Runtime Complexity: TRS Innermost pair #487111880

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	n140.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	279.513 seconds
cpu usage	953.402
user time	944.828
system time	8.57302
max virtual memory	1.8985196E7
max residence set size	1.4515432E7

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

WORST_CASE(NON_POLY, ?)
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(INF, INF).

(0) CpxRelTRS
(1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 369 ms]
(2) CpxRelTRS
(3) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(4) TRS for Loop Detection
(5) DecreasingLoopProof [LOWER BOUND(ID), 108 ms]
(6) BEST
    (7) proven lower bound
        (8) LowerBoundPropagationProof [FINISHED, 0 ms]
        (9) BOUNDS(n^1, INF)
    (10) TRS for Loop Detection
        (11) InfiniteLowerBoundProof [FINISHED, 160.2 s]
        (12) BOUNDS(INF, INF)


----------------------------------------

(0)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(INF, INF).


The TRS R consists of the following rules:

   getNodeFromEdge(S(S(x')), E(x, y)) -> y
   via(u, v, Cons(E(x, y), xs), edges) -> via[Ite](!EQ(u, x), u, v, Cons(E(x, y), xs), edges)
   getNodeFromEdge(S(0), E(x, y)) -> x
   member(x', Cons(x, xs)) -> member[Ite](eqEdge(x', x), x', Cons(x, xs))
   getNodeFromEdge(0, E(x, y)) -> x
   eqEdge(E(e11, e12), E(e21, e22)) -> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12)
   via(u, v, Nil, edges) -> Nil
   notEmpty(Cons(x, xs)) -> True
   notEmpty(Nil) -> False
   member(x, Nil) -> False
   reach(u, v, edges) -> reach[Ite](member(E(u, v), edges), u, v, edges)
   goal(u, v, edges) -> reach(u, v, edges)

The (relative) TRS S consists of the following rules:

   !EQ(S(x), S(y)) -> !EQ(x, y)
   !EQ(0, S(y)) -> False
   !EQ(S(x), 0) -> False
   !EQ(0, 0) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   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))
   via[Let](u, v, Cons(x, xs), edges, Nil) -> via(u, v, xs, edges)
   via[Let](u, v, Cons(x, xs), edges, Cons(x', xs')) -> Cons(x, Cons(x', xs'))
   via[Ite](False, u, v, Cons(x, xs), edges) -> via(u, v, xs, edges)
   member[Ite](False, x', Cons(x, xs)) -> member(x', xs)
   reach[Ite](False, u, v, edges) -> via(u, v, edges, edges)
   reach[Ite](True, u, v, edges) -> Cons(E(u, v), Nil)
   member[Ite](True, x, xs) -> True
   eqEdge[Ite](False, e21, e22, e11, e12) -> False
   eqEdge[Ite](True, e21, e22, e11, e12) -> True

Rewrite Strategy: INNERMOST
----------------------------------------

(1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
proved innermost termination of relative rules
----------------------------------------

(2)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(INF, INF).


The TRS R consists of the following rules:

   getNodeFromEdge(S(S(x')), E(x, y)) -> y
   via(u, v, Cons(E(x, y), xs), edges) -> via[Ite](!EQ(u, x), u, v, Cons(E(x, y), xs), edges)
   getNodeFromEdge(S(0), E(x, y)) -> x
   member(x', Cons(x, xs)) -> member[Ite](eqEdge(x', x), x', Cons(x, xs))
   getNodeFromEdge(0, E(x, y)) -> x
   eqEdge(E(e11, e12), E(e21, e22)) -> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12)
   via(u, v, Nil, edges) -> Nil
   notEmpty(Cons(x, xs)) -> True
   notEmpty(Nil) -> False
   member(x, Nil) -> False
   reach(u, v, edges) -> reach[Ite](member(E(u, v), edges), u, v, edges)
   goal(u, v, edges) -> reach(u, v, edges)

The (relative) TRS S consists of the following rules:

   !EQ(S(x), S(y)) -> !EQ(x, y)
   !EQ(0, S(y)) -> False
   !EQ(S(x), 0) -> False
   !EQ(0, 0) -> True
   and(False, False) -> False
   and(True, False) -> False

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