details

property	value
status	complete
benchmark	size-12-alpha-3-num-495.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n167.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	8.89711 seconds
cpu usage	31.602
user time	30.2643
system time	1.3377
max virtual memory	4.1971396E7
max residence set size	3889032.0

stage attributes

key	value
starexec-result	YES

output

31.01/8.75 YES 31.21/8.81 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 31.21/8.81 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 31.21/8.81 31.21/8.81 31.21/8.81 Termination w.r.t. Q of the given QTRS could be proven: 31.21/8.81 31.21/8.81 (0) QTRS 31.21/8.81 (1) DependencyPairsProof [EQUIVALENT, 4 ms] 31.21/8.81 (2) QDP 31.21/8.81 (3) DependencyGraphProof [EQUIVALENT, 0 ms] 31.21/8.81 (4) AND 31.21/8.81 (5) QDP 31.21/8.81 (6) UsableRulesProof [EQUIVALENT, 0 ms] 31.21/8.81 (7) QDP 31.21/8.81 (8) QDPSizeChangeProof [EQUIVALENT, 2 ms] 31.21/8.81 (9) YES 31.21/8.81 (10) QDP 31.21/8.81 (11) QDPOrderProof [EQUIVALENT, 108 ms] 31.21/8.81 (12) QDP 31.21/8.81 (13) QDPOrderProof [EQUIVALENT, 0 ms] 31.21/8.81 (14) QDP 31.21/8.81 (15) PisEmptyProof [EQUIVALENT, 0 ms] 31.21/8.81 (16) YES 31.21/8.81 31.21/8.81 31.21/8.81 ---------------------------------------- 31.21/8.81 31.21/8.81 (0) 31.21/8.81 Obligation: 31.21/8.81 Q restricted rewrite system: 31.21/8.81 The TRS R consists of the following rules: 31.21/8.81 31.21/8.81 a(a(x1)) -> b(x1) 31.21/8.81 b(c(x1)) -> a(x1) 31.21/8.81 c(b(x1)) -> b(c(c(a(x1)))) 31.21/8.81 31.21/8.81 Q is empty. 31.21/8.81 31.21/8.81 ---------------------------------------- 31.21/8.81 31.21/8.81 (1) DependencyPairsProof (EQUIVALENT) 31.21/8.81 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 31.21/8.81 ---------------------------------------- 31.21/8.81 31.21/8.81 (2) 31.21/8.81 Obligation: 31.21/8.81 Q DP problem: 31.21/8.81 The TRS P consists of the following rules: 31.21/8.81 31.21/8.81 A(a(x1)) -> B(x1) 31.21/8.81 B(c(x1)) -> A(x1) 31.21/8.81 C(b(x1)) -> B(c(c(a(x1)))) 31.21/8.81 C(b(x1)) -> C(c(a(x1))) 31.21/8.81 C(b(x1)) -> C(a(x1)) 31.21/8.81 C(b(x1)) -> A(x1) 31.21/8.81 31.21/8.81 The TRS R consists of the following rules: 31.21/8.81 31.21/8.81 a(a(x1)) -> b(x1) 31.21/8.81 b(c(x1)) -> a(x1) 31.21/8.81 c(b(x1)) -> b(c(c(a(x1)))) 31.21/8.81 31.21/8.81 Q is empty. 31.21/8.81 We have to consider all minimal (P,Q,R)-chains. 31.21/8.81 ---------------------------------------- 31.21/8.81 31.21/8.81 (3) DependencyGraphProof (EQUIVALENT) 31.21/8.81 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 2 less nodes. 31.21/8.81 ---------------------------------------- 31.21/8.81 31.21/8.81 (4) 31.21/8.81 Complex Obligation (AND) 31.21/8.81 31.21/8.81 ---------------------------------------- 31.21/8.81 31.21/8.81 (5) 31.21/8.81 Obligation: 31.21/8.81 Q DP problem: 31.21/8.81 The TRS P consists of the following rules: 31.21/8.81 31.21/8.81 B(c(x1)) -> A(x1) 31.21/8.81 A(a(x1)) -> B(x1) 31.21/8.81 31.21/8.81 The TRS R consists of the following rules: 31.21/8.81 31.21/8.81 a(a(x1)) -> b(x1) 31.21/8.81 b(c(x1)) -> a(x1) 31.21/8.81 c(b(x1)) -> b(c(c(a(x1)))) 31.21/8.81 31.21/8.81 Q is empty. 31.21/8.81 We have to consider all minimal (P,Q,R)-chains. 31.21/8.81 ---------------------------------------- 31.21/8.81 31.21/8.81 (6) UsableRulesProof (EQUIVALENT) 31.21/8.81 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. 31.21/8.81 ---------------------------------------- 31.21/8.81 31.21/8.81 (7) 31.21/8.81 Obligation: popout

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all output return to SRS_Standard 2019-03-29 03.29