details

property	value
status	complete
benchmark	z003.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.62763 seconds
cpu usage	3.65785
user time	3.48655
system time	0.171301
max virtual memory	1.8809892E7
max residence set size	261384.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(c(a(x1))) -> a(b(a(b(c(x1))))) b(x1) -> c(c(x1)) c(d(x1)) -> a(b(c(a(x1)))) a(a(x1)) -> a(c(b(a(x1)))) Q is empty. ---------------------------------------- (1) QTRS Reverse (EQUIVALENT) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(c(b(x1))) -> c(b(a(b(a(x1))))) b(x1) -> c(c(x1)) d(c(x1)) -> a(c(b(a(x1)))) a(a(x1)) -> a(b(c(a(x1)))) Q is empty. ---------------------------------------- (3) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R. The following rules were used to construct the certificate: a(c(b(x1))) -> c(b(a(b(a(x1))))) b(x1) -> c(c(x1)) d(c(x1)) -> a(c(b(a(x1)))) a(a(x1)) -> a(b(c(a(x1)))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 3, 4, 6, 8, 10, 12, 16, 17, 18, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 50, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 77, 78, 79, 80, 81, 82, 83 Node 3 is start node and node 4 is final node. Those nodes are connected through the following edges: * 3 to 6 labelled c_1(0)* 3 to 16 labelled a_1(0)* 3 to 22 labelled a_1(0)* 3 to 36 labelled c_1(1)* 4 to 4 labelled #_1(0)* 6 to 8 labelled b_1(0)* 6 to 4 labelled c_1(0)* 6 to 25 labelled c_1(1)* 8 to 10 labelled a_1(0)* 10 to 12 labelled b_1(0)* 10 to 26 labelled c_1(1)* 12 to 4 labelled a_1(0)* 12 to 29 labelled c_1(1)* 12 to 33 labelled a_1(1)* 16 to 17 labelled c_1(0)* 17 to 18 labelled b_1(0)* 17 to 27 labelled c_1(1)* 18 to 4 labelled a_1(0)* 18 to 29 labelled c_1(1)* 18 to 33 labelled a_1(1)* 22 to 23 labelled b_1(0)* 22 to 28 labelled c_1(1)* 23 to 24 labelled c_1(0)* 24 to 4 labelled a_1(0)* 24 to 29 labelled c_1(1)* 24 to 33 labelled a_1(1)* 25 to 8 labelled c_1(1)* 26 to 12 labelled c_1(1)* 27 to 18 labelled c_1(1)* 28 to 23 labelled c_1(1)* 29 to 30 labelled b_1(1)* 29 to 50 labelled c_1(2)* 30 to 31 labelled a_1(1)* 31 to 32 labelled b_1(1)* 31 to 55 labelled c_1(2)* 32 to 4 labelled a_1(1)* 32 to 29 labelled c_1(1)* 32 to 33 labelled a_1(1)* 33 to 34 labelled b_1(1)* 33 to 56 labelled c_1(2)* 34 to 35 labelled c_1(1)* 35 to 4 labelled a_1(1)* 35 to 29 labelled c_1(1)* 35 to 33 labelled a_1(1)* 36 to 37 labelled b_1(1)* 36 to 57 labelled c_1(2)* 37 to 38 labelled a_1(1)* 38 to 39 labelled b_1(1)* 38 to 58 labelled c_1(2)* 39 to 18 labelled a_1(1)* 39 to 33 labelled a_1(1)* 39 to 59 labelled a_1(2)* 39 to 62 labelled c_1(2)* 50 to 30 labelled c_1(2)* 55 to 32 labelled c_1(2)* 56 to 34 labelled c_1(2)* 57 to 37 labelled c_1(2)* 58 to 39 labelled c_1(2)* 59 to 60 labelled b_1(2)* 59 to 77 labelled c_1(3)* 60 to 61 labelled c_1(2)* 61 to 33 labelled a_1(2)* 62 to 63 labelled b_1(2)* 62 to 78 labelled c_1(3)* 63 to 64 labelled a_1(2)* 64 to 65 labelled b_1(2)* 64 to 79 labelled c_1(3)* 65 to 30 labelled a_1(2)* 65 to 80 labelled a_1(2)* 77 to 60 labelled c_1(3)* 78 to 63 labelled c_1(3)* 79 to 65 labelled c_1(3)* 80 to 81 labelled b_1(2)* 80 to 83 labelled c_1(3)* 81 to 82 labelled c_1(2)* 82 to 31 labelled a_1(2)* 83 to 81 labelled c_1(3) ---------------------------------------- (4) YES popout

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