details

property	value
status	complete
benchmark	size-12-alpha-3-num-281.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n047.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	9.63603 seconds
cpu usage	33.7154
user time	32.4255
system time	1.28994
max virtual memory	4.1953192E7
max residence set size	3730800.0

stage attributes

key	value
starexec-result	YES

output

33.32/9.48 YES 33.36/9.51 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 33.36/9.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 33.36/9.51 33.36/9.51 33.36/9.51 Termination w.r.t. Q of the given QTRS could be proven: 33.36/9.51 33.36/9.51 (0) QTRS 33.36/9.51 (1) DependencyPairsProof [EQUIVALENT, 29 ms] 33.36/9.51 (2) QDP 33.36/9.51 (3) DependencyGraphProof [EQUIVALENT, 0 ms] 33.36/9.51 (4) AND 33.36/9.51 (5) QDP 33.36/9.51 (6) UsableRulesProof [EQUIVALENT, 1 ms] 33.36/9.51 (7) QDP 33.36/9.51 (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] 33.36/9.51 (9) YES 33.36/9.51 (10) QDP 33.36/9.51 (11) QDPOrderProof [EQUIVALENT, 138 ms] 33.36/9.51 (12) QDP 33.36/9.51 (13) QDPOrderProof [EQUIVALENT, 0 ms] 33.36/9.51 (14) QDP 33.36/9.51 (15) PisEmptyProof [EQUIVALENT, 0 ms] 33.36/9.51 (16) YES 33.36/9.51 33.36/9.51 33.36/9.51 ---------------------------------------- 33.36/9.51 33.36/9.51 (0) 33.36/9.51 Obligation: 33.36/9.51 Q restricted rewrite system: 33.36/9.51 The TRS R consists of the following rules: 33.36/9.51 33.36/9.51 a(x1) -> x1 33.36/9.51 a(b(x1)) -> c(b(a(a(x1)))) 33.36/9.51 b(x1) -> c(x1) 33.36/9.51 c(c(x1)) -> b(x1) 33.36/9.51 33.36/9.51 Q is empty. 33.36/9.51 33.36/9.51 ---------------------------------------- 33.36/9.51 33.36/9.51 (1) DependencyPairsProof (EQUIVALENT) 33.36/9.51 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 33.36/9.51 ---------------------------------------- 33.36/9.51 33.36/9.51 (2) 33.36/9.51 Obligation: 33.36/9.51 Q DP problem: 33.36/9.51 The TRS P consists of the following rules: 33.36/9.51 33.36/9.51 A(b(x1)) -> C(b(a(a(x1)))) 33.36/9.51 A(b(x1)) -> B(a(a(x1))) 33.36/9.51 A(b(x1)) -> A(a(x1)) 33.36/9.51 A(b(x1)) -> A(x1) 33.36/9.51 B(x1) -> C(x1) 33.36/9.51 C(c(x1)) -> B(x1) 33.36/9.51 33.36/9.51 The TRS R consists of the following rules: 33.36/9.51 33.36/9.51 a(x1) -> x1 33.36/9.51 a(b(x1)) -> c(b(a(a(x1)))) 33.36/9.51 b(x1) -> c(x1) 33.36/9.51 c(c(x1)) -> b(x1) 33.36/9.51 33.36/9.51 Q is empty. 33.36/9.51 We have to consider all minimal (P,Q,R)-chains. 33.36/9.51 ---------------------------------------- 33.36/9.51 33.36/9.51 (3) DependencyGraphProof (EQUIVALENT) 33.36/9.51 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 2 less nodes. 33.36/9.51 ---------------------------------------- 33.36/9.51 33.36/9.51 (4) 33.36/9.51 Complex Obligation (AND) 33.36/9.51 33.36/9.51 ---------------------------------------- 33.36/9.51 33.36/9.51 (5) 33.36/9.51 Obligation: 33.36/9.51 Q DP problem: 33.36/9.51 The TRS P consists of the following rules: 33.36/9.51 33.36/9.51 C(c(x1)) -> B(x1) 33.36/9.51 B(x1) -> C(x1) 33.36/9.51 33.36/9.51 The TRS R consists of the following rules: 33.36/9.51 33.36/9.51 a(x1) -> x1 33.36/9.51 a(b(x1)) -> c(b(a(a(x1)))) 33.36/9.51 b(x1) -> c(x1) 33.36/9.51 c(c(x1)) -> b(x1) 33.36/9.51 33.36/9.51 Q is empty. 33.36/9.51 We have to consider all minimal (P,Q,R)-chains. 33.36/9.51 ---------------------------------------- 33.36/9.51 33.36/9.51 (6) UsableRulesProof (EQUIVALENT) 33.36/9.51 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. 33.36/9.51 ---------------------------------------- popout

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