Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS_Innermost 2019-03-28 22.12 pair #432271170
details
property
value
status
complete
benchmark
Ex15_Luc06_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n166.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.80338 seconds
cpu usage
4.07846
user time
3.89224
system time
0.186213
max virtual memory
1.8873804E7
max residence set size
300004.0
stage attributes
key
value
starexec-result
YES
output
3.76/1.74 YES 3.76/1.76 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.76/1.76 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.76/1.76 3.76/1.76 3.76/1.76 Termination w.r.t. Q of the given QTRS could be proven: 3.76/1.76 3.76/1.76 (0) QTRS 3.76/1.76 (1) QTRS Reverse [SOUND, 0 ms] 3.76/1.76 (2) QTRS 3.76/1.76 (3) RFCMatchBoundsTRSProof [EQUIVALENT, 24 ms] 3.76/1.76 (4) YES 3.76/1.76 3.76/1.76 3.76/1.76 ---------------------------------------- 3.76/1.76 3.76/1.76 (0) 3.76/1.76 Obligation: 3.76/1.76 Q restricted rewrite system: 3.76/1.76 The TRS R consists of the following rules: 3.76/1.76 3.76/1.76 active(f(f(a))) -> mark(f(g(f(a)))) 3.76/1.76 active(g(X)) -> g(active(X)) 3.76/1.76 g(mark(X)) -> mark(g(X)) 3.76/1.76 proper(f(X)) -> f(proper(X)) 3.76/1.76 proper(a) -> ok(a) 3.76/1.76 proper(g(X)) -> g(proper(X)) 3.76/1.76 f(ok(X)) -> ok(f(X)) 3.76/1.76 g(ok(X)) -> ok(g(X)) 3.76/1.76 top(mark(X)) -> top(proper(X)) 3.76/1.76 top(ok(X)) -> top(active(X)) 3.76/1.76 3.76/1.76 The set Q consists of the following terms: 3.76/1.76 3.76/1.76 active(f(f(a))) 3.76/1.76 active(g(x0)) 3.76/1.76 g(mark(x0)) 3.76/1.76 proper(f(x0)) 3.76/1.76 proper(a) 3.76/1.76 proper(g(x0)) 3.76/1.76 f(ok(x0)) 3.76/1.76 g(ok(x0)) 3.76/1.76 top(mark(x0)) 3.76/1.76 top(ok(x0)) 3.76/1.76 3.76/1.76 3.76/1.76 ---------------------------------------- 3.76/1.76 3.76/1.76 (1) QTRS Reverse (SOUND) 3.76/1.76 We applied the QTRS Reverse Processor [REVERSE]. 3.76/1.76 ---------------------------------------- 3.76/1.76 3.76/1.76 (2) 3.76/1.76 Obligation: 3.76/1.76 Q restricted rewrite system: 3.76/1.76 The TRS R consists of the following rules: 3.76/1.76 3.76/1.76 a'(f(f(active(x)))) -> a'(f(g(f(mark(x))))) 3.76/1.76 g(active(X)) -> active(g(X)) 3.76/1.76 mark(g(X)) -> g(mark(X)) 3.76/1.76 f(proper(X)) -> proper(f(X)) 3.76/1.76 a'(proper(x)) -> a'(ok(x)) 3.76/1.76 g(proper(X)) -> proper(g(X)) 3.76/1.76 ok(f(X)) -> f(ok(X)) 3.76/1.76 ok(g(X)) -> g(ok(X)) 3.76/1.76 mark(top(X)) -> proper(top(X)) 3.76/1.76 ok(top(X)) -> active(top(X)) 3.76/1.76 3.76/1.76 Q is empty. 3.76/1.76 3.76/1.76 ---------------------------------------- 3.76/1.76 3.76/1.76 (3) RFCMatchBoundsTRSProof (EQUIVALENT) 3.76/1.76 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 6. This implies Q-termination of R. 3.76/1.76 The following rules were used to construct the certificate: 3.76/1.76 3.76/1.76 a'(f(f(active(x)))) -> a'(f(g(f(mark(x))))) 3.76/1.76 g(active(X)) -> active(g(X)) 3.76/1.76 mark(g(X)) -> g(mark(X)) 3.76/1.76 f(proper(X)) -> proper(f(X)) 3.76/1.76 a'(proper(x)) -> a'(ok(x)) 3.76/1.76 g(proper(X)) -> proper(g(X)) 3.76/1.76 ok(f(X)) -> f(ok(X)) 3.76/1.76 ok(g(X)) -> g(ok(X)) 3.76/1.76 mark(top(X)) -> proper(top(X)) 3.76/1.76 ok(top(X)) -> active(top(X)) 3.76/1.76 3.76/1.76 The certificate found is represented by the following graph. 