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TRS_Innermost 2019-03-28 22.12 pair #432271008
details
property
value
status
complete
benchmark
Ex23_Luc06_iGM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n152.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.94099 seconds
cpu usage
3.75879
user time
3.5875
system time
0.171293
max virtual memory
1.89414E7
max residence set size
276056.0
stage attributes
key
value
starexec-result
YES
output
3.45/1.72 YES 3.68/1.74 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 3.68/1.74 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.68/1.74 3.68/1.74 3.68/1.74 Termination w.r.t. Q of the given QTRS could be proven: 3.68/1.74 3.68/1.74 (0) QTRS 3.68/1.74 (1) RFCMatchBoundsTRSProof [EQUIVALENT, 35 ms] 3.68/1.74 (2) YES 3.68/1.74 3.68/1.74 3.68/1.74 ---------------------------------------- 3.68/1.74 3.68/1.74 (0) 3.68/1.74 Obligation: 3.68/1.74 Q restricted rewrite system: 3.68/1.74 The TRS R consists of the following rules: 3.68/1.74 3.68/1.74 active(f(f(a))) -> mark(c(f(g(f(a))))) 3.68/1.74 mark(f(X)) -> active(f(mark(X))) 3.68/1.74 mark(a) -> active(a) 3.68/1.74 mark(c(X)) -> active(c(X)) 3.68/1.74 mark(g(X)) -> active(g(mark(X))) 3.68/1.74 f(mark(X)) -> f(X) 3.68/1.74 f(active(X)) -> f(X) 3.68/1.74 c(mark(X)) -> c(X) 3.68/1.74 c(active(X)) -> c(X) 3.68/1.74 g(mark(X)) -> g(X) 3.68/1.74 g(active(X)) -> g(X) 3.68/1.74 3.68/1.74 The set Q consists of the following terms: 3.68/1.74 3.68/1.74 active(f(f(a))) 3.68/1.74 mark(f(x0)) 3.68/1.74 mark(a) 3.68/1.74 mark(c(x0)) 3.68/1.74 mark(g(x0)) 3.68/1.74 f(mark(x0)) 3.68/1.74 f(active(x0)) 3.68/1.74 c(mark(x0)) 3.68/1.74 c(active(x0)) 3.68/1.74 g(mark(x0)) 3.68/1.74 g(active(x0)) 3.68/1.74 3.68/1.74 3.68/1.74 ---------------------------------------- 3.68/1.74 3.68/1.74 (1) RFCMatchBoundsTRSProof (EQUIVALENT) 3.68/1.74 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R. 3.68/1.74 The following rules were used to construct the certificate: 3.68/1.74 3.68/1.74 active(f(f(a))) -> mark(c(f(g(f(a))))) 3.68/1.74 mark(f(X)) -> active(f(mark(X))) 3.68/1.74 mark(a) -> active(a) 3.68/1.74 mark(c(X)) -> active(c(X)) 3.68/1.74 mark(g(X)) -> active(g(mark(X))) 3.68/1.74 f(mark(X)) -> f(X) 3.68/1.74 f(active(X)) -> f(X) 3.68/1.74 c(mark(X)) -> c(X) 3.68/1.74 c(active(X)) -> c(X) 3.68/1.74 g(mark(X)) -> g(X) 3.68/1.74 g(active(X)) -> g(X) 3.68/1.74 3.68/1.74 The certificate found is represented by the following graph. 