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TRS_Innermost 2019-03-28 22.12 pair #432271054
details
property
value
status
complete
benchmark
Ex6_GM04_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n037.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.74897 seconds
cpu usage
3.97926
user time
3.8071
system time
0.172157
max virtual memory
3.737184E7
max residence set size
278860.0
stage attributes
key
value
starexec-result
YES
output
3.84/1.69 YES 3.84/1.71 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.84/1.71 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.84/1.71 3.84/1.71 3.84/1.71 Termination w.r.t. Q of the given QTRS could be proven: 3.84/1.71 3.84/1.71 (0) QTRS 3.84/1.71 (1) QTRS Reverse [SOUND, 0 ms] 3.84/1.71 (2) QTRS 3.84/1.71 (3) RFCMatchBoundsTRSProof [EQUIVALENT, 4 ms] 3.84/1.71 (4) YES 3.84/1.71 3.84/1.71 3.84/1.71 ---------------------------------------- 3.84/1.71 3.84/1.71 (0) 3.84/1.71 Obligation: 3.84/1.71 Q restricted rewrite system: 3.84/1.71 The TRS R consists of the following rules: 3.84/1.71 3.84/1.71 active(c) -> mark(f(g(c))) 3.84/1.71 active(f(g(X))) -> mark(g(X)) 3.84/1.71 proper(c) -> ok(c) 3.84/1.71 proper(f(X)) -> f(proper(X)) 3.84/1.71 proper(g(X)) -> g(proper(X)) 3.84/1.71 f(ok(X)) -> ok(f(X)) 3.84/1.71 g(ok(X)) -> ok(g(X)) 3.84/1.71 top(mark(X)) -> top(proper(X)) 3.84/1.71 top(ok(X)) -> top(active(X)) 3.84/1.71 3.84/1.71 The set Q consists of the following terms: 3.84/1.71 3.84/1.71 active(c) 3.84/1.71 active(f(g(x0))) 3.84/1.71 proper(c) 3.84/1.71 proper(f(x0)) 3.84/1.71 proper(g(x0)) 3.84/1.71 f(ok(x0)) 3.84/1.71 g(ok(x0)) 3.84/1.71 top(mark(x0)) 3.84/1.71 top(ok(x0)) 3.84/1.71 3.84/1.71 3.84/1.71 ---------------------------------------- 3.84/1.71 3.84/1.71 (1) QTRS Reverse (SOUND) 3.84/1.71 We applied the QTRS Reverse Processor [REVERSE]. 3.84/1.71 ---------------------------------------- 3.84/1.71 3.84/1.71 (2) 3.84/1.71 Obligation: 3.84/1.71 Q restricted rewrite system: 3.84/1.71 The TRS R consists of the following rules: 3.84/1.71 3.84/1.71 c'(active(x)) -> c'(g(f(mark(x)))) 3.84/1.71 g(f(active(X))) -> g(mark(X)) 3.84/1.71 c'(proper(x)) -> c'(ok(x)) 3.84/1.71 f(proper(X)) -> proper(f(X)) 3.84/1.71 g(proper(X)) -> proper(g(X)) 3.84/1.71 ok(f(X)) -> f(ok(X)) 3.84/1.71 ok(g(X)) -> g(ok(X)) 3.84/1.71 mark(top(X)) -> proper(top(X)) 3.84/1.71 ok(top(X)) -> active(top(X)) 3.84/1.71 3.84/1.71 Q is empty. 3.84/1.71 3.84/1.71 ---------------------------------------- 3.84/1.71 3.84/1.71 (3) RFCMatchBoundsTRSProof (EQUIVALENT) 3.84/1.71 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 5. This implies Q-termination of R. 3.84/1.71 The following rules were used to construct the certificate: 3.84/1.71 3.84/1.71 c'(active(x)) -> c'(g(f(mark(x)))) 3.84/1.71 g(f(active(X))) -> g(mark(X)) 3.84/1.71 c'(proper(x)) -> c'(ok(x)) 3.84/1.71 f(proper(X)) -> proper(f(X)) 3.84/1.71 g(proper(X)) -> proper(g(X)) 3.84/1.71 ok(f(X)) -> f(ok(X)) 3.84/1.71 ok(g(X)) -> g(ok(X)) 3.84/1.71 mark(top(X)) -> proper(top(X)) 3.84/1.71 ok(top(X)) -> active(top(X)) 3.84/1.71 3.84/1.71 The certificate found is represented by the following graph. 