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TRS_Innermost 2019-03-28 22.12 pair #432271416
details
property
value
status
complete
benchmark
#4.16.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n097.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.77506 seconds
cpu usage
3.56914
user time
3.39616
system time
0.172977
max virtual memory
1.8408888E7
max residence set size
236116.0
stage attributes
key
value
starexec-result
YES
output
3.42/1.73 YES 3.42/1.73 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.42/1.73 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.42/1.73 3.42/1.73 3.42/1.73 Termination w.r.t. Q of the given QTRS could be proven: 3.42/1.73 3.42/1.73 (0) QTRS 3.42/1.73 (1) DependencyPairsProof [EQUIVALENT, 0 ms] 3.42/1.73 (2) QDP 3.42/1.73 (3) DependencyGraphProof [EQUIVALENT, 0 ms] 3.42/1.73 (4) QDP 3.42/1.73 (5) UsableRulesProof [EQUIVALENT, 0 ms] 3.42/1.73 (6) QDP 3.42/1.73 (7) QReductionProof [EQUIVALENT, 0 ms] 3.42/1.73 (8) QDP 3.42/1.73 (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] 3.42/1.73 (10) YES 3.42/1.73 3.42/1.73 3.42/1.73 ---------------------------------------- 3.42/1.73 3.42/1.73 (0) 3.42/1.73 Obligation: 3.42/1.73 Q restricted rewrite system: 3.42/1.73 The TRS R consists of the following rules: 3.42/1.73 3.42/1.73 f(s(0), g(x)) -> f(x, g(x)) 3.42/1.73 g(s(x)) -> g(x) 3.42/1.73 3.42/1.73 The set Q consists of the following terms: 3.42/1.73 3.42/1.73 f(s(0), g(x0)) 3.42/1.73 g(s(x0)) 3.42/1.73 3.42/1.73 3.42/1.73 ---------------------------------------- 3.42/1.73 3.42/1.73 (1) DependencyPairsProof (EQUIVALENT) 3.42/1.73 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 3.42/1.73 ---------------------------------------- 3.42/1.73 3.42/1.73 (2) 3.42/1.73 Obligation: 3.42/1.73 Q DP problem: 3.42/1.73 The TRS P consists of the following rules: 3.42/1.73 3.42/1.73 F(s(0), g(x)) -> F(x, g(x)) 3.42/1.73 G(s(x)) -> G(x) 3.42/1.73 3.42/1.73 The TRS R consists of the following rules: 3.42/1.73 3.42/1.73 f(s(0), g(x)) -> f(x, g(x)) 3.42/1.73 g(s(x)) -> g(x) 3.42/1.73 3.42/1.73 The set Q consists of the following terms: 3.42/1.73 3.42/1.73 f(s(0), g(x0)) 3.42/1.73 g(s(x0)) 3.42/1.73 3.42/1.73 We have to consider all minimal (P,Q,R)-chains. 3.42/1.73 ---------------------------------------- 3.42/1.73 3.42/1.73 (3) DependencyGraphProof (EQUIVALENT) 3.42/1.73 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 3.42/1.73 ---------------------------------------- 3.42/1.73 3.42/1.73 (4) 3.42/1.73 Obligation: 3.42/1.73 Q DP problem: 3.42/1.73 The TRS P consists of the following rules: 3.42/1.73 3.42/1.73 G(s(x)) -> G(x) 3.42/1.73 3.42/1.73 The TRS R consists of the following rules: 3.42/1.73 3.42/1.73 f(s(0), g(x)) -> f(x, g(x)) 3.42/1.73 g(s(x)) -> g(x) 3.42/1.73 3.42/1.73 The set Q consists of the following terms: 3.42/1.73 3.42/1.73 f(s(0), g(x0)) 3.42/1.73 g(s(x0)) 3.42/1.73 3.42/1.73 We have to consider all minimal (P,Q,R)-chains. 3.42/1.73 ---------------------------------------- 3.42/1.73 3.42/1.73 (5) UsableRulesProof (EQUIVALENT) 3.42/1.73 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 3.42/1.73 ---------------------------------------- 3.42/1.73 3.42/1.73 (6) 3.42/1.73 Obligation: 3.42/1.73 Q DP problem: 3.42/1.73 The TRS P consists of the following rules: 3.42/1.73 3.42/1.73 G(s(x)) -> G(x) 3.42/1.73 3.42/1.73 R is empty. 3.42/1.73 The set Q consists of the following terms:
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