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SRS_Standard 2019-03-29 03.29 pair #432295075
details
property
value
status
complete
benchmark
03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n118.star.cs.uiowa.edu
space
Zantema_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
42.341 seconds
cpu usage
162.775
user time
159.745
system time
3.03013
max virtual memory
8.3771024E7
max residence set size
5341936.0
stage attributes
key
value
starexec-result
YES
output
162.18/42.18 YES 162.55/42.25 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 162.55/42.25 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 162.55/42.25 162.55/42.25 162.55/42.25 Termination w.r.t. Q of the given QTRS could be proven: 162.55/42.25 162.55/42.25 (0) QTRS 162.55/42.25 (1) DependencyPairsProof [EQUIVALENT, 32 ms] 162.55/42.25 (2) QDP 162.55/42.25 (3) DependencyGraphProof [EQUIVALENT, 1 ms] 162.55/42.25 (4) AND 162.55/42.25 (5) QDP 162.55/42.25 (6) UsableRulesProof [EQUIVALENT, 0 ms] 162.55/42.25 (7) QDP 162.55/42.25 (8) QDPSizeChangeProof [EQUIVALENT, 1 ms] 162.55/42.25 (9) YES 162.55/42.25 (10) QDP 162.55/42.25 (11) QDPOrderProof [EQUIVALENT, 30 ms] 162.55/42.25 (12) QDP 162.55/42.25 (13) QDPOrderProof [EQUIVALENT, 2671 ms] 162.55/42.25 (14) QDP 162.55/42.25 (15) QDPOrderProof [EQUIVALENT, 3127 ms] 162.55/42.25 (16) QDP 162.55/42.25 (17) PisEmptyProof [EQUIVALENT, 0 ms] 162.55/42.25 (18) YES 162.55/42.25 162.55/42.25 162.55/42.25 ---------------------------------------- 162.55/42.25 162.55/42.25 (0) 162.55/42.25 Obligation: 162.55/42.25 Q restricted rewrite system: 162.55/42.25 The TRS R consists of the following rules: 162.55/42.25 162.55/42.25 a(a(b(b(x1)))) -> b(b(b(a(a(a(x1)))))) 162.55/42.25 a(c(x1)) -> c(a(x1)) 162.55/42.25 c(b(x1)) -> b(c(x1)) 162.55/42.25 162.55/42.25 Q is empty. 162.55/42.25 162.55/42.25 ---------------------------------------- 162.55/42.25 162.55/42.25 (1) DependencyPairsProof (EQUIVALENT) 162.55/42.25 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 162.55/42.25 ---------------------------------------- 162.55/42.25 162.55/42.25 (2) 162.55/42.25 Obligation: 162.55/42.25 Q DP problem: 162.55/42.25 The TRS P consists of the following rules: 162.55/42.25 162.55/42.25 A(a(b(b(x1)))) -> A(a(a(x1))) 162.55/42.25 A(a(b(b(x1)))) -> A(a(x1)) 162.55/42.25 A(a(b(b(x1)))) -> A(x1) 162.55/42.25 A(c(x1)) -> C(a(x1)) 162.55/42.25 A(c(x1)) -> A(x1) 162.55/42.25 C(b(x1)) -> C(x1) 162.55/42.25 162.55/42.25 The TRS R consists of the following rules: 162.55/42.25 162.55/42.25 a(a(b(b(x1)))) -> b(b(b(a(a(a(x1)))))) 162.55/42.25 a(c(x1)) -> c(a(x1)) 162.55/42.25 c(b(x1)) -> b(c(x1)) 162.55/42.25 162.55/42.25 Q is empty. 162.55/42.25 We have to consider all minimal (P,Q,R)-chains. 162.55/42.25 ---------------------------------------- 162.55/42.25 162.55/42.25 (3) DependencyGraphProof (EQUIVALENT) 162.55/42.25 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node. 162.55/42.25 ---------------------------------------- 162.55/42.25 162.55/42.25 (4) 162.55/42.25 Complex Obligation (AND) 162.55/42.25 162.55/42.25 ---------------------------------------- 162.55/42.25 162.55/42.25 (5) 162.55/42.25 Obligation: 162.55/42.25 Q DP problem: 162.55/42.25 The TRS P consists of the following rules: 162.55/42.25 162.55/42.25 C(b(x1)) -> C(x1) 162.55/42.25 162.55/42.25 The TRS R consists of the following rules: 162.55/42.25 162.55/42.25 a(a(b(b(x1)))) -> b(b(b(a(a(a(x1)))))) 162.55/42.25 a(c(x1)) -> c(a(x1)) 162.55/42.25 c(b(x1)) -> b(c(x1)) 162.55/42.25 162.55/42.25 Q is empty. 162.55/42.25 We have to consider all minimal (P,Q,R)-chains. 162.55/42.25 ---------------------------------------- 162.55/42.25 162.55/42.25 (6) UsableRulesProof (EQUIVALENT) 162.55/42.25 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 162.55/42.25 ---------------------------------------- 162.55/42.25 162.55/42.25 (7)
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