details

property	value
status	complete
benchmark	lambdaint_typed.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	292.016 seconds
cpu usage	1144.81
user time	1134.1
system time	10.718
max virtual memory	3.8085692E7
max residence set size	1.4807648E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), ?)

output

WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 305 ms] (2) CpxRelTRS (3) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (4) TRS for Loop Detection (5) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (6) BEST (7) proven lower bound (8) LowerBoundPropagationProof [FINISHED, 0 ms] (9) BOUNDS(n^1, INF) (10) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: subst(x, a, App(e1, e2)) -> mkapp(subst(x, a, e1), subst(x, a, e2)) subst(x, a, Lam(var, exp)) -> subst[True][Ite](eqTerm(x, V(var)), x, a, Lam(var, exp)) red(App(e1, e2)) -> red[Let](App(e1, e2), red(e1)) red(Lam(int, term)) -> Lam(int, term) subst(x, a, V(int)) -> subst[Ite](eqTerm(x, V(int)), x, a, V(int)) red(V(int)) -> V(int) eqTerm(App(t11, t12), App(t21, t22)) -> and(eqTerm(t11, t21), eqTerm(t12, t22)) eqTerm(App(t11, t12), Lam(i2, l2)) -> False eqTerm(App(t11, t12), V(v2)) -> False eqTerm(Lam(i1, l1), App(t21, t22)) -> False eqTerm(Lam(i1, l1), Lam(i2, l2)) -> and(!EQ(i1, i2), eqTerm(l1, l2)) eqTerm(Lam(i1, l1), V(v2)) -> False eqTerm(V(v1), App(t21, t22)) -> False eqTerm(V(v1), Lam(i2, l2)) -> False eqTerm(V(v1), V(v2)) -> !EQ(v1, v2) mklam(V(name), e) -> Lam(name, e) lamvar(Lam(var, exp)) -> V(var) lambody(Lam(var, exp)) -> exp isvar(App(t1, t2)) -> False isvar(Lam(int, term)) -> False isvar(V(int)) -> True islam(App(t1, t2)) -> False islam(Lam(int, term)) -> True islam(V(int)) -> False appe2(App(e1, e2)) -> e2 appe1(App(e1, e2)) -> e1 mkapp(e1, e2) -> App(e1, e2) lambdaint(e) -> red(e) The (relative) TRS S consists of the following rules: and(False, False) -> False and(True, False) -> False and(False, True) -> False and(True, True) -> True !EQ(S(x), S(y)) -> !EQ(x, y) !EQ(0, S(y)) -> False !EQ(S(x), 0) -> False !EQ(0, 0) -> True red[Let][Let](e, Lam(var, exp), a) -> red(subst(V(var), a, exp)) subst[True][Ite](False, x, a, Lam(var, exp)) -> mklam(V(var), subst(x, a, exp)) red[Let][Let](e, App(t1, t2), e2) -> App(App(t1, t2), e2) red[Let][Let](e, V(int), e2) -> App(V(int), e2) red[Let](App(e1, e2), f) -> red[Let][Let](App(e1, e2), f, red(e2)) subst[True][Ite](True, x, a, e) -> e subst[Ite](False, x, a, e) -> e subst[Ite](True, x, a, e) -> a 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(n^1, INF). The TRS R consists of the following rules: subst(x, a, App(e1, e2)) -> mkapp(subst(x, a, e1), subst(x, a, e2)) subst(x, a, Lam(var, exp)) -> subst[True][Ite](eqTerm(x, V(var)), x, a, Lam(var, exp)) red(App(e1, e2)) -> red[Let](App(e1, e2), red(e1)) red(Lam(int, term)) -> Lam(int, term) subst(x, a, V(int)) -> subst[Ite](eqTerm(x, V(int)), x, a, V(int)) red(V(int)) -> V(int) eqTerm(App(t11, t12), App(t21, t22)) -> and(eqTerm(t11, t21), eqTerm(t12, t22)) eqTerm(App(t11, t12), Lam(i2, l2)) -> False eqTerm(App(t11, t12), V(v2)) -> False popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Runtime Complexity: TRS Innermost