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TRS_Innermost 2019-03-28 22.12 pair #432270886
details
property
value
status
complete
benchmark
ExAppendixB_AEL03_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n077.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
46.8532 seconds
cpu usage
166.48
user time
163.365
system time
3.11507
max virtual memory
3.710488E7
max residence set size
4168908.0
stage attributes
key
value
starexec-result
YES
output
165.77/46.62 YES 165.77/46.67 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 165.77/46.67 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 165.77/46.67 165.77/46.67 165.77/46.67 Termination w.r.t. Q of the given QTRS could be proven: 165.77/46.67 165.77/46.67 (0) QTRS 165.77/46.67 (1) DependencyPairsProof [EQUIVALENT, 96 ms] 165.77/46.67 (2) QDP 165.77/46.67 (3) QDPOrderProof [EQUIVALENT, 480 ms] 165.77/46.67 (4) QDP 165.77/46.67 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 165.77/46.67 (6) QDP 165.77/46.67 (7) QDPOrderProof [EQUIVALENT, 458 ms] 165.77/46.67 (8) QDP 165.77/46.67 (9) QDPOrderProof [EQUIVALENT, 357 ms] 165.77/46.67 (10) QDP 165.77/46.67 (11) DependencyGraphProof [EQUIVALENT, 0 ms] 165.77/46.67 (12) QDP 165.77/46.67 (13) QDPOrderProof [EQUIVALENT, 360 ms] 165.77/46.67 (14) QDP 165.77/46.67 (15) QDPOrderProof [EQUIVALENT, 413 ms] 165.77/46.67 (16) QDP 165.77/46.67 (17) DependencyGraphProof [EQUIVALENT, 0 ms] 165.77/46.67 (18) QDP 165.77/46.67 (19) QDPOrderProof [EQUIVALENT, 414 ms] 165.77/46.67 (20) QDP 165.77/46.67 (21) QDPOrderProof [EQUIVALENT, 424 ms] 165.77/46.67 (22) QDP 165.77/46.67 (23) QDPOrderProof [EQUIVALENT, 331 ms] 165.77/46.67 (24) QDP 165.77/46.67 (25) QDPOrderProof [EQUIVALENT, 335 ms] 165.77/46.67 (26) QDP 165.77/46.67 (27) QDPOrderProof [EQUIVALENT, 360 ms] 165.77/46.67 (28) QDP 165.77/46.67 (29) QDPOrderProof [EQUIVALENT, 392 ms] 165.77/46.67 (30) QDP 165.77/46.67 (31) QDPOrderProof [EQUIVALENT, 262 ms] 165.77/46.67 (32) QDP 165.77/46.67 (33) QDPOrderProof [EQUIVALENT, 311 ms] 165.77/46.67 (34) QDP 165.77/46.67 (35) QDPOrderProof [EQUIVALENT, 368 ms] 165.77/46.67 (36) QDP 165.77/46.67 (37) QDPOrderProof [EQUIVALENT, 300 ms] 165.77/46.67 (38) QDP 165.77/46.67 (39) QDPOrderProof [EQUIVALENT, 548 ms] 165.77/46.67 (40) QDP 165.77/46.67 (41) DependencyGraphProof [EQUIVALENT, 0 ms] 165.77/46.67 (42) QDP 165.77/46.67 (43) UsableRulesProof [EQUIVALENT, 0 ms] 165.77/46.67 (44) QDP 165.77/46.67 (45) QReductionProof [EQUIVALENT, 0 ms] 165.77/46.67 (46) QDP 165.77/46.67 (47) QDPSizeChangeProof [EQUIVALENT, 0 ms] 165.77/46.67 (48) YES 165.77/46.67 165.77/46.67 165.77/46.67 ---------------------------------------- 165.77/46.67 165.77/46.67 (0) 165.77/46.67 Obligation: 165.77/46.67 Q restricted rewrite system: 165.77/46.67 The TRS R consists of the following rules: 165.77/46.67 165.77/46.67 a__from(X) -> cons(mark(X), from(s(X))) 165.77/46.67 a__2ndspos(0, Z) -> rnil 165.77/46.67 a__2ndspos(s(N), cons(X, Z)) -> a__2ndspos(s(mark(N)), cons2(X, mark(Z))) 165.77/46.67 a__2ndspos(s(N), cons2(X, cons(Y, Z))) -> rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z))) 165.77/46.67 a__2ndsneg(0, Z) -> rnil 165.77/46.67 a__2ndsneg(s(N), cons(X, Z)) -> a__2ndsneg(s(mark(N)), cons2(X, mark(Z))) 165.77/46.67 a__2ndsneg(s(N), cons2(X, cons(Y, Z))) -> rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z))) 165.77/46.67 a__pi(X) -> a__2ndspos(mark(X), a__from(0)) 165.77/46.67 a__plus(0, Y) -> mark(Y) 165.77/46.67 a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y))) 165.77/46.67 a__times(0, Y) -> 0 165.77/46.67 a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y))) 165.77/46.67 a__square(X) -> a__times(mark(X), mark(X)) 165.77/46.67 mark(from(X)) -> a__from(mark(X)) 165.77/46.67 mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2)) 165.77/46.67 mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2)) 165.77/46.67 mark(pi(X)) -> a__pi(mark(X)) 165.77/46.67 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 165.77/46.67 mark(times(X1, X2)) -> a__times(mark(X1), mark(X2)) 165.77/46.67 mark(square(X)) -> a__square(mark(X)) 165.77/46.67 mark(0) -> 0 165.77/46.67 mark(s(X)) -> s(mark(X)) 165.77/46.67 mark(posrecip(X)) -> posrecip(mark(X)) 165.77/46.67 mark(negrecip(X)) -> negrecip(mark(X)) 165.77/46.67 mark(nil) -> nil 165.77/46.67 mark(cons(X1, X2)) -> cons(mark(X1), X2) 165.77/46.67 mark(cons2(X1, X2)) -> cons2(X1, mark(X2)) 165.77/46.67 mark(rnil) -> rnil 165.77/46.67 mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2)) 165.77/46.67 a__from(X) -> from(X) 165.77/46.67 a__2ndspos(X1, X2) -> 2ndspos(X1, X2) 165.77/46.67 a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2) 165.77/46.67 a__pi(X) -> pi(X) 165.77/46.67 a__plus(X1, X2) -> plus(X1, X2) 165.77/46.67 a__times(X1, X2) -> times(X1, X2)
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