9.17/3.20	YES
9.45/3.21	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
9.45/3.21	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.45/3.21	
9.45/3.21	
9.45/3.21	Termination of the given C Problem could be proven:
9.45/3.21	
9.45/3.21	(0) C Problem
9.45/3.21	(1) CToIRSProof [EQUIVALENT, 0 ms]
9.45/3.21	(2) IntTRS
9.45/3.21	(3) IRS2T2 [EQUIVALENT, 4 ms]
9.45/3.21	(4) T2IntSys
9.45/3.21	(5) T2 [EQUIVALENT, 1308 ms]
9.45/3.21	(6) YES
9.45/3.21	
9.45/3.21	
9.45/3.21	----------------------------------------
9.45/3.21	
9.45/3.21	(0)
9.45/3.21	Obligation:
9.45/3.21	c file /export/starexec/sandbox/benchmark/theBenchmark.c
9.45/3.21	----------------------------------------
9.45/3.21	
9.45/3.21	(1) CToIRSProof (EQUIVALENT)
9.45/3.21	Parsed C Integer Program as IRS.
9.45/3.21	----------------------------------------
9.45/3.21	
9.45/3.21	(2)
9.45/3.21	Obligation:
9.45/3.21	Rules:
9.45/3.21	f1(x, y, res) -> f2(x_1, y, res) :|: TRUE
9.45/3.21	f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
9.45/3.21	f3(x5, x6, x7) -> f4(x5, x6, 0) :|: TRUE
9.45/3.21	f5(x8, x9, x10) -> f6(arith, x9, x10) :|: TRUE && arith = x8 - 1
9.45/3.21	f6(x53, x54, x55) -> f7(x53, x56, x55) :|: TRUE && x56 = x54 - 1
9.45/3.21	f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x14 > 0 && x15 > 0
9.45/3.21	f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
9.45/3.21	f4(x20, x21, x22) -> f8(x20, x21, x22) :|: x20 <= 0
9.45/3.21	f4(x57, x58, x59) -> f8(x57, x58, x59) :|: x58 <= 0
9.45/3.21	f9(x60, x61, x62) -> f10(x60, x63, x62) :|: TRUE && x63 = x61 + 1
9.45/3.21	f10(x64, x65, x66) -> f11(x64, x65, x67) :|: TRUE && x67 = x66 + 1
9.45/3.21	f12(x68, x69, x70) -> f13(x71, x69, x70) :|: TRUE && x71 = x68 - 1
9.45/3.21	f13(x72, x73, x74) -> f14(x72, x75, x74) :|: TRUE && x75 = x73 - 1
9.45/3.21	f11(x35, x36, x37) -> f12(x35, x36, x37) :|: x35 > 0 && x36 > 0
9.45/3.21	f14(x38, x39, x40) -> f11(x38, x39, x40) :|: TRUE
9.45/3.21	f11(x41, x42, x43) -> f15(x41, x42, x43) :|: x41 <= 0
9.45/3.21	f11(x76, x77, x78) -> f15(x76, x77, x78) :|: x77 <= 0
9.45/3.21	f8(x44, x45, x46) -> f9(x44, x45, x46) :|: x44 > 0
9.45/3.21	f15(x47, x48, x49) -> f8(x47, x48, x49) :|: TRUE
9.45/3.21	f8(x50, x51, x52) -> f16(x50, x51, x52) :|: x50 <= 0
9.45/3.21	Start term: f1(x, y, res)
9.45/3.21	
9.45/3.21	----------------------------------------
9.45/3.21	
9.45/3.21	(3) IRS2T2 (EQUIVALENT)
9.45/3.21	Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs:
9.45/3.21	
9.45/3.21	   (f1_3,1)
9.45/3.21	   (f2_3,2)
9.45/3.21	   (f3_3,3)
9.45/3.21	   (f4_3,4)
9.45/3.21	   (f5_3,5)
9.45/3.21	   (f6_3,6)
9.45/3.21	   (f7_3,7)
9.45/3.21	   (f8_3,8)
9.45/3.21	   (f9_3,9)
9.45/3.21	   (f10_3,10)
9.45/3.21	   (f11_3,11)
9.45/3.21	   (f12_3,12)
9.45/3.21	   (f13_3,13)
9.45/3.21	   (f14_3,14)
9.45/3.21	   (f15_3,15)
9.45/3.21	   (f16_3,16)
9.45/3.21	
9.45/3.21	----------------------------------------
9.45/3.21	
9.45/3.21	(4)
9.45/3.21	Obligation:
9.45/3.21	START: 1;
9.45/3.21	
9.45/3.21	FROM: 1;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	oldX3 := nondet();
9.45/3.21	assume(0 = 0);
9.45/3.21	x0 := oldX3;
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 2;
9.45/3.21	
9.45/3.21	FROM: 2;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	oldX3 := nondet();
9.45/3.21	assume(0 = 0);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := oldX3;
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 3;
9.45/3.21	
9.45/3.21	FROM: 3;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	assume(0 = 0);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := 0;
9.45/3.21	TO: 4;
9.45/3.21	
9.45/3.21	FROM: 5;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	oldX3 := -(1 - oldX0);
9.45/3.21	assume(0 = 0 && oldX3 = oldX0 - 1);
9.45/3.21	x0 := -(1 - oldX0);
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 6;
9.45/3.21	
9.45/3.21	FROM: 6;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	oldX3 := -(1 - oldX1);
9.45/3.21	assume(0 = 0 && oldX3 = oldX1 - 1);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := -(1 - oldX1);
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 7;
9.45/3.21	
9.45/3.21	FROM: 4;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	assume(oldX0 > 0 && oldX1 > 0);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 5;
9.45/3.21	
9.45/3.21	FROM: 7;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	assume(0 = 0);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 4;
9.45/3.21	
