9.36/3.31	YES
9.78/3.31	proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
9.78/3.31	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.78/3.31	
9.78/3.31	
9.78/3.31	Termination of the given C Problem could be proven:
9.78/3.31	
9.78/3.31	(0) C Problem
9.78/3.31	(1) CToIRSProof [EQUIVALENT, 0 ms]
9.78/3.31	(2) IntTRS
9.78/3.31	(3) IRS2T2 [EQUIVALENT, 11 ms]
9.78/3.31	(4) T2IntSys
9.78/3.31	(5) T2 [EQUIVALENT, 1333 ms]
9.78/3.31	(6) YES
9.78/3.31	
9.78/3.31	
9.78/3.31	----------------------------------------
9.78/3.31	
9.78/3.31	(0)
9.78/3.31	Obligation:
9.78/3.31	c file /export/starexec/sandbox2/benchmark/theBenchmark.c
9.78/3.31	----------------------------------------
9.78/3.31	
9.78/3.31	(1) CToIRSProof (EQUIVALENT)
9.78/3.31	Parsed C Integer Program as IRS.
9.78/3.31	----------------------------------------
9.78/3.31	
9.78/3.31	(2)
9.78/3.31	Obligation:
9.78/3.31	Rules:
9.78/3.31	f1(c, x, y) -> f2(c, x_1, y) :|: TRUE
9.78/3.31	f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE
9.78/3.31	f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE
9.78/3.31	f6(x8, x9, x10) -> f9(x8, arith, x10) :|: TRUE && arith = x9 - 1
9.78/3.31	f10(x50, x51, x52) -> f13(x50, x51, x53) :|: TRUE && x53 = x52 - 1
9.78/3.31	f7(x14, x15, x16) -> f10(x14, x15, x16) :|: x16 > 0
9.78/3.31	f7(x17, x18, x19) -> f11(x17, x18, x19) :|: x19 <= 0
9.78/3.31	f13(x20, x21, x22) -> f12(x20, x21, x22) :|: TRUE
9.78/3.31	f11(x23, x24, x25) -> f12(x23, x24, x25) :|: TRUE
9.78/3.31	f5(x26, x27, x28) -> f6(x26, x27, x28) :|: x27 > 0
9.78/3.31	f5(x29, x30, x31) -> f7(x29, x30, x31) :|: x30 <= 0
9.78/3.31	f9(x32, x33, x34) -> f8(x32, x33, x34) :|: TRUE
9.78/3.31	f12(x35, x36, x37) -> f8(x35, x36, x37) :|: TRUE
9.78/3.31	f8(x54, x55, x56) -> f14(x57, x55, x56) :|: TRUE && x57 = x54 + 1
9.78/3.31	f4(x41, x42, x43) -> f5(x41, x42, x43) :|: x42 > 0
9.78/3.31	f4(x58, x59, x60) -> f5(x58, x59, x60) :|: x60 > 0
9.78/3.31	f14(x44, x45, x46) -> f4(x44, x45, x46) :|: TRUE
9.78/3.31	f4(x47, x48, x49) -> f15(x47, x48, x49) :|: x48 <= 0 && x49 <= 0
9.78/3.31	Start term: f1(c, x, y)
9.78/3.31	
9.78/3.31	----------------------------------------
9.78/3.31	
9.78/3.31	(3) IRS2T2 (EQUIVALENT)
9.78/3.31	Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs:
9.78/3.31	
9.78/3.31	   (f1_3,1)
9.78/3.31	   (f2_3,2)
9.78/3.31	   (f3_3,3)
9.78/3.31	   (f4_3,4)
9.78/3.31	   (f6_3,5)
9.78/3.31	   (f9_3,6)
9.78/3.31	   (f10_3,7)
9.78/3.31	   (f13_3,8)
9.78/3.31	   (f7_3,9)
9.78/3.31	   (f11_3,10)
9.78/3.31	   (f12_3,11)
9.78/3.31	   (f5_3,12)
9.78/3.31	   (f8_3,13)
9.78/3.31	   (f14_3,14)
9.78/3.31	   (f15_3,15)
9.78/3.31	
9.78/3.31	----------------------------------------
9.78/3.31	
9.78/3.31	(4)
9.78/3.31	Obligation:
9.78/3.31	START: 1;
9.78/3.31	
9.78/3.31	FROM: 1;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	oldX3 := nondet();
9.78/3.31	assume(0 = 0);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := oldX3;
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 2;
9.78/3.31	
9.78/3.31	FROM: 2;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	oldX3 := nondet();
9.78/3.31	assume(0 = 0);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := oldX3;
9.78/3.31	TO: 3;
9.78/3.31	
9.78/3.31	FROM: 3;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	assume(0 = 0);
9.78/3.31	x0 := 0;
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 4;
9.78/3.31	
9.78/3.31	FROM: 5;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	oldX3 := -(1 - oldX1);
