details

property	value
status	complete
benchmark	351.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n070.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.3432700634 seconds
cpu usage	6.181655221
max memory	4.93473792E8

stage attributes

key	value
output-size	5162
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 72 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 9 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 0 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 0 ms] (10) QTRS (11) RisEmptyProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: ssp(nil, 0) -> nil sub(z, 0) -> z The conditional TRS C consists of the following conditional rules: ssp(cons(y, ys'), v) -> xs <= ssp(ys', v) -> xs ssp(cons(y, ys'), v) -> cons(y, xs') <= sub(v, y) -> w, ssp(ys', w) -> xs' sub(s(v), s(w)) -> z <= sub(v, w) -> z ---------------------------------------- (1) CTRSToQTRSProof (SOUND) The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: ssp(cons(y, ys'), v) -> U1(ssp(ys', v)) U1(xs) -> xs ssp(cons(y, ys'), v) -> U2(sub(v, y), y, ys') U2(w, y, ys') -> U3(ssp(ys', w), y) U3(xs', y) -> cons(y, xs') sub(s(v), s(w)) -> U4(sub(v, w)) U4(z) -> z ssp(nil, 0) -> nil sub(z, 0) -> z Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 2 POL(U1(x_1)) = x_1 POL(U2(x_1, x_2, x_3)) = x_1 + 2*x_2 + 2*x_3 POL(U3(x_1, x_2)) = x_1 + 2*x_2 POL(U4(x_1)) = 2*x_1 POL(cons(x_1, x_2)) = 2*x_1 + x_2 POL(nil) = 0 POL(s(x_1)) = 2*x_1 POL(ssp(x_1, x_2)) = 2*x_1 + x_2 POL(sub(x_1, x_2)) = x_1 + 2*x_2 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: ssp(nil, 0) -> nil sub(z, 0) -> z ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: ssp(cons(y, ys'), v) -> U1(ssp(ys', v)) popout

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actions

all output return to TRS Conditional