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SRS_Standard 2019-03-29 03.29 pair #432292069
details
property
value
status
complete
benchmark
z076.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n127.star.cs.uiowa.edu
space
Zantema_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
7.10187 seconds
cpu usage
13.8934
user time
13.1571
system time
0.736356
max virtual memory
1.18681384E8
max residence set size
1936904.0
stage attributes
key
value
starexec-result
YES
output
13.35/5.28 YES 13.35/5.29 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 13.35/5.29 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 13.35/5.29 13.35/5.29 13.35/5.29 Termination w.r.t. Q of the given QTRS could be proven: 13.35/5.29 13.35/5.29 (0) QTRS 13.35/5.29 (1) QTRSRRRProof [EQUIVALENT, 39 ms] 13.35/5.29 (2) QTRS 13.35/5.29 (3) Overlay + Local Confluence [EQUIVALENT, 3 ms] 13.35/5.29 (4) QTRS 13.35/5.29 (5) DependencyPairsProof [EQUIVALENT, 4 ms] 13.35/5.29 (6) QDP 13.35/5.29 (7) DependencyGraphProof [EQUIVALENT, 3 ms] 13.35/5.29 (8) QDP 13.35/5.29 (9) UsableRulesProof [EQUIVALENT, 0 ms] 13.35/5.29 (10) QDP 13.35/5.29 (11) QReductionProof [EQUIVALENT, 0 ms] 13.35/5.29 (12) QDP 13.35/5.29 (13) QDPOrderProof [EQUIVALENT, 9 ms] 13.35/5.29 (14) QDP 13.35/5.29 (15) PisEmptyProof [EQUIVALENT, 0 ms] 13.35/5.29 (16) YES 13.35/5.29 13.35/5.29 13.35/5.29 ---------------------------------------- 13.35/5.29 13.35/5.29 (0) 13.35/5.29 Obligation: 13.35/5.29 Q restricted rewrite system: 13.35/5.29 The TRS R consists of the following rules: 13.35/5.29 13.35/5.29 f(s(x1)) -> s(s(f(p(s(x1))))) 13.35/5.29 f(0(x1)) -> 0(x1) 13.35/5.29 p(s(x1)) -> x1 13.35/5.29 13.35/5.29 Q is empty. 13.35/5.29 13.35/5.29 ---------------------------------------- 13.35/5.29 13.35/5.29 (1) QTRSRRRProof (EQUIVALENT) 13.35/5.29 Used ordering: 13.35/5.29 Polynomial interpretation [POLO]: 13.35/5.29 13.35/5.29 POL(0(x_1)) = x_1 13.35/5.29 POL(f(x_1)) = 1 + x_1 13.35/5.29 POL(p(x_1)) = x_1 13.35/5.29 POL(s(x_1)) = x_1 13.35/5.29 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 13.35/5.29 13.35/5.29 f(0(x1)) -> 0(x1) 13.35/5.29 13.35/5.29 13.35/5.29 13.35/5.29 13.35/5.29 ---------------------------------------- 13.35/5.29 13.35/5.29 (2) 13.35/5.29 Obligation: 13.35/5.29 Q restricted rewrite system: 13.35/5.29 The TRS R consists of the following rules: 13.35/5.29 13.35/5.29 f(s(x1)) -> s(s(f(p(s(x1))))) 13.35/5.29 p(s(x1)) -> x1 13.35/5.29 13.35/5.29 Q is empty. 13.35/5.29 13.35/5.29 ---------------------------------------- 13.35/5.29 13.35/5.29 (3) Overlay + Local Confluence (EQUIVALENT) 13.35/5.29 The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. 13.35/5.29 ---------------------------------------- 13.35/5.29 13.35/5.29 (4) 13.35/5.29 Obligation: 13.35/5.29 Q restricted rewrite system: 13.35/5.29 The TRS R consists of the following rules: 13.35/5.29 13.35/5.29 f(s(x1)) -> s(s(f(p(s(x1))))) 13.35/5.29 p(s(x1)) -> x1 13.35/5.29 13.35/5.29 The set Q consists of the following terms: 13.35/5.29 13.35/5.29 f(s(x0)) 13.35/5.29 p(s(x0)) 13.35/5.29 13.35/5.29 13.35/5.29 ---------------------------------------- 13.35/5.29 13.35/5.29 (5) DependencyPairsProof (EQUIVALENT) 13.35/5.29 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 13.35/5.29 ---------------------------------------- 13.35/5.29 13.35/5.29 (6) 13.35/5.29 Obligation: 13.35/5.29 Q DP problem: 13.35/5.29 The TRS P consists of the following rules: 13.35/5.29 13.35/5.29 F(s(x1)) -> F(p(s(x1)))
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