3.84/1.71 The certificate consists of the following enumerated nodes: 3.84/1.71 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86 3.84/1.71 3.84/1.71 Node 43 is start node and node 44 is final node. 3.84/1.71 3.84/1.71 Those nodes are connected through the following edges: 3.84/1.71 3.84/1.71 * 43 to 45 labelled c'_1(0), f_1(0), g_1(0)* 43 to 47 labelled g_1(0)* 43 to 48 labelled proper_1(0), active_1(0)* 43 to 53 labelled c'_1(1)* 43 to 56 labelled proper_1(1)* 43 to 55 labelled g_1(1)* 43 to 64 labelled proper_1(2)* 43 to 69 labelled c'_1(2)* 43 to 83 labelled c'_1(3)* 44 to 44 labelled #_1(0)* 45 to 46 labelled g_1(0)* 45 to 44 labelled ok_1(0)* 45 to 49 labelled f_1(1), g_1(1)* 45 to 50 labelled active_1(1)* 45 to 58 labelled proper_1(1)* 45 to 63 labelled g_1(2)* 45 to 66 labelled proper_1(3)* 45 to 70 labelled proper_1(2)* 46 to 47 labelled f_1(0)* 46 to 57 labelled proper_1(1)* 47 to 44 labelled mark_1(0)* 47 to 50 labelled proper_1(1)* 48 to 44 labelled f_1(0), g_1(0), top_1(0)* 48 to 51 labelled proper_1(1)* 48 to 52 labelled g_1(1)* 48 to 61 labelled proper_1(2)* 49 to 44 labelled ok_1(1)* 49 to 49 labelled f_1(1), g_1(1)* 49 to 50 labelled active_1(1)* 49 to 63 labelled g_1(2)* 49 to 66 labelled proper_1(3)* 49 to 70 labelled proper_1(2)* 50 to 44 labelled top_1(1)* 51 to 44 labelled f_1(1), g_1(1)* 51 to 51 labelled proper_1(1)* 51 to 52 labelled g_1(1)* 51 to 61 labelled proper_1(2)* 52 to 44 labelled mark_1(1)* 52 to 50 labelled proper_1(1)* 53 to 54 labelled g_1(1)* 53 to 58 labelled ok_1(1)* 53 to 67 labelled proper_1(2)* 53 to 68 labelled g_1(2)* 53 to 66 labelled ok_1(1)* 53 to 70 labelled ok_1(1)* 53 to 73 labelled f_1(2), g_1(2)* 53 to 76 labelled g_1(3)* 53 to 79 labelled proper_1(4)* 54 to 55 labelled f_1(1)* 54 to 65 labelled proper_1(2)* 55 to 50 labelled mark_1(1)* 55 to 62 labelled proper_1(2)* 56 to 50 labelled g_1(1)* 56 to 58 labelled f_1(1), g_1(1)* 56 to 66 labelled f_1(1), g_1(1)* 56 to 70 labelled f_1(1), g_1(1)* 57 to 50 labelled f_1(1)* 58 to 57 labelled g_1(1)* 61 to 50 labelled g_1(2)* 62 to 44 labelled top_1(2)* 63 to 50 labelled mark_1(2)* 63 to 62 labelled proper_1(2)* 64 to 62 labelled g_1(2)* 65 to 62 labelled f_1(2)* 66 to 62 labelled g_1(3)* 67 to 65 labelled g_1(2)* 68 to 57 labelled ok_1(2)* 68 to 71 labelled f_1(2)* 68 to 62 labelled ok_1(2)* 68 to 75 labelled active_1(3)* 69 to 67 labelled ok_1(2)* 69 to 72 labelled g_1(3)* 69 to 80 labelled g_1(4)* 69 to 79 labelled ok_1(2)* 69 to 82 labelled proper_1(5)* 70 to 66 labelled f_1(2), g_1(2)* 70 to 70 labelled f_1(2), g_1(2)* 71 to 50 labelled ok_1(2)* 71 to 62 labelled active_1(2)* 72 to 65 labelled ok_1(3)* 72 to 74 labelled f_1(3)* 72 to 75 labelled ok_1(3)* 72 to 81 labelled active_1(4)* 73 to 66 labelled ok_1(2)* 73 to 70 labelled ok_1(2)* 73 to 74 labelled g_1(3)* 73 to 77 labelled f_1(3), g_1(3)* 74 to 62 labelled ok_1(3)* 74 to 75 labelled active_1(3)* 75 to 44 labelled top_1(3)* 76 to 62 labelled mark_1(3)* 76 to 75 labelled proper_1(3)* 77 to 66 labelled ok_1(3)* 77 to 70 labelled ok_1(3)* 77 to 78 labelled g_1(4)* 77 to 77 labelled f_1(3), g_1(3)* 78 to 62 labelled ok_1(4)* 78 to 75 labelled active_1(3)* 79 to 75 labelled g_1(4)* 80 to 75 labelled mark_1(4)* 80 to 81 labelled proper_1(4)* 81 to 44 labelled top_1(4)* 82 to 81 labelled g_1(5)* 83 to 82 labelled ok_1(3)* 83 to 85 labelled g_1(4)* 85 to 81 labelled ok_1(4)* 85 to 86 labelled active_1(5)* 86 to 44 labelled top_1(5) 3.84/1.71 3.84/1.71 3.84/1.71 ---------------------------------------- 3.84/1.71 3.84/1.71 (4) 3.84/1.71 YES 3.96/1.74 EOF
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