.04/291.53 1097.04/291.53 active(zeros) -> mark(cons(0, zeros)) 1097.04/291.53 active(tail(cons(X, XS))) -> mark(XS) 1097.04/291.53 active(cons(X1, X2)) -> cons(active(X1), X2) 1097.04/291.53 active(tail(X)) -> tail(active(X)) 1097.04/291.53 cons(mark(X1), X2) -> mark(cons(X1, X2)) 1097.04/291.53 tail(mark(X)) -> mark(tail(X)) 1097.04/291.53 proper(zeros) -> ok(zeros) 1097.04/291.53 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 1097.04/291.53 proper(0) -> ok(0) 1097.04/291.53 proper(tail(X)) -> tail(proper(X)) 1097.04/291.53 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 1097.04/291.53 tail(ok(X)) -> ok(tail(X)) 1097.04/291.53 top(mark(X)) -> top(proper(X)) 1097.04/291.53 top(ok(X)) -> top(active(X)) 1097.04/291.53 1097.04/291.53 S is empty. 1097.04/291.53 Rewrite Strategy: FULL 1097.04/291.53 ---------------------------------------- 1097.04/291.53 1097.04/291.53 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 1097.04/291.53 The following defined symbols can occur below the 0th argument of cons: active, proper, cons 1097.04/291.53 The following defined symbols can occur below the 1th argument of cons: active, proper, cons 1097.04/291.53 The following defined symbols can occur below the 0th argument of top: active, proper, cons 1097.04/291.53 The following defined symbols can occur below the 0th argument of proper: active, proper, cons 1097.04/291.53 The following defined symbols can occur below the 0th argument of active: active, proper, cons 1097.04/291.53 1097.04/291.53 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 1097.04/291.53 active(tail(cons(X, XS))) -> mark(XS) 1097.04/291.53 active(tail(X)) -> tail(active(X)) 1097.04/291.53 proper(tail(X)) -> tail(proper(X)) 1097.04/291.53 1097.04/291.53 ---------------------------------------- 1097.04/291.53 1097.04/291.53 (2) 1097.04/291.53 Obligation: 1097.04/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 1097.04/291.53 1097.04/291.53 1097.04/291.53 The TRS R consists of the following rules: 1097.04/291.53 1097.04/291.53 active(zeros) -> mark(cons(0, zeros)) 1097.04/291.53 active(cons(X1, X2)) -> cons(active(X1), X2) 1097.04/291.53 cons(mark(X1), X2) -> mark(cons(X1, X2)) 1097.04/291.53 tail(mark(X)) -> mark(tail(X)) 1097.04/291.53 proper(zeros) -> ok(zeros) 1097.04/291.53 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 1097.04/291.53 proper(0) -> ok(0) 1097.04/291.53 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 1097.04/291.53 tail(ok(X)) -> ok(tail(X)) 1097.04/291.53 top(mark(X)) -> top(proper(X)) 1097.04/291.53 top(ok(X)) -> top(active(X)) 1097.04/291.53 1097.04/291.53 S is empty. 1097.04/291.53 Rewrite Strategy: FULL 1097.04/291.53 ---------------------------------------- 1097.04/291.53 1097.04/291.53 (3) RelTrsToTrsProof (UPPER BOUND(ID)) 1097.04/291.53 transformed relative TRS to TRS 1097.04/291.53 ---------------------------------------- 1097.04/291.53 1097.04/291.53 (4) 1097.04/291.53 Obligation: 1097.04/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 1097.04/291.53 1097.04/291.53 1097.04/291.53 The TRS R consists of the following rules: 1097.04/291.53
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