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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313864
details
property
value
status
complete
benchmark
reach.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n119.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
242.912 seconds
cpu usage
868.248
user time
859.886
system time
8.36237
max virtual memory
3.750676E7
max residence set size
1.4852404E7
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
867.89/242.79 WORST_CASE(NON_POLY, ?) 867.89/242.79 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 867.89/242.79 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 867.89/242.79 867.89/242.79 867.89/242.79 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(INF, INF). 867.89/242.79 867.89/242.79 (0) CpxRelTRS 867.89/242.79 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 367 ms] 867.89/242.79 (2) CpxRelTRS 867.89/242.79 (3) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 867.89/242.79 (4) TRS for Loop Detection 867.89/242.79 (5) DecreasingLoopProof [LOWER BOUND(ID), 83 ms] 867.89/242.79 (6) BEST 867.89/242.79 (7) proven lower bound 867.89/242.79 (8) LowerBoundPropagationProof [FINISHED, 0 ms] 867.89/242.79 (9) BOUNDS(n^1, INF) 867.89/242.79 (10) TRS for Loop Detection 867.89/242.79 (11) InfiniteLowerBoundProof [FINISHED, 158.1 s] 867.89/242.79 (12) BOUNDS(INF, INF) 867.89/242.79 867.89/242.79 867.89/242.79 ---------------------------------------- 867.89/242.79 867.89/242.79 (0) 867.89/242.79 Obligation: 867.89/242.79 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(INF, INF). 867.89/242.79 867.89/242.79 867.89/242.79 The TRS R consists of the following rules: 867.89/242.79 867.89/242.79 getNodeFromEdge(S(S(x')), E(x, y)) -> y 867.89/242.79 via(u, v, Cons(E(x, y), xs), edges) -> via[Ite](!EQ(u, x), u, v, Cons(E(x, y), xs), edges) 867.89/242.79 getNodeFromEdge(S(0), E(x, y)) -> x 867.89/242.79 member(x', Cons(x, xs)) -> member[Ite](eqEdge(x', x), x', Cons(x, xs)) 867.89/242.79 getNodeFromEdge(0, E(x, y)) -> x 867.89/242.79 eqEdge(E(e11, e12), E(e21, e22)) -> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12) 867.89/242.79 via(u, v, Nil, edges) -> Nil 867.89/242.79 notEmpty(Cons(x, xs)) -> True 867.89/242.79 notEmpty(Nil) -> False 867.89/242.79 member(x, Nil) -> False 867.89/242.79 reach(u, v, edges) -> reach[Ite](member(E(u, v), edges), u, v, edges) 867.89/242.79 goal(u, v, edges) -> reach(u, v, edges) 867.89/242.79 867.89/242.79 The (relative) TRS S consists of the following rules: 867.89/242.79 867.89/242.79 !EQ(S(x), S(y)) -> !EQ(x, y) 867.89/242.79 !EQ(0, S(y)) -> False 867.89/242.79 !EQ(S(x), 0) -> False 867.89/242.79 !EQ(0, 0) -> True 867.89/242.79 and(False, False) -> False 867.89/242.79 and(True, False) -> False 867.89/242.79 and(False, True) -> False 867.89/242.79 and(True, True) -> True 867.89/242.79 via[Ite](True, u, v, Cons(E(x, y), xs), edges) -> via[Let](u, v, Cons(E(x, y), xs), edges, reach(y, v, edges)) 867.89/242.79 via[Let](u, v, Cons(x, xs), edges, Nil) -> via(u, v, xs, edges) 867.89/242.79 via[Let](u, v, Cons(x, xs), edges, Cons(x', xs')) -> Cons(x, Cons(x', xs')) 867.89/242.79 via[Ite](False, u, v, Cons(x, xs), edges) -> via(u, v, xs, edges) 867.89/242.79 member[Ite](False, x', Cons(x, xs)) -> member(x', xs) 867.89/242.79 reach[Ite](False, u, v, edges) -> via(u, v, edges, edges) 867.89/242.79 reach[Ite](True, u, v, edges) -> Cons(E(u, v), Nil) 867.89/242.79 member[Ite](True, x, xs) -> True 867.89/242.79 eqEdge[Ite](False, e21, e22, e11, e12) -> False 867.89/242.79 eqEdge[Ite](True, e21, e22, e11, e12) -> True 867.89/242.79 867.89/242.79 Rewrite Strategy: INNERMOST 867.89/242.79 ---------------------------------------- 867.89/242.79 867.89/242.79 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 867.89/242.79 proved termination of relative rules 867.89/242.79 ---------------------------------------- 867.89/242.79 867.89/242.79 (2) 867.89/242.79 Obligation: 867.89/242.79 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(INF, INF). 867.89/242.79 867.89/242.79 867.89/242.79 The TRS R consists of the following rules: 867.89/242.79 867.89/242.79 getNodeFromEdge(S(S(x')), E(x, y)) -> y 867.89/242.79 via(u, v, Cons(E(x, y), xs), edges) -> via[Ite](!EQ(u, x), u, v, Cons(E(x, y), xs), edges) 867.89/242.79 getNodeFromEdge(S(0), E(x, y)) -> x 867.89/242.79 member(x', Cons(x, xs)) -> member[Ite](eqEdge(x', x), x', Cons(x, xs)) 867.89/242.79 getNodeFromEdge(0, E(x, y)) -> x 867.89/242.79 eqEdge(E(e11, e12), E(e21, e22)) -> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12) 867.89/242.79 via(u, v, Nil, edges) -> Nil 867.89/242.79 notEmpty(Cons(x, xs)) -> True 867.89/242.79 notEmpty(Nil) -> False 867.89/242.79 member(x, Nil) -> False 867.89/242.79 reach(u, v, edges) -> reach[Ite](member(E(u, v), edges), u, v, edges) 867.89/242.79 goal(u, v, edges) -> reach(u, v, edges) 867.89/242.79 867.89/242.79 The (relative) TRS S consists of the following rules: 867.89/242.79 867.89/242.79 !EQ(S(x), S(y)) -> !EQ(x, y) 867.89/242.79 !EQ(0, S(y)) -> False 867.89/242.79 !EQ(S(x), 0) -> False 867.89/242.79 !EQ(0, 0) -> True 867.89/242.79 and(False, False) -> False 867.89/242.79 and(True, False) -> False
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40
