details

property	value
status	complete
benchmark	307.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n010.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.13873696327 seconds
cpu usage	5.485791224
max memory	4.73915392E8

stage attributes

key	value
output-size	2359
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 82 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: plus(0, X) -> X plus(s(X), Y) -> plus(X, s(Y)) fib(0) -> pair(s(0), 0) The conditional TRS C consists of the following conditional rules: fib(s(X)) -> pair(W, Y) <= fib(X) -> pair(Y, Z), plus(Y, Z) -> W ---------------------------------------- (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: fib(s(X)) -> U1(fib(X)) U1(pair(Y, Z)) -> U2(plus(Y, Z), Y) U2(W, Y) -> pair(W, Y) plus(0, X) -> X plus(s(X), Y) -> plus(X, s(Y)) fib(0) -> pair(s(0), 0) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: fib_1 > [U1_1, U2_2, plus_2] > s_1 fib_1 > [U1_1, U2_2, plus_2] > pair_2 fib_1 > 0 Status: fib_1: multiset status s_1: multiset status U1_1: [1] pair_2: multiset status U2_2: [2,1] plus_2: [1,2] 0: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: fib(s(X)) -> U1(fib(X)) U1(pair(Y, Z)) -> U2(plus(Y, Z), Y) U2(W, Y) -> pair(W, Y) plus(0, X) -> X plus(s(X), Y) -> plus(X, s(Y)) fib(0) -> pair(s(0), 0) ---------------------------------------- (4) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (5) RisEmptyProof (EQUIVALENT) popout

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all output return to TRS Conditional