9.45/3.21	FROM: 4;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	assume(oldX0 <= 0);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 8;
9.45/3.21	
9.45/3.21	FROM: 4;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	assume(oldX1 <= 0);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 8;
9.45/3.21	
9.45/3.21	FROM: 9;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	oldX3 := -(-(oldX1 + 1));
9.45/3.21	assume(0 = 0 && oldX3 = oldX1 + 1);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := -(-(oldX1 + 1));
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 10;
9.45/3.21	
9.45/3.21	FROM: 10;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	oldX3 := -(-(oldX2 + 1));
9.45/3.21	assume(0 = 0 && oldX3 = oldX2 + 1);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := -(-(oldX2 + 1));
9.45/3.21	TO: 11;
9.45/3.21	
9.45/3.21	FROM: 12;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	oldX3 := -(1 - oldX0);
9.45/3.21	assume(0 = 0 && oldX3 = oldX0 - 1);
9.45/3.21	x0 := -(1 - oldX0);
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 13;
9.45/3.21	
9.45/3.21	FROM: 13;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	oldX3 := -(1 - oldX1);
9.45/3.21	assume(0 = 0 && oldX3 = oldX1 - 1);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := -(1 - oldX1);
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 14;
9.45/3.21	
9.45/3.21	FROM: 11;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	assume(oldX0 > 0 && oldX1 > 0);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 12;
9.45/3.21	
9.45/3.21	FROM: 14;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	assume(0 = 0);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 11;
9.45/3.21	
9.45/3.21	FROM: 11;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	assume(oldX0 <= 0);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 15;
9.45/3.21	
9.45/3.21	FROM: 11;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	assume(oldX1 <= 0);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 15;
9.45/3.21	
9.45/3.21	FROM: 8;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	assume(oldX0 > 0);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 9;
9.45/3.21	
9.45/3.21	FROM: 15;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	assume(0 = 0);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 8;
9.45/3.21	
9.45/3.21	FROM: 8;
9.45/3.21	oldX0 := x0;
9.45/3.21	oldX1 := x1;
9.45/3.21	oldX2 := x2;
9.45/3.21	assume(oldX0 <= 0);
9.45/3.21	x0 := oldX0;
9.45/3.21	x1 := oldX1;
9.45/3.21	x2 := oldX2;
9.45/3.21	TO: 16;
9.45/3.21	
9.45/3.21	
9.45/3.21	----------------------------------------
9.45/3.21	
9.45/3.21	(5) T2 (EQUIVALENT)
9.45/3.21	Initially, performed program simplifications using lexicographic rank functions:
9.45/3.21	 * Removed transitions 17, 20, 21, 22, 32, 35, 36, 39 using the following rank functions:
9.45/3.21	    - Rank function 1:
9.45/3.21	      RF for loc. 11: 3*x0
9.45/3.21	      RF for loc. 12: 3*x0
9.45/3.21	      RF for loc. 17: 3*x0
9.45/3.21	      RF for loc. 21: 3*x0
9.45/3.21	      Bound for (chained) transitions 20: 3
9.45/3.21	    - Rank function 2:
9.45/3.21	      RF for loc. 11: 3-4*x1
9.45/3.21	      RF for loc. 12: 1-4*x1
9.45/3.21	      RF for loc. 17: 2-4*x1
9.45/3.21	      RF for loc. 21: -4*x1
9.45/3.21	      Bound for (chained) transitions 22: 2
9.45/3.21	    - Rank function 3:
9.45/3.21	      RF for loc. 11: 3
9.45/3.21	      RF for loc. 12: 1+4*x0
9.45/3.21	      RF for loc. 17: 2
9.45/3.21	      RF for loc. 21: 4*x0
9.45/3.21	      Bound for (chained) transitions 17: 3
9.45/3.21	      Bound for (chained) transitions 21: 2
9.45/3.21	      Bound for (chained) transitions 35: 4
9.45/3.21	      Bound for (chained) transitions 36: 4
9.45/3.21	    - Rank function 4:
9.45/3.21	      RF for loc. 12: oldX2
9.45/3.21	      RF for loc. 21: 0
9.45/3.21	      Bound for (chained) transitions 32, 39: 1
9.45/3.21	 * Removed transitions 5, 9, 10 using the following rank functions:
9.45/3.21	    - Rank function 1:
9.45/3.21	      RF for loc. 9: 1+x0+x1
9.45/3.21	      RF for loc. 13: x0+x1
9.45/3.21	      Bound for (chained) transitions 9: 2
9.45/3.21	      Bound for (chained) transitions 10: 2
9.45/3.21	    - Rank function 2:
9.45/3.21	      RF for loc. 9: 0
9.45/3.21	      RF for loc. 13: -1
9.45/3.21	      Bound for (chained) transitions 5: 0
9.45/3.21	
9.45/3.21	----------------------------------------
9.45/3.21	
9.45/3.21	(6)
9.45/3.21	YES
9.57/3.26	EOF