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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308466
details
property
value
status
complete
benchmark
3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.59581 seconds
cpu usage
3.56321
user time
3.43781
system time
0.125402
max virtual memory
1.8277336E7
max residence set size
227044.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(1))
output
3.43/1.56 WORST_CASE(?, O(1)) 3.43/1.57 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 3.43/1.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.43/1.57 3.43/1.57 3.43/1.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). 3.43/1.57 3.43/1.57 (0) CpxTRS 3.43/1.57 (1) DependencyGraphProof [UPPER BOUND(ID), 0 ms] 3.43/1.57 (2) CpxTRS 3.43/1.57 (3) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 3.43/1.57 (4) CpxTRS 3.43/1.57 (5) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms] 3.43/1.57 (6) BOUNDS(1, 1) 3.43/1.57 3.43/1.57 3.43/1.57 ---------------------------------------- 3.43/1.57 3.43/1.57 (0) 3.43/1.57 Obligation: 3.43/1.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). 3.43/1.57 3.43/1.57 3.43/1.57 The TRS R consists of the following rules: 3.43/1.57 3.43/1.57 i(x, x) -> i(a, b) 3.43/1.57 g(x, x) -> g(a, b) 3.43/1.57 h(s(f(x))) -> h(f(x)) 3.43/1.57 f(s(x)) -> s(s(f(h(s(x))))) 3.43/1.57 f(g(s(x), y)) -> f(g(x, s(y))) 3.43/1.57 h(g(x, s(y))) -> h(g(s(x), y)) 3.43/1.57 h(i(x, y)) -> i(i(c, h(h(y))), x) 3.43/1.57 g(a, g(x, g(b, g(a, g(x, y))))) -> g(a, g(a, g(a, g(x, g(b, g(b, y)))))) 3.43/1.57 3.43/1.57 S is empty. 3.43/1.57 Rewrite Strategy: FULL 3.43/1.57 ---------------------------------------- 3.43/1.57 3.43/1.57 (1) DependencyGraphProof (UPPER BOUND(ID)) 3.43/1.57 The following rules are not reachable from basic terms in the dependency graph and can be removed: 3.43/1.57 3.43/1.57 g(a, g(x, g(b, g(a, g(x, y))))) -> g(a, g(a, g(a, g(x, g(b, g(b, y)))))) 3.43/1.57 3.43/1.57 ---------------------------------------- 3.43/1.57 3.43/1.57 (2) 3.43/1.57 Obligation: 3.43/1.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). 3.43/1.57 3.43/1.57 3.43/1.57 The TRS R consists of the following rules: 3.43/1.57 3.43/1.57 i(x, x) -> i(a, b) 3.43/1.57 g(x, x) -> g(a, b) 3.43/1.57 h(s(f(x))) -> h(f(x)) 3.43/1.57 f(s(x)) -> s(s(f(h(s(x))))) 3.43/1.57 f(g(s(x), y)) -> f(g(x, s(y))) 3.43/1.57 h(g(x, s(y))) -> h(g(s(x), y)) 3.43/1.57 h(i(x, y)) -> i(i(c, h(h(y))), x) 3.43/1.57 3.43/1.57 S is empty. 3.43/1.57 Rewrite Strategy: FULL 3.43/1.57 ---------------------------------------- 3.43/1.57 3.43/1.57 (3) NestedDefinedSymbolProof (UPPER BOUND(ID)) 3.43/1.57 The following defined symbols can occur below the 0th argument of f: h 3.43/1.57 The following defined symbols can occur below the 0th argument of h: h 3.43/1.57 3.43/1.57 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 3.43/1.57 h(s(f(x))) -> h(f(x)) 3.43/1.57 f(g(s(x), y)) -> f(g(x, s(y))) 3.43/1.57 h(g(x, s(y))) -> h(g(s(x), y)) 3.43/1.57 h(i(x, y)) -> i(i(c, h(h(y))), x) 3.43/1.57 3.43/1.57 ---------------------------------------- 3.43/1.57 3.43/1.57 (4) 3.43/1.57 Obligation: 3.43/1.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). 3.43/1.57 3.43/1.57 3.43/1.57 The TRS R consists of the following rules: 3.43/1.57 3.43/1.57 i(x, x) -> i(a, b) 3.43/1.57 g(x, x) -> g(a, b) 3.43/1.57 f(s(x)) -> s(s(f(h(s(x))))) 3.43/1.57 3.43/1.57 S is empty. 3.43/1.57 Rewrite Strategy: FULL 3.43/1.57 ---------------------------------------- 3.43/1.57 3.43/1.57 (5) NarrowingOnBasicTermsTerminatesProof (FINISHED) 3.43/1.57 Constant runtime complexity proven by termination of constructor-based narrowing. 3.43/1.57 3.43/1.57 The maximal most general narrowing sequences give rise to the following rewrite sequences: 3.43/1.57 3.43/1.57 g(x0, x0) ->^* g(a, b) 3.43/1.57 3.43/1.57 i(x0, x0) ->^* i(a, b) 3.43/1.57
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