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Logic_Programming 2019-04-02 08.22 pair #434324527
details
property
value
status
complete
benchmark
times.pl
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n129.star.cs.uiowa.edu
space
SGST06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.83245 seconds
cpu usage
4.17691
user time
4.00261
system time
0.174298
max virtual memory
1.86101E7
max residence set size
338256.0
stage attributes
key
value
starexec-result
YES
output
3.89/1.80 YES 4.14/1.81 proof of /export/starexec/sandbox/benchmark/theBenchmark.pl 4.14/1.81 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.14/1.81 4.14/1.81 4.14/1.81 Left Termination of the query pattern 4.14/1.81 4.14/1.81 times(g,g,a) 4.14/1.81 4.14/1.81 w.r.t. the given Prolog program could successfully be proven: 4.14/1.81 4.14/1.81 (0) Prolog 4.14/1.81 (1) PrologToPiTRSProof [SOUND, 0 ms] 4.14/1.81 (2) PiTRS 4.14/1.81 (3) DependencyPairsProof [EQUIVALENT, 15 ms] 4.14/1.81 (4) PiDP 4.14/1.81 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 4.14/1.81 (6) PiDP 4.14/1.81 (7) UsableRulesProof [EQUIVALENT, 0 ms] 4.14/1.81 (8) PiDP 4.14/1.81 (9) PiDPToQDPProof [SOUND, 8 ms] 4.14/1.81 (10) QDP 4.14/1.81 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 4.14/1.81 (12) YES 4.14/1.81 4.14/1.81 4.14/1.81 ---------------------------------------- 4.14/1.81 4.14/1.81 (0) 4.14/1.81 Obligation: 4.14/1.81 Clauses: 4.14/1.81 4.14/1.81 times(X, Y, Z) :- mult(X, Y, 0, Z). 4.14/1.81 mult(0, Y, 0, 0). 4.14/1.81 mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z). 4.14/1.81 mult(X, Y, s(W), s(Z)) :- mult(X, Y, W, Z). 4.14/1.81 4.14/1.81 4.14/1.81 Query: times(g,g,a) 4.14/1.81 ---------------------------------------- 4.14/1.81 4.14/1.81 (1) PrologToPiTRSProof (SOUND) 4.14/1.81 We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: 4.14/1.81 4.14/1.81 times_in_3: (b,b,f) 4.14/1.81 4.14/1.81 mult_in_4: (b,b,b,f) 4.14/1.81 4.14/1.81 Transforming Prolog into the following Term Rewriting System: 4.14/1.81 4.14/1.81 Pi-finite rewrite system: 4.14/1.81 The TRS R consists of the following rules: 4.14/1.81 4.14/1.81 times_in_gga(X, Y, Z) -> U1_gga(X, Y, Z, mult_in_ggga(X, Y, 0, Z)) 4.14/1.81 mult_in_ggga(0, Y, 0, 0) -> mult_out_ggga(0, Y, 0, 0) 4.14/1.81 mult_in_ggga(s(U), Y, 0, Z) -> U2_ggga(U, Y, Z, mult_in_ggga(U, Y, Y, Z)) 4.14/1.81 mult_in_ggga(X, Y, s(W), s(Z)) -> U3_ggga(X, Y, W, Z, mult_in_ggga(X, Y, W, Z)) 4.14/1.81 U3_ggga(X, Y, W, Z, mult_out_ggga(X, Y, W, Z)) -> mult_out_ggga(X, Y, s(W), s(Z)) 4.14/1.81 U2_ggga(U, Y, Z, mult_out_ggga(U, Y, Y, Z)) -> mult_out_ggga(s(U), Y, 0, Z) 4.14/1.81 U1_gga(X, Y, Z, mult_out_ggga(X, Y, 0, Z)) -> times_out_gga(X, Y, Z) 4.14/1.81 4.14/1.81 The argument filtering Pi contains the following mapping: 4.14/1.81 times_in_gga(x1, x2, x3) = times_in_gga(x1, x2) 4.14/1.81 4.14/1.81 U1_gga(x1, x2, x3, x4) = U1_gga(x4) 4.14/1.81 4.14/1.81 mult_in_ggga(x1, x2, x3, x4) = mult_in_ggga(x1, x2, x3) 4.14/1.81 4.14/1.81 0 = 0 4.14/1.81 4.14/1.81 mult_out_ggga(x1, x2, x3, x4) = mult_out_ggga(x4) 4.14/1.81 4.14/1.81 s(x1) = s(x1) 4.14/1.81 4.14/1.81 U2_ggga(x1, x2, x3, x4) = U2_ggga(x4) 4.14/1.81 4.14/1.81 U3_ggga(x1, x2, x3, x4, x5) = U3_ggga(x5) 4.14/1.81 4.14/1.81 times_out_gga(x1, x2, x3) = times_out_gga(x3) 4.14/1.81 4.14/1.81 4.14/1.81 4.14/1.81 4.14/1.81 4.14/1.81 Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog 4.14/1.81 4.14/1.81 4.14/1.81 4.14/1.81 ---------------------------------------- 4.14/1.81 4.14/1.81 (2) 4.14/1.81 Obligation: 4.14/1.81 Pi-finite rewrite system: 4.14/1.81 The TRS R consists of the following rules: 4.14/1.81 4.14/1.81 times_in_gga(X, Y, Z) -> U1_gga(X, Y, Z, mult_in_ggga(X, Y, 0, Z)) 4.14/1.81 mult_in_ggga(0, Y, 0, 0) -> mult_out_ggga(0, Y, 0, 0) 4.14/1.81 mult_in_ggga(s(U), Y, 0, Z) -> U2_ggga(U, Y, Z, mult_in_ggga(U, Y, Y, Z)) 4.14/1.81 mult_in_ggga(X, Y, s(W), s(Z)) -> U3_ggga(X, Y, W, Z, mult_in_ggga(X, Y, W, Z)) 4.14/1.81 U3_ggga(X, Y, W, Z, mult_out_ggga(X, Y, W, Z)) -> mult_out_ggga(X, Y, s(W), s(Z))
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