details

property	value
status	complete
benchmark	PastaB11.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n048.star.cs.uiowa.edu
space	Adapted_from_Stroeder_15

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	1.40075 seconds
cpu usage	2.46902
user time	2.28415
system time	0.184869
max virtual memory	1.8273644E7
max residence set size	186140.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(n^1))

output

2.26/1.37 WORST_CASE(?, O(n^1)) 2.26/1.38 proof of /export/starexec/sandbox2/output/output_files/bench.koat 2.26/1.38 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.26/1.38 2.26/1.38 2.26/1.38 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.26/1.38 2.26/1.38 (0) CpxIntTrs 2.26/1.38 (1) Koat Proof [FINISHED, 187 ms] 2.26/1.38 (2) BOUNDS(1, n^1) 2.26/1.38 2.26/1.38 2.26/1.38 ---------------------------------------- 2.26/1.38 2.26/1.38 (0) 2.26/1.38 Obligation: 2.26/1.38 Complexity Int TRS consisting of the following rules: 2.26/1.38 eval_foo_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE 2.26/1.38 eval_foo_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_x, v_y)) :|: TRUE 2.26/1.38 eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 + v_.01 > 0 2.26/1.38 eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 + v_.01 <= 0 2.26/1.38 eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 > v_.01 2.26/1.38 eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 <= v_.01 2.26/1.38 eval_foo_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01, v_x, v_y)) :|: TRUE 2.26/1.38 eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01, v_x, v_y)) :|: v_.0 >= v_.01 && v_.0 <= v_.01 2.26/1.38 eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 >= v_.01 && v_.0 <= v_.01 && v_.0 < v_.01 2.26/1.38 eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 >= v_.01 && v_.0 <= v_.01 && v_.0 > v_.01 2.26/1.38 eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01 - 1, v_x, v_y)) :|: v_.0 < v_.01 && v_.0 >= v_.01 && v_.0 <= v_.01 2.26/1.38 eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01 - 1, v_x, v_y)) :|: v_.0 > v_.01 && v_.0 >= v_.01 && v_.0 <= v_.01 2.26/1.38 eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 - 1, v_x, v_y)) :|: v_.0 < v_.01 2.26/1.38 eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 - 1, v_x, v_y)) :|: v_.0 < v_.01 && v_.0 > v_.01 2.26/1.38 eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 - 1, v_x, v_y)) :|: v_.0 > v_.01 2.26/1.38 eval_foo_bb5_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE 2.26/1.38 2.26/1.38 The start-symbols are:[eval_foo_start_4] 2.26/1.38 2.26/1.38 2.26/1.38 ---------------------------------------- 2.26/1.38 2.26/1.38 (1) Koat Proof (FINISHED) 2.26/1.38 YES(?, 6*ar_1 + 6*ar_3 + 12) 2.26/1.38 2.26/1.38 2.26/1.38 2.26/1.38 Initial complexity problem: 2.26/1.38 2.26/1.38 1: T: 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 + ar_2 >= 1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + ar_2 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= ar_0 + 1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 + 1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_0 >= ar_2 + 1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) 2.26/1.38 2.26/1.38 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.26/1.38 2.26/1.38 start location: koat_start 2.26/1.38 2.26/1.38 leaf cost: 0 2.26/1.38 2.26/1.38 2.26/1.38 2.26/1.38 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.26/1.38 2.26/1.38 evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ] 2.26/1.38 2.26/1.38 evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ] 2.26/1.38 2.26/1.38 evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ] 2.26/1.38 2.26/1.38 evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ] 2.26/1.38 2.26/1.38 evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 + 1 ] 2.26/1.38 popout

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

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actions

all output return to Complexity_C_Integer 2019-03-21 04.38