details

property	value
status	complete
benchmark	size-11-alpha-3-num-16.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n012.star.cs.uiowa.edu
space	Waldmann_07_size11

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.13515 seconds
cpu usage	9.18655
user time	8.68609
system time	0.500463
max virtual memory	1.980776E7
max residence set size	1393344.0

stage attributes

key	value
starexec-result	YES

output

8.53/2.98 YES 9.08/3.08 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 9.08/3.08 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.08/3.08 9.08/3.08 9.08/3.08 Termination w.r.t. Q of the given QTRS could be proven: 9.08/3.08 9.08/3.08 (0) QTRS 9.08/3.08 (1) QTRS Reverse [EQUIVALENT, 0 ms] 9.08/3.08 (2) QTRS 9.08/3.08 (3) DependencyPairsProof [EQUIVALENT, 1 ms] 9.08/3.08 (4) QDP 9.08/3.08 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 9.08/3.08 (6) QDP 9.08/3.08 (7) QDPSizeChangeProof [EQUIVALENT, 2 ms] 9.08/3.08 (8) YES 9.08/3.08 9.08/3.08 9.08/3.08 ---------------------------------------- 9.08/3.08 9.08/3.08 (0) 9.08/3.08 Obligation: 9.08/3.08 Q restricted rewrite system: 9.08/3.08 The TRS R consists of the following rules: 9.08/3.08 9.08/3.08 a(x1) -> x1 9.08/3.08 a(a(x1)) -> a(b(c(x1))) 9.08/3.08 c(b(x1)) -> a(c(a(x1))) 9.08/3.08 9.08/3.08 Q is empty. 9.08/3.08 9.08/3.08 ---------------------------------------- 9.08/3.08 9.08/3.08 (1) QTRS Reverse (EQUIVALENT) 9.08/3.08 We applied the QTRS Reverse Processor [REVERSE]. 9.08/3.08 ---------------------------------------- 9.08/3.08 9.08/3.08 (2) 9.08/3.08 Obligation: 9.08/3.08 Q restricted rewrite system: 9.08/3.08 The TRS R consists of the following rules: 9.08/3.08 9.08/3.08 a(x1) -> x1 9.08/3.08 a(a(x1)) -> c(b(a(x1))) 9.08/3.08 b(c(x1)) -> a(c(a(x1))) 9.08/3.08 9.08/3.08 Q is empty. 9.08/3.08 9.08/3.08 ---------------------------------------- 9.08/3.08 9.08/3.08 (3) DependencyPairsProof (EQUIVALENT) 9.08/3.08 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 9.08/3.08 ---------------------------------------- 9.08/3.08 9.08/3.08 (4) 9.08/3.08 Obligation: 9.08/3.08 Q DP problem: 9.08/3.08 The TRS P consists of the following rules: 9.08/3.08 9.08/3.08 A(a(x1)) -> B(a(x1)) 9.08/3.08 B(c(x1)) -> A(c(a(x1))) 9.08/3.08 B(c(x1)) -> A(x1) 9.08/3.08 9.08/3.08 The TRS R consists of the following rules: 9.08/3.08 9.08/3.08 a(x1) -> x1 9.08/3.08 a(a(x1)) -> c(b(a(x1))) 9.08/3.08 b(c(x1)) -> a(c(a(x1))) 9.08/3.08 9.08/3.08 Q is empty. 9.08/3.08 We have to consider all minimal (P,Q,R)-chains. 9.08/3.08 ---------------------------------------- 9.08/3.08 9.08/3.08 (5) DependencyGraphProof (EQUIVALENT) 9.08/3.08 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 9.08/3.08 ---------------------------------------- 9.08/3.08 9.08/3.08 (6) 9.08/3.08 Obligation: 9.08/3.08 Q DP problem: 9.08/3.08 The TRS P consists of the following rules: 9.08/3.08 9.08/3.08 B(c(x1)) -> A(x1) 9.08/3.08 A(a(x1)) -> B(a(x1)) 9.08/3.08 9.08/3.08 The TRS R consists of the following rules: 9.08/3.08 9.08/3.08 a(x1) -> x1 9.08/3.08 a(a(x1)) -> c(b(a(x1))) 9.08/3.08 b(c(x1)) -> a(c(a(x1))) 9.08/3.08 9.08/3.08 Q is empty. 9.08/3.08 We have to consider all minimal (P,Q,R)-chains. 9.08/3.08 ---------------------------------------- 9.08/3.08 9.08/3.08 (7) QDPSizeChangeProof (EQUIVALENT) 9.08/3.08 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 9.08/3.08 9.08/3.08 From the DPs we obtained the following set of size-change graphs: 9.08/3.08 *A(a(x1)) -> B(a(x1)) popout

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