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Logic Progr 19030 pair #381919963
details
property
value
status
complete
benchmark
ack.pl
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n049.star.cs.uiowa.edu
space
talp_mixed
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.73128604889 seconds
cpu usage
4.121030691
max memory
2.90205696E8
stage attributes
key
value
output-size
9255
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.pl /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern ack(g,g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof [SOUND, 0 ms] (2) PiTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) PiDP (7) PiDPToQDPProof [SOUND, 0 ms] (8) QDP (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Clauses: ack(0, N, s(N)). ack(s(M), 0, A) :- ack(M, s(0), A). ack(s(M), s(N), A) :- ','(ack(s(M), N, A1), ack(M, A1, A)). Query: ack(g,g,a) ---------------------------------------- (1) PrologToPiTRSProof (SOUND) We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: ack_in_3: (b,b,f) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: ack_in_gga(0, N, s(N)) -> ack_out_gga(0, N, s(N)) ack_in_gga(s(M), 0, A) -> U1_gga(M, A, ack_in_gga(M, s(0), A)) ack_in_gga(s(M), s(N), A) -> U2_gga(M, N, A, ack_in_gga(s(M), N, A1)) U2_gga(M, N, A, ack_out_gga(s(M), N, A1)) -> U3_gga(M, N, A, ack_in_gga(M, A1, A)) U3_gga(M, N, A, ack_out_gga(M, A1, A)) -> ack_out_gga(s(M), s(N), A) U1_gga(M, A, ack_out_gga(M, s(0), A)) -> ack_out_gga(s(M), 0, A) The argument filtering Pi contains the following mapping: ack_in_gga(x1, x2, x3) = ack_in_gga(x1, x2) 0 = 0 ack_out_gga(x1, x2, x3) = ack_out_gga(x3) s(x1) = s(x1) U1_gga(x1, x2, x3) = U1_gga(x3) U2_gga(x1, x2, x3, x4) = U2_gga(x1, x4) U3_gga(x1, x2, x3, x4) = U3_gga(x4) Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog ---------------------------------------- (2) Obligation: Pi-finite rewrite system: The TRS R consists of the following rules: ack_in_gga(0, N, s(N)) -> ack_out_gga(0, N, s(N)) ack_in_gga(s(M), 0, A) -> U1_gga(M, A, ack_in_gga(M, s(0), A)) ack_in_gga(s(M), s(N), A) -> U2_gga(M, N, A, ack_in_gga(s(M), N, A1)) U2_gga(M, N, A, ack_out_gga(s(M), N, A1)) -> U3_gga(M, N, A, ack_in_gga(M, A1, A)) U3_gga(M, N, A, ack_out_gga(M, A1, A)) -> ack_out_gga(s(M), s(N), A) U1_gga(M, A, ack_out_gga(M, s(0), A)) -> ack_out_gga(s(M), 0, A) The argument filtering Pi contains the following mapping: ack_in_gga(x1, x2, x3) = ack_in_gga(x1, x2)
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