details

property	value
status	complete
benchmark	recursion-10.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n191.star.cs.uiowa.edu
space	TCT_12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.82539 seconds
cpu usage	4.3214
user time	4.14173
system time	0.179675
max virtual memory	1.841578E7
max residence set size	259948.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 171 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f_0(x) -> a f_1(x) -> g_1(x, x) g_1(s(x), y) -> b(f_0(y), g_1(x, y)) f_2(x) -> g_2(x, x) g_2(s(x), y) -> b(f_1(y), g_2(x, y)) f_3(x) -> g_3(x, x) g_3(s(x), y) -> b(f_2(y), g_3(x, y)) f_4(x) -> g_4(x, x) g_4(s(x), y) -> b(f_3(y), g_4(x, y)) f_5(x) -> g_5(x, x) g_5(s(x), y) -> b(f_4(y), g_5(x, y)) f_6(x) -> g_6(x, x) g_6(s(x), y) -> b(f_5(y), g_6(x, y)) f_7(x) -> g_7(x, x) g_7(s(x), y) -> b(f_6(y), g_7(x, y)) f_8(x) -> g_8(x, x) g_8(s(x), y) -> b(f_7(y), g_8(x, y)) f_9(x) -> g_9(x, x) g_9(s(x), y) -> b(f_8(y), g_9(x, y)) f_10(x) -> g_10(x, x) g_10(s(x), y) -> b(f_9(y), g_10(x, y)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: s_1 > [f_3_1, g_4_2] > [f_2_1, g_3_2] > [f_1_1, g_2_2] > g_1_2 > [f_0_1, a] s_1 > [f_3_1, g_4_2] > [f_2_1, g_3_2] > [f_1_1, g_2_2] > g_1_2 > b_2 f_10_1 > [f_9_1, g_10_2] > g_9_2 > f_8_1 > [f_7_1, g_8_2] > [f_6_1, g_7_2] > [f_5_1, g_6_2] > [f_4_1, g_5_2] > [f_3_1, g_4_2] > [f_2_1, g_3_2] > [f_1_1, g_2_2] > g_1_2 > [f_0_1, a] f_10_1 > [f_9_1, g_10_2] > g_9_2 > f_8_1 > [f_7_1, g_8_2] > [f_6_1, g_7_2] > [f_5_1, g_6_2] > [f_4_1, g_5_2] > [f_3_1, g_4_2] > [f_2_1, g_3_2] > [f_1_1, g_2_2] > g_1_2 > b_2 Status: f_0_1: [1] a: multiset status f_1_1: multiset status g_1_2: multiset status s_1: multiset status b_2: multiset status f_2_1: multiset status g_2_2: multiset status f_3_1: multiset status g_3_2: multiset status f_4_1: multiset status g_4_2: multiset status f_5_1: multiset status g_5_2: multiset status f_6_1: multiset status g_6_2: multiset status f_7_1: multiset status g_7_2: multiset status f_8_1: [1] g_8_2: multiset status f_9_1: multiset status g_9_2: multiset status f_10_1: [1] g_10_2: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f_0(x) -> a f_1(x) -> g_1(x, x) g_1(s(x), y) -> b(f_0(y), g_1(x, y)) f_2(x) -> g_2(x, x) g_2(s(x), y) -> b(f_1(y), g_2(x, y)) f_3(x) -> g_3(x, x) g_3(s(x), y) -> b(f_2(y), g_3(x, y)) f_4(x) -> g_4(x, x) g_4(s(x), y) -> b(f_3(y), g_4(x, y)) f_5(x) -> g_5(x, x) g_5(s(x), y) -> b(f_4(y), g_5(x, y)) f_6(x) -> g_6(x, x) g_6(s(x), y) -> b(f_5(y), g_6(x, y)) f_7(x) -> g_7(x, x) g_7(s(x), y) -> b(f_6(y), g_7(x, y)) f_8(x) -> g_8(x, x) popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to TRS Standard