3.68/1.74 The certificate consists of the following enumerated nodes: 3.68/1.74 1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 38, 39, 40, 41, 42, 57 3.68/1.74 3.68/1.74 Node 1 is start node and node 2 is final node. 3.68/1.74 3.68/1.74 Those nodes are connected through the following edges: 3.68/1.74 3.68/1.74 * 1 to 5 labelled mark_1(0)* 1 to 10 labelled active_1(0)* 1 to 9 labelled active_1(0)* 1 to 12 labelled active_1(0)* 1 to 2 labelled f_1(0), c_1(0), g_1(0), f_1(1), c_1(1), g_1(1)* 1 to 23 labelled active_1(1)* 1 to 28 labelled mark_1(1)* 1 to 33 labelled active_1(2)* 2 to 2 labelled #_1(0)* 5 to 6 labelled c_1(0)* 6 to 7 labelled f_1(0)* 7 to 8 labelled g_1(0)* 8 to 9 labelled f_1(0)* 9 to 2 labelled a(0)* 10 to 11 labelled f_1(0)* 10 to 2 labelled c_1(0), c_1(1), f_1(1)* 10 to 24 labelled f_1(1)* 10 to 10 labelled f_1(1)* 10 to 26 labelled f_1(1)* 10 to 28 labelled f_1(1)* 10 to 33 labelled f_1(1)* 10 to 38 labelled f_1(1)* 10 to 57 labelled f_1(1)* 11 to 2 labelled mark_1(0)* 11 to 24 labelled active_1(1)* 11 to 10 labelled active_1(1)* 11 to 26 labelled active_1(1)* 11 to 28 labelled mark_1(1)* 11 to 33 labelled active_1(2)* 11 to 38 labelled mark_1(2)* 11 to 57 labelled active_1(3)* 12 to 13 labelled g_1(0)* 12 to 2 labelled g_1(1)* 12 to 24 labelled g_1(1)* 12 to 10 labelled g_1(1)* 12 to 26 labelled g_1(1)* 12 to 28 labelled g_1(1)* 12 to 33 labelled g_1(1)* 12 to 38 labelled g_1(1)* 12 to 57 labelled g_1(1)* 13 to 2 labelled mark_1(0)* 13 to 24 labelled active_1(1)* 13 to 10 labelled active_1(1)* 13 to 26 labelled active_1(1)* 13 to 28 labelled mark_1(1)* 13 to 33 labelled active_1(2)* 13 to 38 labelled mark_1(2)* 13 to 57 labelled active_1(3)* 23 to 6 labelled c_1(1)* 24 to 25 labelled f_1(1)* 24 to 2 labelled a(1), f_1(2), f_1(1)* 24 to 24 labelled f_1(2)* 24 to 10 labelled f_1(2)* 24 to 26 labelled f_1(2)* 24 to 28 labelled f_1(2)* 24 to 38 labelled f_1(2)* 24 to 33 labelled f_1(2)* 24 to 57 labelled f_1(2)* 25 to 2 labelled mark_1(1)* 25 to 24 labelled active_1(1)* 25 to 10 labelled active_1(1)* 25 to 26 labelled active_1(1)* 25 to 28 labelled mark_1(1)* 25 to 38 labelled mark_1(2)* 25 to 33 labelled active_1(2)* 25 to 57 labelled active_1(3)* 26 to 27 labelled g_1(1)* 26 to 2 labelled g_1(2), g_1(1)* 26 to 24 labelled g_1(2)* 26 to 10 labelled g_1(2)* 26 to 26 labelled g_1(2)* 26 to 28 labelled g_1(2)* 26 to 38 labelled g_1(2)* 26 to 33 labelled g_1(2)* 26 to 57 labelled g_1(2)* 27 to 2 labelled mark_1(1)* 27 to 24 labelled active_1(1)* 27 to 10 labelled active_1(1)* 27 to 26 labelled active_1(1)* 27 to 28 labelled mark_1(1)* 27 to 38 labelled mark_1(2)* 27 to 33 labelled active_1(2)* 27 to 57 labelled active_1(3)* 28 to 29 labelled c_1(1)* 29 to 30 labelled f_1(1)* 30 to 31 labelled g_1(1)* 31 to 32 labelled f_1(1)* 32 to 2 labelled a(1)* 33 to 29 labelled c_1(2)* 38 to 39 labelled c_1(2)* 39 to 40 labelled f_1(2)* 40 to 41 labelled g_1(2)* 41 to 42 labelled f_1(2)* 42 to 2 labelled a(2)* 57 to 39 labelled c_1(3) 3.68/1.74 3.68/1.74 3.68/1.74 ---------------------------------------- 3.68/1.74 3.68/1.74 (2) 3.68/1.74 YES 3.74/2.94 EOF
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