3.76/1.76 The certificate consists of the following enumerated nodes: 3.76/1.76 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 78, 79, 80, 81, 82, 83, 84, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 102 3.76/1.76 3.76/1.76 Node 52 is start node and node 53 is final node. 3.76/1.76 3.76/1.76 Those nodes are connected through the following edges: 3.76/1.76 3.76/1.76 * 52 to 54 labelled a'_1(0), f_1(0), g_1(0)* 52 to 58 labelled active_1(0), proper_1(0)* 52 to 57 labelled g_1(0)* 52 to 59 labelled proper_1(0)* 52 to 65 labelled active_1(1), proper_1(1)* 52 to 69 labelled a'_1(1)* 52 to 87 labelled a'_1(2)* 53 to 53 labelled #_1(0)* 54 to 55 labelled f_1(0)* 54 to 53 labelled ok_1(0)* 54 to 60 labelled f_1(1), g_1(1)* 54 to 61 labelled active_1(1)* 54 to 67 labelled active_1(2)* 54 to 73 labelled proper_1(1)* 55 to 56 labelled g_1(0)* 55 to 68 labelled proper_1(1)* 56 to 57 labelled f_1(0)* 56 to 66 labelled proper_1(1)* 57 to 53 labelled mark_1(0)* 57 to 62 labelled g_1(1)* 57 to 61 labelled proper_1(1)* 57 to 67 labelled proper_1(2)* 58 to 53 labelled g_1(0), top_1(0)* 58 to 63 labelled active_1(1), proper_1(1)* 59 to 53 labelled f_1(0)* 59 to 64 labelled proper_1(1)* 60 to 53 labelled ok_1(1)* 60 to 60 labelled f_1(1), g_1(1)* 60 to 61 labelled active_1(1)* 60 to 67 labelled active_1(2)* 61 to 53 labelled top_1(1)* 62 to 53 labelled mark_1(1)* 62 to 62 labelled g_1(1)* 62 to 61 labelled proper_1(1)* 62 to 67 labelled proper_1(2)* 63 to 53 labelled g_1(1)* 63 to 63 labelled active_1(1), proper_1(1)* 64 to 53 labelled f_1(1)* 64 to 64 labelled proper_1(1)* 65 to 61 labelled g_1(1)* 65 to 67 labelled g_1(1)* 65 to 73 labelled f_1(1), g_1(1)* 66 to 61 labelled f_1(1)* 66 to 67 labelled f_1(1)* 67 to 61 labelled g_1(2)* 67 to 67 labelled g_1(2)* 68 to 66 labelled g_1(1)* 69 to 70 labelled f_1(1)* 69 to 73 labelled ok_1(1)* 69 to 79 labelled f_1(2)* 69 to 82 labelled proper_1(2)* 70 to 71 labelled g_1(1)* 70 to 80 labelled proper_1(2)* 71 to 72 labelled f_1(1)* 71 to 76 labelled proper_1(2)* 72 to 61 labelled mark_1(1)* 72 to 74 labelled proper_1(2)* 72 to 67 labelled mark_1(1)* 72 to 78 labelled g_1(2)* 72 to 83 labelled proper_1(3)* 73 to 68 labelled f_1(1)* 74 to 53 labelled top_1(2)* 76 to 74 labelled f_1(2)* 76 to 83 labelled f_1(2)* 78 to 61 labelled mark_1(2)* 78 to 67 labelled mark_1(2)* 78 to 74 labelled proper_1(2)* 78 to 81 labelled g_1(3)* 78 to 83 labelled proper_1(3)* 78 to 90 labelled proper_1(4)* 79 to 68 labelled ok_1(2)* 79 to 84 labelled g_1(2)* 80 to 76 labelled g_1(2)* 81 to 61 labelled mark_1(3)* 81 to 67 labelled mark_1(3)* 81 to 74 labelled proper_1(2)* 81 to 81 labelled g_1(3)* 81 to 83 labelled proper_1(3)* 81 to 90 labelled proper_1(4)* 82 to 80 labelled f_1(2)* 83 to 74 labelled g_1(3)* 83 to 83 labelled g_1(3)* 83 to 90 labelled g_1(3)* 84 to 66 labelled ok_1(2)* 84 to 88 labelled f_1(2)* 87 to 82 labelled ok_1(2)* 87 to 91 labelled f_1(3)* 88 to 61 labelled ok_1(2)* 88 to 67 labelled ok_1(2)* 88 to 74 labelled active_1(2)* 88 to 89 labelled g_1(3)* 88 to 83 labelled active_1(3)* 88 to 90 labelled active_1(4)* 89 to 61 labelled ok_1(3)* 89 to 67 labelled ok_1(3)* 89 to 74 labelled active_1(2)* 89 to 89 labelled g_1(3)* 89 to 83 labelled active_1(3)* 89 to 90 labelled active_1(4)* 90 to 83 labelled g_1(4)* 90 to 90 labelled g_1(4)* 91 to 80 labelled ok_1(3)* 91 to 92 labelled g_1(3)* 92 to 76 labelled ok_1(3)* 92 to 93 labelled f_1(3)* 93 to 74 labelled ok_1(3)* 93 to 83 labelled ok_1(3)* 93 to 94 labelled active_1(3)* 93 to 95 labelled g_1(4)* 93 to 97 labelled active_1(4)* 93 to 98 labelled active_1(5)* 94 to 53 labelled top_1(3)* 95 to 74 labelled ok_1(4)* 95 to 83 labelled ok_1(4)* 95 to 90 labelled ok_1(4)* 95 to 94 labelled active_1(3)* 95 to 95 labelled g_1(4)* 95 to 96 labelled g_1(5)* 95 to 97 labelled active_1(4)* 95 to 98 labelled active_1(5)* 95 to 102 labelled active_1(6)* 96 to 83 labelled ok_1(5)* 96 to 90 labelled ok_1(5)* 96 to 95 labelled g_1(4)* 96 to 96 labelled g_1(5)* 96 to 97 labelled active_1(4)* 96 to 98 labelled active_1(5)* 96 to 102 labelled active_1(6)* 97 to 94 labelled g_1(4)* 98 to 97 labelled g_1(5)* 98 to 98 labelled g_1(5)* 98 to 102 labelled g_1(5)* 102 to 98 labelled g_1(6)* 102 to 102 labelled g_1(6) 3.76/1.76 3.76/1.76 3.76/1.76 ---------------------------------------- 3.76/1.76
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS_Innermost 2019-03-28 22.12