9.78/3.31	assume(0 = 0 && oldX3 = oldX1 - 1);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := -(1 - oldX1);
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 6;
9.78/3.31	
9.78/3.31	FROM: 7;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	oldX3 := -(1 - oldX2);
9.78/3.31	assume(0 = 0 && oldX3 = oldX2 - 1);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := -(1 - oldX2);
9.78/3.31	TO: 8;
9.78/3.31	
9.78/3.31	FROM: 9;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	assume(oldX2 > 0);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 7;
9.78/3.31	
9.78/3.31	FROM: 9;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	assume(oldX2 <= 0);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 10;
9.78/3.31	
9.78/3.31	FROM: 8;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	assume(0 = 0);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 11;
9.78/3.31	
9.78/3.31	FROM: 10;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	assume(0 = 0);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 11;
9.78/3.31	
9.78/3.31	FROM: 12;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	assume(oldX1 > 0);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 5;
9.78/3.31	
9.78/3.31	FROM: 12;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	assume(oldX1 <= 0);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 9;
9.78/3.31	
9.78/3.31	FROM: 6;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	assume(0 = 0);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 13;
9.78/3.31	
9.78/3.31	FROM: 11;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	assume(0 = 0);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 13;
9.78/3.31	
9.78/3.31	FROM: 13;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	oldX3 := -(-(oldX0 + 1));
9.78/3.31	assume(0 = 0 && oldX3 = oldX0 + 1);
9.78/3.31	x0 := -(-(oldX0 + 1));
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 14;
9.78/3.31	
9.78/3.31	FROM: 4;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	assume(oldX1 > 0);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 12;
9.78/3.31	
9.78/3.31	FROM: 4;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	assume(oldX2 > 0);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 12;
9.78/3.31	
9.78/3.31	FROM: 14;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	assume(0 = 0);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 4;
9.78/3.31	
9.78/3.31	FROM: 4;
9.78/3.31	oldX0 := x0;
9.78/3.31	oldX1 := x1;
9.78/3.31	oldX2 := x2;
9.78/3.31	assume(oldX1 <= 0 && oldX2 <= 0);
9.78/3.31	x0 := oldX0;
9.78/3.31	x1 := oldX1;
9.78/3.31	x2 := oldX2;
9.78/3.31	TO: 15;
9.78/3.31	
9.78/3.31	
9.78/3.31	----------------------------------------
9.78/3.31	
9.78/3.31	(5) T2 (EQUIVALENT)
9.78/3.31	Initially, performed program simplifications using lexicographic rank functions:
9.78/3.31	 * Removed transitions 11, 13 using the following rank functions:
9.78/3.31	    - Rank function 1:
9.78/3.31	      RF for loc. 11: x2
9.78/3.31	      RF for loc. 12: x2
9.78/3.31	      RF for loc. 13: x2
9.78/3.31	      RF for loc. 14: x2
9.78/3.31	      RF for loc. 15: x2
9.78/3.31	      Bound for (chained) transitions 11: 1
9.78/3.31	    - Rank function 2:
9.78/3.31	      RF for loc. 11: 2*x1
9.78/3.31	      RF for loc. 12: 2*x1
9.78/3.31	      RF for loc. 13: 2*x1
9.78/3.31	      RF for loc. 14: 2*x1
9.78/3.31	      RF for loc. 15: 2*x1
9.78/3.31	      Bound for (chained) transitions 13: 2
9.78/3.31	
9.78/3.31	----------------------------------------
9.78/3.31	
9.78/3.31	(6)
9.78/3.31	YES
9.78/3.35	EOF